Motion Simulation and Mechanism Design with COSMOSMotion 2007

Motion Simulation and Mechanism (Design with COSMOSMotion 2007

Kuang-Hua Chang, Ph.D. School of Aerospace and Mechanical Engineering The University of Oklahoma

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Motion Simulation m£ Mechanism (Design with COSMOSMotion 2007

Kuang-Hua Chang, Ph.D. School of Aerospace and Mechanical Engineering The University of Oklahoma

ISBN: 978-1-58503-482-6

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Copyright © 2008 by Kuang-Hua Chang. All rights reserved. This document may not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose without the express written consent of the publisher Scnroff Development Corporation.

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Electronic Files: Any electronic files associated with this book are licensee to the original user only. These files may not be transferred to any other party

Mechanism

Design

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Preface This b o o k is written to help y o u b e c o m e familiar w i t h COSMOSMotion, an add-on m o d u l e of the SolidWorks software family, w h i c h supports m o d e l i n g a n d analysis (or simulation) of m e c h a n i s m s in a virtual (computer) environment. Capabilities in COSMOSMotion support y o u to use solid m o d e l s created in SolidWorks to simulate and visualize m e c h a n i s m m o t i o n and performance. Using COSMOSMotion early in the product development stage could prevent costly (and sometimes painful) redesign due to design defects found in the physical testing phase. Therefore, using COSMOSMotion for support of design decision m a k i n g contributes to a m o r e cost effective, reliable, and efficient product design process. This b o o k covers the basic concepts and frequently used c o m m a n d s required to advance readers from a novice to an intermediate level in using COSMOSMotion. Basic concepts discussed in this b o o k include m o d e l generation, such as assigning m o v i n g parts and creating j o i n t s and constraints; carrying out simulation and animation; and visualizing simulation results, such as graphs and spreadsheet data. These concepts are introduced using simple, yet realistic examples. Verifying the results obtained from the computer simulation is extremely important. O n e of the u n i q u e features of this b o o k is the incorporation of theoretical discussions for kinematic a n d dynamic analyses in conjunction with the simulation results obtained using COSMOSMotion. T h e p u r p o s e of the theoretical discussions lies in solely supporting the verification of simulation results, rather than providing an in-depth discussion on the subject of m e c h a n i s m design. COSMOSMotion is not foolproof. It requires a certain level of experience and expertise to master the software. Before arriving at that level, it is critical for y o u to verify the simulation results w h e n e v e r possible. Verifying the simulation results will increase y o u r confidence in using the software and prevent y o u from being fooled (hopefully, only occasionally) by any erroneous simulations produced by the software. E x a m p l e files h a v e b e e n p r e p a r e d for y o u to go t h r o u g h the lessons, including SolidWorks parts and assemblies, as well as completed COSMOSMotion m o d e l s . Y o u m a y w a n t to start each lesson by reviewing the introduction and m o d e l sections and opening the assembly in COSMOSMotion to see the m o t i o n simulation, in h o p e of gaining m o r e understanding about the e x a m p l e problems. In addition, Excel spreadsheets that support the theoretical verifications of selected examples are also available. Y o u m a y d o w n l o a d all m o d e l files and Excel spreadsheets from the w e b site of Schroff Development Corporation at: http://www.schroff.com/resources This b o o k is written following a project-based learning approach and is intentionally k e p t simple to help y o u learn COSMOSMotion. Therefore, this b o o k m a y not contain every single detail about COSMOSMotion. F o r a complete reference of COSMOSMotion, y o u m a y use on-line help in COSMOSMotion, or visit the w e b site of SolidWorks Corporation at: http://www.solidworks.com/ This b o o k should serve self-learners well. If such describes y o u , y o u are expected to h a v e basic Physics and Mathematics background, preferably a B a c h e l o r ' s degree in science or engineering. In addition, this b o o k assumes that y o u are familiar with the basic concept and operation of SolidWorks part and assembly m o d e s . A self-learner should be able to complete all lessons in this b o o k in about fifty hours. An investment of fifty hours should advance y o u from a novice to an intermediate level user. This b o o k also serves class instructions well. The b o o k will m o s t likely be used as a supplemental textbook for courses like Mechanism Design, Rigid Body Dynamics, Computer-Aided Design, or

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Computer-Aided Engineering. This b o o k should cover four to six w e e k s of class instruction, depending on h o w the courses are taught and the technical b a c k g r o u n d of the students. S o m e of the exercise problems given at the end of the lessons m a y require significant effort for students to complete. The author strongly encourages instructors and/or teaching assistants to go through those exercises before assigning t h e m to students.

KHC Norman, Oklahoma May 15,2008 Copyright 2 0 0 8 by K u a n g - H u a C h a n g . All rights reserved. This d o c u m e n t m a y not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose without the express written consent of the publisher Schroff D e v e l o p m e n t Corporation.

Acknowledgements I w o u l d like to thank my family for the patience and support they h a v e given to me in completing this book, especially, my wife Sheng-Mei for her unconditional giving and encouragement. T h a n k s are due to my children, Charles and Annie, for their understanding, caring, a n d appreciation. Especially, I appreciate their patience in reviewing the w h o l e b o o k and correcting a few sentences for m e . A c k n o w l e d g m e n t is due to Mr. Stephen Schroff at Schroff D e v e l o p m e n t Corporation for his e n c o u r a g e m e n t and help. Without his encouragement, this b o o k w o u l d still be in its primitive stage. T h a n k s are also due to undergraduate students at the University of O k l a h o m a ( O U ) for their help in testing e x a m p l e s included in this book. T h e y m a d e n u m e r o u s suggestions that i m p r o v e d clarity of presentation and found n u m e r o u s errors that w o u l d h a v e otherwise crept into the book. Their contributions to this b o o k are greatly appreciated. I am grateful to my current and former students, T h o m a s Cates, Petr Sramek, and Tyler Bunting, for their excellent contribution in creating examples for the application lesson; i.e., Lesson 8. T h e assistive device project e m p l o y e d as the example in Lesson 8 was successful and well recognized. Finally, I w o u l d like to thank our Creator, w h o has given me the strength and intelligence to complete this book.

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About the Author Dr. K u a n g - H u a C h a n g is a Williams Companies Foundation Presidential Professor at the University of O k l a h o m a ( O U ) , N o r m a n , OK. He received his diploma in Mechanical Engineering from the National Taipei Institute of Technology, Taiwan, in 1980; and a M . S . and P h . D . in Mechanical Engineering from the University of I o w a in 1987 and 1990, respectively. Since then, he has j o i n e d the Center for ComputerA i d e d D e s i g n ( C C A D ) at I o w a as a Research Scientist a n d C A E Technical Manager. In 1996, he j o i n e d N o r t h e r n Illinois University as an Assistant Professor. In 1997, he j o i n e d O U . Dr. C h a n g teaches m e c h a n i c a l design and manufacturing, in addition to conducting research in computer-aided m o d e l i n g and simulation for design and manufacturing of mechanical systems as well as bioengineering applications. His research w o r k has b e e n published in m o r e than 100 articles in international j o u r n a l s and conference proceedings. He has b e e n invited to deliver talks a n d offer short courses for US and foreign companies and universities. He has also served as a technical consultant to US industry and foreign companies. Dr. C h a n g w o n awards in b o t h teaching and research in the past few years. He is a recipient of the S A E R a l p h R . Teetor A w a r d (2006), Outstanding Asian A m e r i c a n A w a r d sponsored b y O k l a h o m a Asian A m e r i c a n Association (2003), a n d Public E m p l o y e e A w a r d o f O K C M a y o r ' s C o m m i t t e e A w a r d o n Disability Concerns (2002). In addition, he received several awards from O U , including the OU A l u m n i Teaching A w a r d (Spring 2007 and Fall 2007), R e g e n t s ' A w a r d on Superior Research a n d Creative Activities (2004), B P A M O C O G o o d Teaching A w a r d (2002), and Junior Faculty A w a r d (1999). Dr. C h a n g w a s n a m e d Williams Companies Foundation Presidential Professor in 2005 by OU President D a v i d L. B o r e n for meeting the highest standards of excellence in scholarship and teaching.

About the Cover Page T h e picture displayed on the cover p a g e is the m o t i o n m o d e l of an assistive device designed and built by engineering students at the University of O k l a h o m a ( O U ) during 2 0 0 7 - 2 0 0 8 . Go Sooners! This device w a s created for the purpose of enhancing experience and encouraging children with physical disabilities to participate in a soccer g a m e . This is a special m e c h a n i s m that can be m o u n t e d on a wheelchair to m i m i c soccer ball-kicking action while being operated by a child sitting on the wheelchair with limited mobility a n d h a n d strength. This example w a s extracted from an undergraduate student design project that w a s carried out in conjunction with a local children hospital. This device w a s intended primarily to be u s e d in the s u m m e r c a m p sponsored by the children hospital. This device has been e m p l o y e d as the application example to be discussed in Lesson 8 of this book. In addition to the soccer ball kicking device, students at OU h a v e been involved in developing m a n y other assistive devices. Currently, an Undergraduate student t e a m is developing a transporting device that will help a local resident with only functional right h a n d m o v e from her wheelchair to her b e d and vise versa independently. Students w e r e also involved in developing special b a b y crib, pediatric assistive w a l k i n g device, and modification of a child walker, etc., in the past. All these projects require customized features to meet special needs. These projects h a v e b e e n supported by H o n o r s College of O U , Schlumberger, and private donations. All supports are sincerely appreciated.

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Table of Contents Preface

i

Acknowledgments

11

A b o u t the A u t h o r

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A b o u t the Cover P a g e

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Table o f Contents

i v

Lesson 1: Introduction to COSMOSMotion 1.1 1.2 1.3 1.4 1.5

O v e r v i e w of the L e s s o n W h a t is COSMOSMotion? M e c h a n i s m Design and M o t i o n Analysis COSMOSMotion Capabilities Motion Examples

1-1 1-1 1-3 1-5 1-16

Lesson 2: A Ball T h r o w i n g E x a m p l e 2.1 O v e r v i e w of the L e s s o n 2.2 T h e Ball T h r o w i n g E x a m p l e 2.3 U s i n g COSMOSMotion 2.4 Result Verifications Exercises

2-1 2-1 2-3 2-12 2-14

Lesson 3: A Spring M a s s System 3.1 O v e r v i e w of the Lesson 3.2 T h e Spring-Mass System 3.3 U s i n g COSMOSMotion 3.4 Result Verifications Exercises

3-1 3-1 3-3 3-10 3-15

Lesson 4: A Simple P e n d u l u m 4.1 O v e r v i e w of the Lesson 4.2 T h e Simple P e n d u l u m E x a m p l e 4.3 U s i n g COSMOSMotion 4.4 Result Verifications Exercises

4-1 4-1 4-2 4-5 4-9

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L e s s o n 5: A S l i d e r - C r a n k M e c h a n i s m 5.1 O v e r v i e w of the L e s s o n 5.2 The Slider-Crank E x a m p l e 5.3 U s i n g COSMOSMotion 5.4 Result Verifications Exercises

5-1 5-1 5-4 5-13 5-17

Lesson 6: A C o m p o u n d S p u r G e a r Train 6.1 O v e r v i e w of the Lesson 6.2 T h e Gear Train E x a m p l e 6.3 U s i n g COSMOSMotion Exercises

6-1 6-2 6-6 6-9

Lesson 7: C a m a n d Follower 7.1 O v e r v i e w of the Lesson 7.2 The C a m and Follower E x a m p l e 7.3 U s i n g COSMOSMotion Exercises

7-1 7-1 7-6 7-10

Lesson 8: Assistive Device for W h e e l c h a i r Soccer G a m e s 8.1 8.2 8.3 8.4 8.5

O v e r v i e w of the L e s s o n T h e Assistive D e v i c e U s i n g COSMOSMotion Result Discussion C o m m e n t s on COSMOSMotion Capabilities and Limitations

8-1 8-2 8-7 8-20 8-20

A p p e n d i x A : Defining Joints

A-l

A p p e n d i x B : T h e Unit Systems

B-l

A p p e n d i x C: I m p o r t i n g Pro/ENGINEER Parts a n d A s s e m b l i e s

C-l

Notes:

T h e purpose of this lesson is to provide y o u with a brief overview on COSMOSMotion. COSMOSMotion is a virtual prototyping tool that supports m e c h a n i s m analysis and design. Instead of building and testing physical prototypes of the m e c h a n i s m , y o u m a y use COSMOSMotion to evaluate and refine the m e c h a n i s m before finalizing the design a n d entering the functional prototyping stage. COSMOSMotion will help y o u analyze and eventually design better engineering products. M o r e specifically, the software enables y o u to size motors and actuators, determine p o w e r consumption, layout linkages, develop c a m s , understand gear drives, size springs and dampers, and determine h o w contacting parts b e h a v e , w h i c h w o u l d usually require tests of physical prototypes. W i t h such information, y o u will gain insight on h o w the m e c h a n i s m w o r k s a n d w h y it behaves in certain w a y s . Y o u will be able to modify the design and often achieve better design alternatives using the m o r e convenient and less expensive virtual prototypes. In the long run, using virtual prototyping tools, such as COSMOSMotion, will help y o u b e c o m e a m o r e experienced and competent design engineer. In this lesson, we will start with a brief introduction to COSMOSMotion and the various types of physical problems that COSMOSMotion is capable of solving. We will then discuss capabilities offered by COSMOSMotion for creating m o t i o n m o d e l s , conducting m o t i o n analyses, a n d v i e w i n g m o t i o n analysis results. In the final section, we will m e n t i o n examples e m p l o y e d in this b o o k and topics to learn from these examples. N o t e that materials presented in this lesson will be kept brief. M o r e details on various aspects of m e c h a n i s m design and analysis using COSMOSMotion will be given in later lessons. 1.2

W h a t is COSMOSMotion?

COSMOSMotion is a computer software tool that supports engineers to analyze and design m e c h a n i s m s . COSMOSMotion is a m o d u l e of the SolidWorks product family developed by SolidWorks Corporation. This software supports users to create virtual m e c h a n i s m s that answer general questions in product design as described next. An internal combustion engine s h o w n in Figures 1-1 a n d 1-2 will be u s e d to illustrate s o m e typical questions. 1.

Will the c o m p o n e n t s of the m e c h a n i s m collide in operation? For example, will the connecting rod collide with the inner surface of the piston or the inner surface of the engine case during operation?

2.

Will the c o m p o n e n t s in the m e c h a n i s m y o u design m o v e according to y o u r intent? For example, will the piston stay entirely in the piston sleeve? Will the system lock up w h e n the firing force aligns vertically with the connecting rod?

3.

H o w m u c h torque or force does it take to drive the m e c h a n i s m ? For example, w h a t will be the m i n i m u m firing load to m o v e the piston? N o t e that in this case, proper friction forces m u s t be a d d e d to simulate the resistance of the m e c h a n i s m before a realistic firing force can be calculated.

4.

H o w fast will the c o m p o n e n t s m o v e ; e.g., the longitudinal m o t i o n of the piston?

5.

W h a t is the reaction force or torque generated at a connection (also called joint or constraint) b e t w e e n c o m p o n e n t s (or bodies) during m o t i o n ? For example, w h a t is the reaction force at the j o i n t between the connecting r o d and the piston pin? This reaction force is critical since the structural integrity of the piston pin and the connecting r o d m u s t be ensured; i.e., they m u s t be strong and durable e n o u g h to sustain the load in operation.

The capabilities available in COSMOSMotion also help y o u search for better design alternatives. A better design alternative is very m u c h p r o b l e m dependent. It is critical that a design p r o b l e m be clearly defined by the designer up front before searching for better design alternatives. For the engine example, a better design alternative can be a design that reveals: 1. 2.

A smaller reaction force applied to the connecting rod, and No collisions or interference b e t w e e n c o m p o n e n t s .

In order to vary c o m p o n e n t sizes for exploring better design alternatives, the parts and assembly m u s t be adequately parameterized to capture design intents. At the parts level, design parameterization implies creating solid features and relating dimensions properly. At the assembly level, design parameterization involves defining assembly mates and relating dimensions across parts. W h e n a solid m o d e l is fully parameterized, a change in dimension value can be propagated to all parts affected automatically. Parts affected m u s t be rebuilt successfully, and at the same time, they will h a v e to maintain proper position a n d orientation w i t h respect to one another without violating any assembly mates or revealing part penetration or excessive gaps. F o r example, in this engine example, a change in the bore

diameter of the engine case will alter not only the geometry of the case itself, but all other parts affected, such as the piston, piston sleeve, a n d even the crankshaft, as illustrated in Figure 1-3. M o r e o v e r , they all have to be rebuilt properly and the entire assembly must stay intact through assembly mates.

1.3

M e c h a n i s m Design a n d M o t i o n Analysis

A m e c h a n i s m is a mechanical device that transfers m o t i o n and/or force from a source to an output. It can be an abstraction (simplified m o d e l ) of a mechanical system. A linkage consists of links (or bodies), w h i c h are connected by j o i n t s (or connections), such as a revolute joint, to form open or closed chains (or loops, see Figure 1-4). Such kinematic chains, with at least one link fixed, b e c o m e m e c h a n i s m s . In this book, all links are a s s u m e d rigid. In general, a m e c h a n i s m can be represented by its corresponding schematic drawing for analysis purpose. F o r example, a slider-crank m e c h a n i s m represents the engine motion, as s h o w n in Figure 1-5, w h i c h is a closed loop m e c h a n i s m .

In general, there are t w o types of m o t i o n p r o b l e m s that y o u will h a v e to solve in order to answer questions regarding m e c h a n i s m analysis and design: kinematic a n d dynamic. K i n e m a t i c s is the study of m o t i o n w i t h o u t regard for the forces that cause the motion. A kinematic m e c h a n i s m m u s t be driven by a servomotor (or m o t i o n driver) so that the position, velocity, and acceleration of each link of the m e c h a n i s m can be analyzed at any given time. Typically, a kinematic analysis m u s t be conducted before dynamic b e h a v i o r of the m e c h a n i s m can be simulated properly. D y n a m i c analysis is the study of m o t i o n in response to externally applied loads. The d y n a m i c behavior of a m e c h a n i s m is g o v e r n e d by N e w t o n ' s laws of motion. T h e simplest d y n a m i c p r o b l e m is the particle d y n a m i c s introduced in S o p h o m o r e D y n a m i c s — f o r example, a spring-mass-damper system s h o w n in Figure 1-6. In this case, m o t i o n of the m a s s is g o v e r n e d by the following equation derived from N e w t o n ' s second law, (1.1) w h e r e (•) appearing on top of the physical quantities represents t i m e derivative of the quantities, m is the total m a s s of the block, k is the spring constant, and c is the d a m p i n g coefficient. F o r a rigid b o d y , m a s s properties (such as the total m a s s , center of m a s s , m o m e n t of inertia, etc.) are taken into account for d y n a m i c analysis. For example, m o t i o n of a p e n d u l u m s h o w n in Figure 1-7 is g o v e r n e d by the following equation of motion,

Y M = -mgl s i n 0 = 10 = m£ 0 2

d

(1.2)

w h e r e M is the external m o m e n t (or torque), / is the polar m o m e n t of inertia of the p e n d u l u m , m is the p e n d u l u m m a s s , g is the gravitational acceleration, and 6 is the angular acceleration of the p e n d u l u m . D y n a m i c analysis of a rigid b o d y system, such as the single piston engine s h o w n in Figure 1-3, is a lot m o r e complicated than the single b o d y problems. Usually, a system of differential and algebraic equations governs the m o t i o n a n d the d y n a m i c behavior of the system. N e w t o n ' s law m u s t be o b e y e d by every single b o d y in the system at all time. T h e m o t i o n of the system will be determined by the loads acting on the bodies or j o i n t axes (e.g., a torque driving the system). Reaction loads at the j o i n t connections h o l d the bodies together. N o t e that in COSMOSMotion, y o u m a y create a kinematic analysis m o d e l ; e.g., using a m o t i o n driver to drive the m e c h a n i s m ; and then carry out d y n a m i c analyses. In d y n a m i c analysis, position, velocity, and acceleration results are identical to those of kinematic analysis. H o w e v e r , the inertia of the bodies will be t a k e n into account for analysis; therefore, reaction forces will be calculated b e t w e e n bodies.

1.4

COSMOSMotion Capabilities

Ground Parts

The overall process of using COSMOSMotion for analyzing a mechanism consists of three m a i n steps: m o d e l generation, analysis (or simulation), a n d result visualization (or post-processing), as illustrated in Figure 1-8. K e y entities that constitute a m o t i o n m o d e l include ground parts that are always fixed, m o v i n g parts that are m o v a b l e , joints and constraints that connect and restrict relative m o t i o n b e t w e e n parts, servo m o t o r s (or m o t i o n drivers) that drive the m e c h a n i s m for kinematic analysis, external loads (force and torque), and the initial conditions of the m e c h a n i s m . M o r e details about these entities will be discussed later in this lesson. T h e analysis or simulation capabilities in COSMOSMotion e m p l o y simulation engine, ADAMS/Solver, w h i c h solves the equations of m o t i o n for your m e c h a n i s m . ADAMS/Solver calculates the position, velocity, acceleration, and reaction forces acting on each m o v i n g part in the m e c h a n i s m . Typical simulation p r o b l e m s , including static (equilibrium configuration) and m o t i o n (kinematic a n d dynamic), are supported. M o r e details about the analysis capabilities in COSMOSMotion will be discussed later in this lesson. T h e analysis results can be visualized in various forms. Y o u m a y animate m o t i o n of the m e c h a n i s m , or generate graphs for m o r e specific information, such as the reaction force of a j o i n t in t i m e domain. Y o u m a y also query results at specific locations for a given time. Furthermore, y o u m a y ask for a report on results that y o u specified, such as the acceleration of a m o v i n g part in the t i m e domain. Y o u m a y also convert the m o t i o n animation to an A V I for faster v i e w i n g and file portability. In addition to A V I , y o u can export animations to V R M L format for distribution on the Internet. Y o u can then use Cosmo Player, a plug-in to y o u r W e b browser, to v i e w V R M L files. To d o w n l o a d Cosmo Player for Windows, go to http://ovrt.nist.gov/cosmo/. Operation

Mode

COSMOSMotion is e m b e d d e d in SolidWorks. It is indeed an add-on m o d u l e of SolidWorks, and transition from SolidWorks to COSMOSMotion is seamless. All the solid m o d e l s , materials, assembly m a t e s , etc. defined in SolidWorks are automatically carried over into COSMOSMotion. COSMOSMotion can be accessed t h r o u g h m e n u s and w i n d o w s inside SolidWorks. T h e same assembly created in SolidWorks can be directly employed for creating m o t i o n m o d e l s in COSMOSMotion. In addition, part geometry is essential for m a s s property computations in m o t i o n analysis. In COSMOSMotion, all m a s s properties calculated in SolidWorks are ready for use. In addition, the detailed part g e o m e t r y supports interference checking for the m e c h a n i s m during m o t i o n simulation in COSMOSMotion. User

Interfaces

User interface of the COSMOSMotion is identical to that of SolidWorks, as s h o w n in Figure 1-9. SolidWorks users should find it is straightforward to m a n e u v e r in COSMOSMotion.

As s h o w n in Figure 1-9, the user interface w i n d o w of COSMOSMotion consists of pull-down m e n u s , shortcut buttons, the browser, the graphics screen, the m e s s a g e w i n d o w , etc. W h e n COSMOSMotion is active, an extra tab $ (the Motion button) is available on top of the browser. This Motion button will allow y o u to access COSMOSMotion. T h e graphics screen displays the m o t i o n m o d e l with w h i c h y o u are working. T h e global coordinate system at the lower left corner of the graphics screen is fixed and serves as the reference for all the physical parameters defined in the m o t i o n model. T h e p u l l - d o w n m e n u s a n d the shortcut buttons at the top of the screen provide typical SolidWorks functions. T h e assembly shortcut buttons allow y o u to assemble your SolidWorks m o d e l . The COSMOSMotion shortcut buttons on top of the graphics screen s h o w n in Figure 1-9 provide all the functions required to create and modify the m o t i o n m o d e l s , create and run analyses, and visualize results. As y o u m o v e the m o u s e over a button, a brief description about the functionality of the button, such as the Fast Reverse button shown in Figure 1-9, will appear.

W h e n y o u choose a m e n u option, the Message w i n d o w , at the lower left corner s h o w n in Figure 1-9, shows a brief description about the option. In addition to these buttons, a COSMOSMotion pull-down m e n u also provides similar options, as shown in Figure 1-10. W h e n y o u click the Motion button, the b r o w s e r will provide y o u with a graphical, hierarchical v i e w of m o t i o n m o d e l and allow y o u to access all COSMOSMotion functionalities t h r o u g h a combination of drag-and-drop and right-click activated m e n u s . F o r example, y o u m a y drag and drop connectingrod_asm-l under the Assembly Components, as s h o w n in Figure 1-11 to Moving Parts u n d e r the Parts branch to define it as a m o v i n g part. Y o u m a y also right click an entity a n d choose to define or edit its property. F o r example, y o u m a y right click the Springs n o d e u n d e r Forces b r a n c h in Figure 112, and choose Add Translational Spring to add a spring. Switching back and forth b e t w e e n COSMOSMotion and SolidWorks assembly m o d e is straightforward. All y o u h a v e to do is to click the Motion J? or Assembly buttons ^ (on top of the browser) w h e n needed. W h e n y o u click the Motion button
tabbed dialog b o x and a w i z a r d that leads y o u t h r o u g h the process of converting an assembly m o d e l into a m o t i o n m o d e l , performing m o t i o n simulations, and v i e w i n g simulation results.

To u s e the IntelliMotion Builder, click the IntelliMotion Builder button or right-click the Motion Model n o d e (the root entity of the m o t i o n m o d e l ) from the browser, and then select IntelliMotion Builder (see Figure 1-14). T h e first tab is Units, w h i c h brings up the Units p a g e . At the lower-left corner of each p a g e in the IntelliMotion Builder are the Back and Next buttons, w h i c h help y o u m o v e sequentially t h r o u g h the m o t i o n m o d e l creation, simulation, and animation process. Y o u m a y also click a tab on top to j u m p to that p a g e directly, for e x a m p l e Parts, to define g r o u n d and m o v i n g parts. For a new COSMOSMotion user, the IntelliMotion Builder is very helpful in terms of leading y o u t h r o u g h the steps of creating simulations m o d e l s , running simulations, and visualizing the simulation results. F o r a m o r e experienced user, the drag-and-drop and right-click activated m e n u s m a y b e m o r e convenient. Table 1-2 gives a brief explanation of each tab available in the IntelliMotion Builder.

Defining

COSMOSMotion

Entities

T h e basic entities of a valid COSMOSMotion simulation m o d e l consist of g r o u n d parts, m o v i n g parts, constraints (including joints), initial conditions, and forces and/or drivers. E a c h of the basic entities will be briefly discussed next. M o r e details can be found in later lessons.

Ground Parts

(or

Ground Body)

A g r o u n d part, or a g r o u n d body, represents a fixed reference in space. The first c o m p o n e n t brought into the assembly is usually stationary; therefore, often b e c o m i n g a g r o u n d part. Y o u will h a v e to identify m o v i n g and n o n - m o v i n g parts in y o u r assembly, and assign the n o n - m o v i n g parts as ground parts using either the IntelliMotion Builder or the drag-and-drop in the browser. Moving Parts

(or Bodies)

A m o v i n g part or b o d y is an entity represents a single rigid c o m p o n e n t (or link) that m o v e s relatively to other parts (or bodies). A m o v i n g part m a y consist of a single SolidWorks part or an assembly c o m p o s e d of multiple parts. W h e n an assembly is assigned as a m o v i n g part, n o n e of its c o m p o s i n g parts is allowed to m o v e relative to one another within the assembly. A m o v i n g part has six degrees of freedom, three translational and three rotational, while a g r o u n d part has n o n e . That is, a rigid b o d y can translate and rotate along the Y-, a n d Z-axes of a coordinate system. Rotation of a rigid b o d y is m e a s u r e d by referring the orientation of its local coordinate system to the global coordinate system, w h i c h is s h o w n at the lower left corner on the graphics screen. In COSMOSMotion, the local coordinate system is assigned automatically, usually, at the m a s s center of the part. M a s s properties, including total m a s s , inertia, etc., are calculated using part g e o m e t r y and material properties referring to the local coordinate system. A m o v i n g part has a symbol (see Figure l - 1 6 a ) attached, usually located at its m a s s center, as s h o w n in Figure 1-15. Constraints A constraint (or connection) in COSMOSMotion can be a joint, contact, or coupler that connects t w o parts and constrains the relative m o t i o n b e t w e e n them. Typical joints include a revolute, cylindrical, spherical, etc. Each independent m o v e m e n t permitted by a constraint is a free degree of freedom (dof). The degrees of freedom that a constraint allows can be translational or rotational along the three perpendicular axes. T h e free dof is revealed by the symbol of the constraint. F o r example, the symbol of cylindrical joints, such as those defined in the engine e x a m p l e s h o w n in Figure 1-15, show t w o concentric cylinders implying t w o free d o f s, a translational and a rotational, both are along the c o m m o n axis, as illustrated in Figure l - 1 6 b . Also, a revolute joint, for e x a m p l e the one b e t w e e n the propeller and the case shown in Figure 1-15, allows only one rotational dof, as depicted in a hinge symbol s h o w n in Figure 116c. Understanding the j o i n t symbols will enable y o u to read existing m o t i o n m o d e l s . Also, a j o i n t produces equal and opposite reactions (forces and/or torques) on the bodies connected due to N e w t o n ' s 3 L a w . M o r e about j o i n t s will be discussed in later lessons and for a list of c o m m o n l y e m p l o y e d joints, please refer to A p p e n d i x A. r d

COSMOSMotion automatically converts assembly m a t e s to joints. For example, a concentric m a t e together with a coincident m a t e will be converted to a revolute joint. S o m e t i m e s , COSMOSMotion will simply carry over the assembly mates to m o t i o n if there is no adequate j o i n t to convert to, following the m a p p e d mates established internally. F o r a list of c o m m o n m a p p e d m a t e s , please refer to A p p e n d i x A. Y o u m a y either stay w i t h the j o i n t set converted by COSMOSMotion or delete s o m e of t h e m to create your own. H o w e v e r , it is strongly r e c o m m e n d e d that y o u stay with the converted j o i n t set before completing all the examples provided in this book. In all the examples presented in this book, m a p p e d joints or mates are e m p l o y e d without any modification. N o t e that instead of completely fixing all the m o v e m e n t s , certain d o f s (translational and/or rotational) are left to allow designated m o v e m e n t . For example, a m o t i o n driver is defined at the rotation dof of the revolute j o i n t in the engine example, as shown in Figure 1-15. This m o t i o n driver will rotate the

propeller at a prescribed angular velocity. In addition to prescribed velocity, y o u m a y u s e the m o t i o n driver to drive the dof at a prescribed displacement or acceleration, b o t h translation a n d rotational.

In addition to joints, COSMOSMotion provides contact and coupling constraints. T h e contact constraints help to simulate physical p r o b l e m s m o r e realistically. COSMOSMotion supports four types of contact, point-curve, curve-curve, intermittent curve-curve, and 3D contact. Only the first t w o types of contact i m p o s e degree-of-freedom restrictions on the connected parts and are true constraints. T h e 3D contact is e m p l o y e d m o s t frequently, w h i c h applies a force to separate the parts w h e n they are in contact

and prevent t h e m from penetrating each other. The 3D contact constraint will b e c o m e active as soon as the parts are touching. Joint couplers allow the m o t i o n of a revolute, cylindrical, or translational j o i n t to be c o u p l e d to the m o t i o n of another revolute, cylindrical or translational joint. T h e t w o coupled j o i n t s m a y be of the same or different types. For example, a revolute j o i n t m a y be coupled to a translational joint. T h e coupled m o t i o n m a y also be of the same or different type. F o r e x a m p l e , the rotary m o t i o n of a revolute j o i n t m a y be coupled to the rotary m o t i o n of a cylindrical joint, or the translational m o t i o n of a translational j o i n t m a y be coupled to the rotary m o t i o n of a cylindrical joint. A coupler r e m o v e s one additional degree of freedom from the m o t i o n m o d e l . Degrees

of Freedom

As m e n t i o n e d earlier, an unconstrained b o d y in space has six degrees of freedom; i.e., three translational and three rotational. W h e n joints are a d d e d to connect bodies, constraints are i m p o s e d to restrict the relative m o t i o n b e t w e e n them. F o r example, the revolute j o i n t defined in the engine e x a m p l e restricts m o v e m e n t on five d o f s so that only one rotational m o t i o n is allowed b e t w e e n the propeller assembly and the engine case. Since the engine case is a g r o u n d b o d y , the propeller assembly will rotate along the axis of the revolute joint, as illustrated in the s y m b o l s h o w n in Figure 1-16b. Therefore, there is only one degree of freedom left for the propeller assembly. F o r a given m o t i o n m o d e l , y o u can determine its n u m b e r of degrees of freedom u s i n g the G r u e b l e r ' s count. COSMOSMotion uses the following equation to calculate the G r u e b l e r ' s count: D = 6M-N-0

(1.3)

w h e r e D is the G r u e b l e r ' s count representing the total degrees of freedom of the m e c h a n i s m , M i s the n u m b e r of bodies excluding the g r o u n d b o d y , TV is the n u m b e r of d o f s restricted by all joints, and O is the n u m b e r of m o t i o n drivers defined in the system. In general, a valid m o t i o n m o d e l should h a v e a G r u e b l e r ' s count 0. H o w e v e r , in creating m o t i o n m o d e l s , s o m e joints r e m o v e redundant d o f s . F o r example, t w o hinges, m o d e l e d using t w o revolute joints, support a door. T h e second revolute j o i n t adds five r e d u n d a n t d o f s. T h e G r u e b l e r ' s count b e c o m e s : D = 6x1 -2x5 = -4 For kinematic analysis, the G r u e b l e r ' s count m u s t be equal to or less than 0. T h e ADAMS/Solver recognizes a n d deactivates redundant constraints during analysis. For a k i n e m a t i c analysis, if y o u create a m o d e l and try to animate it with a G r u e b l e r ' s count greater than 0, the animation will n o t r u n and an error m e s s a g e will appear. T h e single-piston engine s h o w n in Figure 1-15 consists of three bodies (excluding the ground body), one revolute j o i n t and three cylindrical joints. A revolute j o i n t r e m o v e s five degrees of freedom, and a cylindrical j o i n t r e m o v e s four d o f s. In addition, a m o t i o n driver is a d d e d to the rotational d o f of the revolute joint. Therefore, according to Eq. 1.3, the G r u e b l e r ' s count for the engine e x a m p l e is

If the G r u e b l e r ' s count is less than zero, the solver will automatically r e m o v e redundancies. In this engine example, if the t w o of the cylindrical j o i n t s ; b e t w e e n piston and the piston pin, and b e t w e e n the connecting r o d and the crank shaft, are replaced by revolute joints, the G r u e b l e r ' s count b e c o m e s D

=

6x(4-l)-(3x5-1x4)

-

lxl

=

-2

To get the G r u e b l e r ' s count to zero, it is often possible to replace j o i n t s that r e m o v e a large n u m b e r of constraints with j o i n t s that r e m o v e a smaller n u m b e r of constraints a n d still restrict the m e c h a n i s m m o t i o n in the s a m e w a y . COSMOSMotion detects the redundancies a n d ignores r e d u n d a n t d o f s in all analyses, except for d y n a m i c analysis. In d y n a m i c analysis, the redundancies lead to an o u t c o m e with a possibility of incorrect reaction results, yet the m o t i o n is correct. F o r complete a n d accurate reaction forces, it is critical that y o u eliminate redundancies from y o u r m e c h a n i s m . T h e challenge is to find the joints that will i m p o s e n o n - r e d u n d a n t constraints and still allow for the intended motion. E x a m p l e s included in this b o o k should give y o u s o m e ideas in choosing proper j o i n t s . Forces Forces are u s e d to operate a m e c h a n i s m . Physically, forces are p r o d u c e d by m o t o r s , springs, dampers, gravity, tires, etc. A force entity in COSMOSMotion can be a force or torque. COSMOSMotion provides three types of forces: applied forces, flexible connectors, a n d gravity. A p p l i e d forces are forces that cause the m e c h a n i s m to m o v e in certain w a y s . A p p l i e d forces are very general, b u t y o u m u s t supply y o u r o w n description of the force by specifying a constant force value or expression function, such as a h a r m o n i c function. The applied forces in COSMOSMotion include actiononly force or m o m e n t (where force or m o m e n t is applied at a point on a single rigid body, and no reaction forces are calculated), action a n d reaction force and m o m e n t , and impact force. T h e force and m o m e n t symbols in COSMOSMotion are s h o w n in Figure 1-17 and 1-18, respectively.

Figure 1-17 T h e Force (or Translational Driver) S y m b o l

Figure 1-18 T h e M o m e n t (or Rotational Driver) S y m b o l

Flexible connectors resist m o t i o n a n d are simpler and easier to use than applied forces because y o u only supply constant coefficients for the forces, for instance a spring constant. T h e flexible connectors include translational springs, torsional springs, translational dampers, torsional d a m p e r s , a n d bushings, which symbols are s h o w n in Figure 1-19.

A m a g n i t u d e and a direction m u s t be included for a force definition. Y o u m a y select a predefined function, such as a h a r m o n i c function, to define the m a g n i t u d e of the force or m o m e n t . F o r spring and damper, COSMOSMotion automatically m a k e s the force m a g n i t u d e proportional to the distance or velocity b e t w e e n t w o points, b a s e d on the spring constant a n d d a m p i n g coefficient entered, respectively. The direction of a force (or m o m e n t ) can be defined by either along an axis defined by an edge or along the line b e t w e e n t w o points, w h e r e a spring or a d a m p e r is defined. Initial

Conditions

In m o t i o n simulations, initial conditions consist of initial configuration of the m e c h a n i s m a n d initial velocity of one or m o r e c o m p o n e n t s of the m e c h a n i s m . M o t i o n simulation m u s t start with a properly assembled solid m o d e l that determines an initial configuration of the m e c h a n i s m , c o m p o s e d by position and orientation of individual c o m p o n e n t s . T h e initial configuration can be completely defined by assembly m a t e s . H o w e v e r , one or m o r e assembly m a t e s will h a v e to be suppressed, if the assembly is fully constrained, to provide adequate m o v e m e n t . In COSMOSMotion, initial velocity is defined as part of definition of a m o v i n g part. T h e initial velocity can be translational or rotational along one of the three axes. Motion

Drivers

M o t i o n drivers are u s e d to i m p o s e a particular m o v e m e n t of a j o i n t or part over time. A m o t i o n driver specifies position, velocity, or acceleration as a function of time, and can control either translational or rotational motion. T h e driver symbol is identical to those of Figures 1-17 and 1-18, for translational and rotational, respectively. W h e n properly defined, m o t i o n drivers will account for the remaining d o f s of the m e c h a n i s m that brings the G r u e b l e r ' s count to zero or less. In the engine e x a m p l e s h o w n in Figure 1-15, a m o t i o n driver is defined at the revolute j o i n t to rotate the propeller at a constant angular velocity. Motion

Simulation

The ADAMS/Solver employed by COSMOSMotion is capable of solving typical engineering p r o b l e m s , such as static (equilibrium configuration), kinematic, and dynamic, etc. Static analysis is u s e d to find the rest position (equilibrium condition) of a m e c h a n i s m , in w h i c h n o n e of the bodies are m o v i n g . A simple e x a m p l e of the static analysis is illustrated in Figure 1-20, in w h i c h an equilibrium position of the b l o c k is to be determined according to its o w n m a s s m, the t w o spring constants ki and k , and the gravity g. 2

As discussed earlier, kinematics is the study of m o t i o n without regard for the forces that cause the motion. A m e c h a n i s m can be driven by a motion driver (e.g., a servomotor) for a kinematic analysis, w h e r e the position, velocity, a n d acceleration of each link of the m e c h a n i s m can be analyzed at any given time. Figure 1-21 shows a servomotor drives a m e c h a n i s m at a constant angular velocity. D y n a m i c analysis is u s e d to study the m e c h a n i s m m o t i o n in response to loads, as illustrated in Figure 1-22. This is the m o s t complicated a n d c o m m o n , and usually a m o r e t i m e - c o n s u m i n g analysis.

Viewing

Results

In COSMOSMotion, results of the m o t i o n analysis can be realized using animations, graphs, reports, and queries. A n i m a t i o n s show the configuration of the m e c h a n i s m in consecutive time frames. Animations will give y o u a global v i e w on h o w the m e c h a n i s m b e h a v e s , for example, the single-piston engine s h o w n in Figure 1-23. Y o u m a y also export the animation to A V I or V R M L for various purposes.

In addition, y o u m a y choose a j o i n t or a part to generate result graphs, for example, the position vs. time of the piston in the engine e x a m p l e shown in Figure 1-24. T h e s e graphs give y o u a quantitative understanding on the characteristics of the m e c h a n i s m . Y o u m a y also query the results by m o v i n g the cursor closer to the curve and leave the cursor for a short period. T h e result data will appear next to the cursor. In addition, y o u m a y ask COSMOSMotion for a report that includes a complete set of results output in the form of textual data or a Microsoft® Excel spreadsheet. In addition to the capabilities discussed above, COSMOSMotion allows y o u to check interference between bodies during m o t i o n (please see Lesson 5 for m o r e details). Furthermore, the reaction forces calculated can be u s e d to support structural analysis using, for example, COSMOSWorks.

1.5

Motion Examples

N u m e r o u s m o t i o n examples will be introduced in this b o o k to illustrate the step-by-step details of m o d e l i n g , simulation, and result visualization capabilities in COSMOSMotion. In addition, an application e x a m p l e will be introduced to illustrate the steps and principles of using COSMOSMotion for support of m e c h a n i s m design. We will start w i t h a simple ball-throwing example in Lesson 2. This e x a m p l e will give y o u a quick run-through on using COSMOSMotion. Lessons 3 through 7 focus on m o d e l i n g and analysis of basic m e c h a n i s m s and d y n a m i c systems. In these lessons, y o u will learn various j o i n t types, including revolute, planar, cylindrical, etc.; forces and connections, including springs, gears, cam-followers; drivers and forces; various analyses; and graphs and results. Lesson 8 is an application lesson, in w h i c h an assistive soccer ball kicking device that can be m o u n t e d on a wheelchair will be introduced to show y o u h o w to apply w h a t y o u learn to real-world applications. All examples a n d m a i n topics to be discussed in each lesson are s u m m a r i z e d in the following table.

2.1

O v e r v i e w of the L e s s o n

T h e purpose of this lesson is to provide y o u a quick run-through on using COSMOSMotion. This e x a m p l e simulates a ball t h r o w n w i t h an initial velocity at an elevation. D u e to gravity, the ball will travel following a parabolic trajectory and b o u n c e b a c k a few times w h e n it hits the ground, as depicted in Figure 2 - 1 . In this lesson, y o u will learn h o w to create a m o t i o n m o d e l to simulate the ball motion, run a simulation, and animate the ball motion. Simulation results obtained from COSMOSMotion can be verified using particle d y n a m i c s theory that w a s learned in high school Physics. We will review the equations of motion, calculate the position and velocity of the ball, and c o m p a r e our calculations w i t h results obtained from COSMOSMotion. Validating results obtained from computer simulations is extremely important. COSMOSMotion is n o t foolproof. It requires a certain level of experience a n d expertise to master the software. Before y o u arrive at that level, it will be indispensable to verify the simulation results, w h e n e v e r possible. Verifying the simulation results will increase y o u r confidence in using the software a n d prevent y o u from being occasionally fooled by the erroneous simulations p r o d u c e d by the software. N o t e that very often the erroneous results are due to m o d e l i n g errors. 2.2

T h e Ball T h r o w i n g E x a m p l e

Physical

Model

T h e physical m o d e l of the ball e x a m p l e is very simple. T h e ball is m a d e of Cast Alloy Steel with a radius of 10 in. T h e units system e m p l o y e d for this e x a m p l e is IPS (inch, pound, second). T h e gravitational acceleration is 386 i n / s e c . N o t e that y o u m a y check o r c h a n g e the units system b y choosing f r o m the p u l l - d o w n m e n u 2

Tools >

Options

and choose the Document Properties tab in the System Options - General dialog b o x , click the n o d e , and then p i c k the units system y o u prefer, as s h o w n in Figure 2-2.

Units

T h e ball and g r o u n d are a s s u m e d rigid. T h e ball will b o u n c e b a c k w h e n it hits the ground. A coefficient of restitution C = 0.75 is specified to determine the b o u n c e velocity (therefore, the force) w h e n the impact occurs. F o r this e x a m p l e , C = V/V , w h e r e V% and are the velocities of the ball before and after the impact. T h a t is, the b o u n c e velocity will be 7 5 % of the i n c o m i n g velocity, a n d certainly, in the opposite direction. N o t e that in order for COSMOSMotion to capture the m o m e n t w h e n the ball hits the ground, we will define a 3D contact constraint b e t w e e n the ball a n d the ground, and u s e the true g e o m e t r y of the parts for a finer interference calculation during the simulation. R

R

t

SolidWorks

Parts

and Assembly

For this lesson, the parts and assembly h a v e b e e n created for y o u in SolidWorks. There are four files created, ball.SLDPRT, ground. SLDPRT, Lesson2. SLDASM, and Lesson2withresults.SLDASM. You can find these files at the p u b l i s h e r ' s w e b site (ht1p://www.schrofflxom/). We will start with Lesson2.SLDASM, in w h i c h the ball is fully a s s e m b l e d to the ground; i.e., no m o v e m e n t is allowed. In addition, the assembly file Lesson2withresults.SLDASM consists of a complete simulation m o d e l with simulation results, in w h i c h s o m e of the assembly m a t e s w e r e suppressed in order to provide adequate degrees of freedom for the ball to m o v e . Y o u m a y w a n t to open this file to see h o w the ball is supposed to m o v e . Since the gravity is defined in the negative 7-direction of the global coordinate system as default, all parts a n d assembly are created for a m o t i o n simulation that complies with the default setting. T h e assembly Lesson2.SLDASM consists of t w o parts: the ball (ball.SLDPRT) and the ground (ground.SLDPRT). T h e ball is fully assembled with the g r o u n d by three assembly mates of three pairs of reference planes. T h e y are Front (ball)/Front (ground), Right (ball)/'Right (ground), a n d Top (ball)/7b/? (ground), as s h o w n in Figure 2 - 3 . T h e distance b e t w e e n the reference planes Top (ball) and Top (ground) is 100 in., w h i c h defines the initial position of the ball, as s h o w n in Figure 2-4. T h e radius of the ball is 10 in., and the ground is m o d e l e d as a 30*500*0.04 in. rectangular block. 3

N o t e that the 7-axis of the global coordinate system (located at the lower left corner of the SolidWorks graphics screen, as s h o w n in Figure 24) is pointing u p w a r d , w h i c h is consistent with the default direction of the gravity, but in the opposite direction. Motion

Model

In this e x a m p l e , the ball will be the only m o v a b l e b o d y . T w o assembly m a t e s , Distancel and Coincident^, as s h o w n in Figures 2-3a and 2-3c, will be suppressed to allow the ball to m o v e o n the X-Y plane A s m e n t i o n e d earlier, the ball will be t h r o w n with an initial velocity of VQ = 150 in/sec.

R

2

.

4

T

h

e

S

o

l

i

d

W

o

r

k

s

A s s e

mbly

2

A gravitational acceleration -386 i n / s e c is defined in the 7-direction of the global coordinate system. T h e ball will reveal a parabolic trajectory due to gravity. A 3D contact constraint will be added to characterize the impact b e t w e e n the ball and the ground. As discussed earlier, a coefficient of restitution C = 0.75 will be specified to determine the force that acts on the ball w h e n the impact occurs. In this example, no friction is assumed. R

2.3

U s i n g COSMOSMotion Start SolidWorks

and

open

assembly

file

Lesson2.SLDASM.

W h e n COSMOSMotion is active, the browser has an extra tab (the Motion button) for the Motion (see the buttons on top of the browser s h o w n in Figure 2-5). This b r o w s e r provides y o u with a graphical, hierarchical v i e w of the m o t i o n m o d e l a n d allows y o u to access all COSMOSMotion functionalities t h r o u g h a combination of drag-and-drop and right click m e n u s . Switch b a c k a n d forth b e t w e e n COSMOSMotion and SolidWorks assembly m o d e is straightforward. All y o u h a v e to do is to click the Motion Motion

and Assembly button

buttons

w h e n needed. W h e n y o u click the

to enter COSMOSMotion,

a different set of entities

will be listed in the browser, in addition, an additional toolbar is added to SolidWorks, located at the top of the graphics screen, as s h o w n in Figure 2-6. This toolbar provides settings, simulation a n d post processing features. Especially, the Play Simulation button is h a n d y w h e n y o u finish running a simulation and ready to animate the motion. Click some of the buttons and try to get familiar with their functions. In this lesson, we will use the IntelliMotion Builder for m o s t of the steps. The IntelliMotion Builder is the primary interface in COSMOSMotion. It is a t a b b e d dialog b o x and a w i z a r d that leads y o u through

Before we start, we will suppress t w o assembly mates to allow the ball to m o v e on the X-Y plane. C h o o s e the Assembly button on top of the browser, a n d e x p a n d the button in front of it. Mates branch by clicking the small

Choose Distance 1 (Ground< 1 >, ball<1>), press the right m o u s e button, and choose Suppress. R e p e a t the same for Coincident3(Ground,ball). Both mates will b e c o m e inactive. If y o u m o v e the cursor to the root n o d e , Lesson2 (Default), in the browser, y o u should see a rectangular b o x appears in the graphics screen, w h i c h is simply the b o u n d i n g b o x for the assembly (see Figure 2-8). Click the Motion button enter COSMOSMotion. Start

the IntelliMotion

on ton of the b r o w s e r to

Builder

To use the IntelliMotion Builder, right click the Motion Model n o d e from the browser, a n d then select IntelliMotion Builder (see Figure 2-5). The first tab of the IntelliMotion Builder is Units, w h i c h brings up the Units p a g e . As shown in Figure 2-9, the IPS units system h a s b e e n chosen. No action is needed.

At the lower-left corner of each p a g e in the IntelliMotion Builder are the Back a n d Next buttons, which help you move sequentially through the motion model creation, simulation, and animation process. C h o o s e Next or click the Gravity tab. T h e Gravity p a g e (Figure 2-10) shows that the default acceleration is 386.22 i n / s e c and is acting in the negative 7-direction. This is w h a t we want, a n d no action is needed. C h o o s e Next or click the Parts tab. 2

Defining

Bodies

T h e first step in creating a m o t i o n m o d e l is to indicate w h i c h c o m p o n e n t s from y o u r SolidWorks assembly m o d e l participating in the m o t i o n m o d e l . In an assembly that does n o t yet h a v e any m o t i o n parts defined, all of the assembly c o m p o n e n t s are listed u n d e r the Assembly Components b r a n c h (right column) of the Parts p a g e , as s h o w n in Figure 2 - 1 1 . We will m o v e ball-1 to Moving Parts (left c o l u m n ) and Ground-1 to Ground Parts by using the drag-and-drop m e t h o d . Click ball-1 and drag it by holding d o w n the left-mouse button, m o v i n g the m o u s e until the cursor is over the Moving Parts n o d e , a n d then releasing the m o u s e button. Part ball-1 is n o w added to the m o t i o n m o d e l as m o v i n g parts (can m o v e ) . R e p e a t the same steps to m o v e ground-1 to the Ground Parts n o d e . N o w , the part Ground-1 is a d d e d to the m o t i o n m o d e l as a g r o u n d part (cannot m o v e ) . N o t e that y o u m a y select multiple c o m p o n e n t s by h o l d i n g Ctrl k e y and selecting each component. Y o u m a y select multiple c o m p o n e n t s by selecting the first component, pressing and holding Shift key, and then selecting the last component. All of the c o m p o n e n t s b e t w e e n the first and second selected components will be selected. Or y o u can drag-select by pressing the left-mouse button and m o v i n g the

m o u s e so that the selection rectangle intersects the c o m p o n e n t s . In this case, any c o m p o n e n t s within the selection rectangle will be selected.

A n y time a c o m p o n e n t (a part or an assembly) is a d d e d to the m o t i o n m o d e l , COSMOSMotion looks at all of the assembly m a t e s that are attached to that component. If an assembly m a t e b e t w e e n the n e w l y a d d e d c o m p o n e n t a n d another c o m p o n e n t that is already participating in the m o t i o n m o d e l is found, a m o t i o n j o i n t that m a p s to the assembly m a t e is generated. This allows y o u to take a fully assembled m o d e l and quickly build a simulation-ready m o t i o n m o d e l by indicating w h i c h c o m p o n e n t s from the assembly participate in the m o t i o n m o d e l . A list of m a p p i n g s b e t w e e n the assembly and m o t i o n joints that are frequently encountered can be found in A p p e n d i x A. Take a few m i n u t e s to review A p p e n d i x A to b e c o m e m o r e familiar with the m a p p i n g a n d the j o i n t types supported in COSMOSMotion. Understanding joints and the m a p p i n g will help y o u assemble parts adequately for m o t i o n m o d e l s , avoiding unnecessary m o d e l editing and confusion. Defining

Initial

Velocity

We will add an initial velocity Vo =150 in/sec to the x

ball. Click ball-1 from the Parts p a g e , press the right m o u s e button, and choose Properties (see Figure 2-12), the Edit Part dialog b o x will appear. Click the IC's tab and enter 150 for X Velocity, as shown in Figure 2 - 1 3 . Click Apply. T h e initial velocity has b e e n defined. Defining

Joints

C h o o s e Next or click the Joints tab. T h e Joints p a g e allows y o u to modify joints that w e r e automatically created f r o m assembly mates. Y o u m a y add additional joints to the m o t i o n m o d e l if adequate. This p a g e contains a single tree that lists all of the joints in the m o t i o n m o d e l . As s h o w n in Figure 2-14, there is only o n e j o i n t listed, Coincident!, w h i c h m a t e s Front Plane of ball to the Front Plane of the ground to allow a planar m o t i o n for the ball.

On the right, y o u will see a list of j o i n t types y o u can choose to add to y o u r motion m o d e l . The first j o i n t Revolute is selected by default. As indicated in the m e s s a g e , a revolute j o i n t r e m o v e s five degrees of freedom, three translational and t w o rotational. H o w e v e r , for this ball-throwing example, the j o i n t carried over from SolidWorks; i.e., Coincident2, is exactly w h a t we want; therefore, no action is n e e d e d for the time being.

Running

Simulation

Click the Next button three times or click the Simulation tab directly (no spring or driver is n e e d e d for this example; therefore, we are skipping the Spring and Motion tabs). As s h o w n in Figure 2 - 1 5 , the simulation duration is 1 second a n d the n u m b e r of frames is 50 as defaults. We will stay with these default values for the time being. Click Simulate to run a simulation.

After a few seconds, the ball will start m o v i n g . As s h o w n in Figure 2-16 the ball will fall through the ground, w h i c h is n o t realistic. N o t e that the trace path that indicates the trace of the center of the ball is turned on in Figure 2-16. We will learn h o w to do that later. For the time being we will h a v e to add a 3D Contact constraint b e t w e e n the ball and the ground in order to m a k e the ball b o u n c e b a c k w h e n it hits the ground. T h e 3D Contact constraint will create a force to prevent the ball from penetrating the ground. This constraint will be only activated if the ball comes into contact with the ground. Defining a

3D

Contact

Constraint

T h e 3D Contact constraint cannot IntelliMotion Builder. We will h a v e to u s e the d o w n m e n u . Before creating a 3D Contact IntelliMotion Builder, and delete the simulation

be created in the browser or the pullconstraint, close the result by clicking the

Delete Results button JIL at the b o t t o m of the browser (see Figure 2-17 for the location of the delete button). N o w , the ball should return to its initial position. Also, save y o u r m o d e l before m o v i n g forward. F r o m the p u l l - d o w n m e n u , choose COSMOSMotion

>

Contacts >

3D Contact

or from the browser, right click the Contact branch, and then select Add 3D Contact, as s h o w n in Figure 2-17. The Insert 3D Contact dialog b o x will appear (Figure 2-18).

COSMOSMotion calculates w h e t h e r the parts' b o u n d i n g boxes (usually the rectangular box, similar to thai of Figure 2-8, b u t for individual parts) interfere. If they interfere, COSMOSMotion performs a finer interference calculation b e t w e e n the t w o bodies. At the same time, ADAMS/Solver c o m p u t e s and applies an impact force on both bodies. F r o m the browser, select Ground-7, the g r o u n d part will be listed in the first container (upper field), as s h o w n in Figure 2-18. Click the Add Container for contact pairs button (in the m i d d l e ) , and pick ball-1 The part ball-1 will be listed in Container 2 (lower field). Click the Contact tab to define contact parameters. N o t e that we will define a coefficient of restitution for the impact. In the three sets of parameters appearing in the dialog b o x (Figure 2-19). turn off the Use Materials (deselect the entity) and Friction (click None). C h o o s e Coefficient of Restitution I in the middle), and enter 0.75 for Coefficient Restitution, as shown in Figure 2-19. Click Apply to accept the 3D Contact. T h e 3D Contact constraint should appear in the browser, as s h o w n in Figure 2-20. Y o u w i l l h a v e to e x p a n d the Constraints branch and then the Contact branch to see the contact constraint. Rerun

the

Simulation

Before we rerun the simulation, we will h a v e to adjust some of the simulation parameters. Especially we will ask COSMOSMotion to u s e precise geometry to check contact in each frame of simulation. R i g h t click the Motion Model n o d e from the browser and choose Simulation Parameters. In the COSMOS Education Edition Options dialog b o x appearing (Figure 2-21), choose Use Precise Geo/?;, for 3D Contact, and enter 3 seconds for Duration and 500 for Number of Frames. N o t e that we increase the n u m b e r of frame so that we will see smooth graphs in various result displays. Increasing the number of frame will certainly increase the simulation time. H o w e v e r , the increment is insignificant for this simple example. Click OK io accept the definition a n d close the dialog b o x .

R i g h t click the Motion Model n o d e from the b r o w s e r and choose Run Simulation. After a few seconds, the ball starts m o v i n g . As s h o w n in Figure 2-22 the ball will hit the ground and b o u n c e back a

few times before the simulation ends. T h e ball did n o t fall t h r o u g h the g r o u n d this t i m e due to the addition of the 3D Contact constraint. Displaying

Simulation

Results

COSMOSMotion allows y o u to graphically display the path that any point on any m o v i n g part follows. This is called a trace path. N o t e that the trace path of the ball w a s displayed in both Figures 2-16 and 2-22. We will first learn h o w to create a part trace path. F r o m the browser, right click the Results n o d e , a n d choose Create Trace Path (see Figure 2-23) to bring up the Edit Trace Path dialog box, as s h o w n in Figure 2-24. N o t e that Assem2 should be listed in the Select Reference Component text b o x , w h i c h serves as the default reference frame for the trace path. T h e default reference frame is the global reference frame included as part of the g r o u n d body. No change is needed.

To select the part u s e d to generate the trace curve, select the Select Trace Point Component text field (should be highlighted in red already), and then select one m o v i n g part; i.e., the ball, from the graphics screen. The part ball-1 will be listed in the Select Trace Point Component text field, and balll/DDMFace2 is listed in the Select Trace Point on the Trace Point Component text b o x . Click Apply button, y o u should see the trace path appears in the graphics screen, similar to that of Figure 2-22. Next, we will create a graph for the 7-position of the ball using the XY Plots. F r o m the browser, right click ball-1 (under Parts, Moving Parts) a n d choose Plot > CM Position > Y. T h e XY Plot for the CM (Center of M a s s ) position of the ball in the 7-direction will appear, similar to that of Figure 2 - 2 5 . N o t e that y o u m a y adjust properties of the graph, for instance the axis scales, following steps similar to those of Microsoft® Excel spreadsheet graphs. The graph shows that the ball w a s t h r o w n from Y= 100 in. and hits the ground at Y= 10 in. ( C M of the ball) a n d time about t— 0.6 seconds. T h e ball b o u n c e s b a c k and m o v e s up to an elevation determined by the coefficient of restitution. T h e m o t i o n continues until reaching the end of the simulation.

N o t e that y o u m a y click any location in the graph to bring up a fine r e d vertical line that correlates the graph with the position of the ball in animation. As s h o w n in the graph of Figure 2.25, at t = 1.4 seconds, the ball is r o u g h l y at Y= 44 in. T h e snapshot of the ball at that specific time a n d 7-location is shown in the graphics screen.

turned off all friction for the 3D Contact constraint earlier, therefore, no energy loss due to contact. Figure 2-27 shows 7-velocity of the ball. T h e ball m o v e s at a linear velocity due to gravity. The 7velocity is about -263 in/sec at t = 0.67 seconds. Y o u m a y see this data by m o v i n g the cursor close to the corner point of the curve and leave the cursor for a short period. The data will appear. Y o u m a y also convert the XY Plot data to Microsoft® Excel spreadsheet by simply m o v i n g the cursor inside the graph and right click to choose Export CSV. O p e n the spreadsheet to see m o r e detailed simulation data. F r o m the spreadsheet (Figure 2-28), the 7-velocity right before a n d after the ball hits the g r o u n d are -264 and 198 in/sec, respectively. T h e ratio of 198/264 is about 0.75, w h i c h is the coefficient of restitution we defined earlier. In addition, y o u m a y u s e the Export A VI button on top of the graphics screen to create an AVI m o v i e for the m o t i o n animation. In the Export A VI Animation File dialog b o x (Figure 2-29); simply click the Preview button to review the AVI animation. L e a v e all default data for Frame and Time. Click OK to accept the definition. An AVI file will be created in your current folder with a file n a m e , Lesson2.avi. Y o u m a y play the A VI animation using, for example, Window Media Player. Be sure to save y o u r m o d e l before exiting from COSMOSMotion. 2.4

Result Verifications

In this section, we will verify analysis results obtained from COSMOSMotion u s i n g particle dynamics theory y o u learned in high school Physics. There are t w o assumptions that we h a v e to m a k e in order to apply the particle d y n a m i c s theory to this ballt h r o w i n g problem: (i) (ii)

T h e ball is of a concentrated m a s s , a n d No air friction is present.

Equation

of Motion

It is w e l l - k n o w n that the equations that describe the position and velocity of the ball are, respectively,

where P a n d P are the X- and 7-positions of the ball, respectively; V and V are the X- and 7-velocities, x

y

x

y

respectively; P and P y are the initial positions in the X- and 7-directions, respectively; V a n d Vg are 0x

0

0x

y

the initial velocities in the X- and 7-directions, respectively; and g is the gravitational acceleration. T h e s e equations can be i m p l e m e n t e d using, for e x a m p l e , Microsoft® Excel spreadsheet shown in Figure 2-30, for numerical solutions. In Figure 2-30, C o l u m n s B and C s h o w the results of Eqs. 2.1a a n d o t e that w h ewith n the a ball the ground, 2.1b, Nrespectively; timehits interval from 0 we to 3will seconds and increment of 0.01 seconds. C o l u m n s D have to reset the velocity to 7 5 % of that at the prior and E show the results of E q s . 2.2a a n d 2.2b, respectively. time step a n d in the opposite direction. Data in c o l u m n C is graphed in Figure 2 - 3 1 . Columns D and E are graphed in Figure 2-32. C omparing Figure 2-31 with Figure 2-25 and Figure 232 with Figures 2-26 and 2-27, the results obtained from theory and COSMOSMotion are very close, w h i c h -:eans the d y n a m i c m o d e l has b e e n created properly in JSMOSMotion, and COSMOSMotion does its j o b and gives us g o o d results. N o t e that the solution spreadsheet am be found at the p u b l i s h e r ' s website (filename: . on2.xls).

1.

U s e the s a m e m o t i o n m o d e l to conduct a simulation for a different scenario. This t i m e the ball is t h r o w n at an initial velocity of from an elevation of 750 in., as s h o w n in Figure E 2 - 1 . (i)

Create a d y n a m i c simulation m o d e l using COSMOSMotion to simulate the trajectory of the ball. Report position, velocity, a n d acceleration of the ball at 0.5 seconds in both vertical and horizontal directions obtained from COSMOSMotion.

(ii)

Derive and solve the equations that describe the position and velocity of the ball. C o m p a r e your solutions with those obtained from COSMOSMotion.

(iii) Calculate the time for the ball to reach the g r o u n d and the distance it travels. C o m p a r e your calculation with the simulation results obtained from COSMOSMotion. 2.

A 1 "xl "xl" block slides from top of a slope (due to gravity) w i t h o u t friction, as s h o w n in Figure E 2 - 2 . The material of the b l o c k and the slope is AL2014. (i)

Create a d y n a m i c simulation m o d e l using COSMOSMotion to analyze m o t i o n of the block. Report position, velocity, and acceleration of the b l o c k in both vertical and horizontal directions at 0.5 seconds obtained from COSMOSMotion.

(ii)

Create a LimitDistance m a t e to stop the b l o c k w h e n its front lower edge reaches the e n d of the slope. Y o u m a y w a n t to review COSMOSMotion h e l p m e n u or p r e v i e w Lesson 3 to learn m o r e about the LimitDistance m a t e .

(iii) Derive and solve the equation of m o t i o n for the system. C o m p a r e y o u r solutions with those obtained from COSMOSMotion.

3.1

O v e r v i e w of the L e s s o n

In this lesson, we will create a simple spring-mass system and simulate its d y n a m i c responses u n d e r various scenarios. A schematics of the system is s h o w n in Figure 3 - 1 , in w h i c h a steel b l o c k of V'xV'xl" is sliding along a 30° slope with a spring connecting it to the top e n d of the slope. T h e b l o c k will slide b a c k and forth along the slope u n d e r three different scenarios. First, the b l o c k will slide due to a small initial displacement, essentially, a free vibration. F o r the second scenario, we will add a friction b e t w e e n the b l o c k and the slope face. Finally, we will r e m o v e the friction and add a sinusoidal force p(t) therefore, a forced vibration. Gravity will be turned on for all three scenarios. In this lesson, y o u will learn h o w to create the spring-mass m o d e l , r u n a m o t i o n analysis, and visualize the analysis results. In addition, y o u will learn h o w to add a friction to a joint, in this case, a planar (or coincident) joint. T h e analysis results of the spring-mass e x a m p l e can be verified using particle dynamics theory. Similar to Lesson 2, we will formulate the equation of motion, solve the differential equations, graph positions of the block, a n d c o m p a r e our calculations w i t h results obtained from COSMOSMotion. Specifically, we will focus on the first a n d the last scenarios; i.e., free and forced vibrations, respectively. 9

3.2

The Spring-Mass System

Physical

Model

N o t e that the IPS units system will be u s e d for this example. T h e spring constant and unstretched length (or free length) are k = 20 lbf/in. and U = 3 in., respectively. As m e n t i o n e d earlier, the first scenario assumes a free vibration, w h e r e the b l o c k is stretched 1 in. d o w n w a r d along the 30° slope. Friction will be i m p o s e d for Scenario 2, in w h i c h the friction coefficient is a s s u m e d jU = 0.25. In the third scenario, an external force p(t) = 10 cos 360t l b is applied to the block, as s h o w n in Figure 3 - 1 . All three scenarios will a s s u m e a gravity of g = 386 i n / s e c in the negative 7-direction. All three scenarios will be simulated u s i n g COSMOSMotion. f

2

SolidWorks

Parts

and Assembly

F o r this lesson, the parts and assembly h a v e b e e n created for y o u in SolidWorks. There are six files created, block. SLDPRT, ground. SLDPRT, Lesson3. SLDASM, Lesson3Awithresults. SLDASM, Lesson3Bwithresults.SLDASM, and Lesson3Cwithresults.SLDASM. Y o u can find these files at the p u b l i s h e r ' s w e b site (http://www.schroffl.com/). We will start with Lesson3.SLDASM, in w h i c h the b l o c k

is a s s e m b l e d to the g r o u n d and no m o t i o n entities h a v e b e e n added. In addition, the assembly files Lesson3Awithresults. SLDASM, Lesson3Bwithresults. SLDASM, and Lesson3Cwithresults. SLDASM contain the complete simulation m o d e l s with simulation results for the three respective scenarios. In the assembly m o d e l s , there are three a s s e m b l y mates, Coincident3(ground,ball), and LimitDistancel(ground,ball), as

Coincidentl(ground,block), shown in Figure 3-2. m T is allowed allowed to to m m oo vv ee along along the the slope slope face. face. If If yyoouu choose choose the the Move Move Component Component button button component on T hh ee bb ll oo cc kk is top of the graphics screen, and drag the b l o c k in m the graphics screen, y o u should be able to m o v e the b l o c k on the slope face, but not b e y o n d the slope face. This is because the third m a t e is defined to restrict the b l o c k to m o v e b e t w e e n the lower a n d upper limits. We will take a look at the assembly m a t e LimitDistancel. LimitDistance 1. on

F r o m the browser, righ-click the third m a t e , LimitDistance 1, and choose Edit Feature. T h e m a t e is brought b a c k for reviewing or editing, as shown in Figure 3-3. N o t e that the distance b e t w e e n the t w o faces (Face<2>@block-l and Face@ground-l, see Figure 3-2c) is 3.00 in., w h i c h is the neutral position of the b l o c k w h e n the spring is undeformed. T h e upper and lower limits of the distance are 9.00 and 0.00 in., respectively. T h e length of the slope face is 10 in., therefore, the u p p e r limit is set to 9.00 in., so that the b l o c k will stop w h e n its front lower edge reaches the end of the slope face. N o t e that y o u will h a v e to choose Advanced Mates in order to access the limit fields. Motion

Model

A spring with a spring constant k = 20 lb /in. and an unstretched length U = 3 in. will be added to connect the b l o c k (Face<2>, as s h o w n in Figure 3-2c) with the ground (Face). f

By default, the ends of the spring will connect to the center of the corresponding square faces (see Figure 3-4). No reference points are needed. This m o d e l is adequate to support a free vibration simulation u n d e r the first scenario. N o t e that we will m o v e the b l o c k 1 in. d o w n w a r d along the slope face for the simulation. This can be a c c o m p l i s h e d by changing the distance from 3 to 4 in. in the LimitDistancel assembly m a t e . N o t e that before entering COSMOSMotion we will suppress t w o assembly mates, Coincident^ a n d LimitDistancel, a n d only k e e p Coincident 1 in order for COSMOSMotion to impose a planar (or coincident) j o i n t b e t w e e n the b l o c k and the slope face. Y o u m a y unsuppress these m a t e s w h e n y o u w a n t to m a k e a change to the assembly, for example, m o v i n g the b l o c k b a c k to its initial position. As m e n t i o n e d earlier, a friction force will be a d d e d b e t w e e n the b l o c k and the slope face for Scenario 2. In addition, a sinusoidal force p(t) = 10 cos 360t will be a d d e d to the b l o c k for the 3rd scenario. Gravity will be turned on for all three scenarios. 3.3

U s i n g COSMOSMotion Start SolidWorks Before

LimitDistancel. choose

entering

open

assembly

COSMOSMotion,

we

F r o m the Assembly browser,

Suppress.

LimitDistancel.

and

The

Save

mate

Coincident3

file Lesson3.SLDASM. will

suppress

e x p a n d the will

become

two

assembly

Mates branch, inactive.

mates,

right click

Repeat

the

Coincident3

and

Coincident3,

and

same

to

suppress

your model.

F r o m the browser, click the Motion button

on top to enter COSMOSMotion.

In this lesson, instead of using IntelliMotion Builder (as in Lesson 2), we will use the browser, and basic drag-and-drop and right click activated m e n u s to create and simulate the b l o c k motion. Before creating any entities, always check the units system. Similar to Lesson 2, choose from the null-down m e n u

C h o o s e t h e Document Properties t a b in t h e System Options - General d i a l o g b o x , c l i c k t h e Units n o d e . Y o u s h o u l d s e e t h a t the IPS units system has b e e n chosen. In this units system, the gravity is 386 in/sec in the negative 7-direction of the global coordinate system by default. No change is needed. 2

Defining

Bodies

F r o m the browser, e x p a n d the Assembly Components b r a n c h (right underneath the Motion Model node) by clicking the small + button in front of it. Y o u should see t w o parts listed, block-1 a n d ground-7,

as s h o w n in Figure 3-5. A l s o expand the Parts branch; y o u should see Moving Parts and Ground Parts listed. We will m o v e block-1 to Moving Parts and ground-1 to Ground Parts by using the drag-and-drop method. Click block-1 and drag it by holding d o w n the left-mouse button, m o v i n g the m o u s e until the cursor is over the Moving Parts n o d e , and then releasing the m o u s e button. Part block-1 is n o w a d d e d to the m o t i o n m o d e l as m o v i n g parts. R e p e a t the same steps to m o v e ground-1 to the Ground Parts n o d e . N o w , the part ground-1 is a d d e d to the m o t i o n m o d e l as a ground part (completely fixed, as s h o w n in Figure 3-6). E x p a n d the Constraints branch, and then the Joints branch. Y o u should see that only one joint, Coincident1, is listed. E x p a n d the Coincident! b r a n c h to see that the assembly m a t e is defined between ground-! and block-1. Since this coincident j o i n t restricts the b l o c k to m o v e on the slope face of the ground, it is therefore a planar joint. A planar j o i n t symbol should appear in the m o t i o n m o d e l , as s h o w n in Figure 3-4. Defining

Spring

F r o m the browser, right click the Spring n o d e a n d choose Add Translational Spring (see Figure 3-7). In the Insert Spring dialog b o x (Figure 3-8), the Select 1st Component field is highlighted in red and r e a d y for y o u to pick. Pick the face at top right of the g r o u n d (see Figure 3-9), the Select 2nd Component field should n o w highlight in red, a n d ground l/DDMFace4 should appear in the Select Point on 1st Component field, w h i c h indicates that the spring will be connected to the center point of the face. Rotate the view, and then pick the face in the block, as s h o w n in Figure 3-9. N o w , block-1 and block-l/DDMFace3 should appear in the Select 2nd Component field and Select Point on 2nd Component field, respectively. Also, a spring symbol should appear in the graphics screen, connecting the center points of the t w o selected faces.

Defining

Initial

Position

We w o u l d like to stretch the spring 1 in. d o w n w a r d along the slope face as the initial position for the block. T h e b l o c k will be released from this position to simulate a free vibration; i.e., the first scenario. We will go b a c k to the Assembly m o d e , unsuppress LimitDistancel, change the distance d i m e n s i o n from 3 to 4 in., and then sunnress the m a t e before returning to COSMOSMotion. Go b a c k to Assembly by clicking the Assembly button

on top of the browser.

E x p a n d the Mates branch listed in the browser, right click and c h o o s e Unsuppress. Right click the same assembly m a t e and choose Edit Feature. Y o u should see the definition of the assembly m a t e in the dialog b o x like that of Figure 3-3. C h a n g e the distance from 3.00 to 4.00 in., and click the c h e c k m a r k on top to accept the change. In the graphics screen, the b l o c k should m o v e 1 in. d o w n w a r d along the slope face. Click the c h e c k m a r k again to close the assembly m a t e b o x . Right c l i c k L i m i t D i s t a n c e l ( z r o u n d < l > , b a l l < l > ) again and choose Suppress.

Go b a c k to COSMOSMotion by clicking the Motion button (y . Click the Motion Model n o d e , press the right m o u s e button a n d select Simulation Parameters. Enter 0.25 for simulation duration and 500 for the n u m b e r of frames. Click the Motion Model n o d e again, press the right m o u s e button and select Run Simulation. Y o u may also click the Run Simulation button | J | ] right b e l o w the browser to run a simulation. Y o u should see the b l o c k start m o v i n g b a c k and forth along the slope face. We will graph the position of the b l o c k in terms of the m a g n i t u d e (instead o f X - or 7-component) next.

Displaying

Simulation

Results

Since there is no position graph defined for the block, we will h a v e to create one. We will create a graph for the distance b e t w e e n the t w o faces that w e r e selected to define the spring. F r o m the browser, e x p a n d the Results branch, right click the Linear Disp n o d e , and choose Create Linear Displacement (Figure 3-10). In the Insert Linear Displacement dialog b o x (Figure 3-11), the Select First Component field should be highlighted in red a n d ready for y o u to pick. This dialog b o x is very similar to the upper half of the Insert Spring dialog b o x (Figure 3-8). We will select exactly the same t w o faces s h o w n in Figure 3-9 for this displacement. Similar to the spring, p i c k the face of the g r o u n d (see Figure 3-9). Rotate the view, and then pick the face in the block, as shown in Figure 3-9. A straight line that connects the center points of these t w o faces appears, as s h o w n in Figure 312. Click Apply button to accept the definition.

N e x t , we will create a graph for the displacement of the b l o c k using the XY Plots option. This position graph should reveal a sinusoidal function as we h a v e seen in m a n y vibration examples of Physics. F r o m the browser, right click LDisplacement > Plot > Magnitude (see Figure 3-13). A graph like that of Figure 3-14 should appear. F r o m the graph, the block m o v e s along the slope face b e t w e e n 2 and 4 in. This is because the unstretched length of the spring is 3 in. a n d we stretched the spring 1 in. to start the motion. Also, it takes about 0.04 seconds to complete a cycle, w h i c h is small. T h e small vibration period can be attributed to the fact that the spring is fairly stiff (20 lb /in). f

N o t e that y o u can also export the graph data, for example, by right clicking the graph and choosing Export CSV. Open the spreadsheet and e x a m the data. T h e time for the b l o c k to m o v e b a c k to its initial position; i.e., w h e n the distance is 4 in., is 0.037 seconds. We will carry out calculations to verify these results later in Section 3.4. Before we do that, w e will w o r k o n t w o m o r e scenarios: with friction and with the addition of an external force. Save y o u r m o d e l before m o v i n g to the next scenario. Y o u m a y save the m o d e l under different n a m e a n d use it for the next scenario. Scenario 2:

With Friction

We will a d d a friction force to the planar j o i n t {Coincident 1) b e t w e e n the b l o c k and the ground. The friction coefficient is ju = 0.25. Before m a k i n g any change to the definition of the simulation m o d e l , we will h a v e to delete existing simulation results. Click the Delete Results button to delete the results.

at the b o t t o m of the b r o w s e r

Note that for calculating friction effects, COSMOSMotion m o d e l s a planar j o i n t as one b l o c k sliding a n d rotating on the surface of another block, as illustrated in Figure 3-15, w h e r e L is the length of the top (sliding) rectangular block, W is the w i d t h of the top rectangular block, and R is the radius of a circle, centered at the center of the top b l o c k face in contact with the b o t t o m block, w h i c h circumscribes the face of the sliding block.

E x p a n d the Constraints branch and then the Joints branch. Right click the Coincident! n o d e and choose Properties. In the Edit Mate-Defined Joint dialog b o x , choose the Friction tab, click the Use Friction, enter 0.25 for Coefficient (mu), and enter Joint dimensions, Length: 1, Width: 1, a n d Radius: 1.414, as shown in Figure 3-17. Click Apply button to accept the definition. R u n a simulation (with the same simulation parameters as those of Scenario T). Graph the displacement of the block; y o u should see a graph similar to that of Figure 3-18. T h e amplitude of the graph (that is, the distance the b l o c k travels) is decreasing over time due to friction. Save y o u r m o d e l . We will m o v e into Scenario 3. Y o u m a y save the m o d e l again under different n a m e and use it for the next scenario.

In this scenario we will add an external force p(t) = 10 cos 360t at the center of the end face of the block in the d o w n w a r d direction along the slope. At the same time, we will r e m o v e the friction in order to simplify the problem. Before creating a force, we will delete the simulation results and r e m o v e the friction. Delete the results by clicking the Delete Results button

at the b o t t o m of the browser.

Right click the Coincidentl n o d e and choose Properties. In the Edit Mate-Defined Joint dialog b o x , choose the Friction tab, a n d deselect the Use Friction by clicking the small b o x in front of it. All parameters a n d selections on the dialog b o x should b e c o m e inactive. Click Apply button to accept the change. The force can be a d d e d by expanding the Forces branch, right clicking the Action Only n o d e , a n d choosing Add Action-Only Force, as s h o w n in Figure 3-19. In the Insert Action-Only Force dialog b o x (see Figure 3-20), the Select Component to which Force is Applied field will be active (highlighted in red) and ready for y o u pick the component. Pick the end face of the block, as s h o w n in Figure 3 - 2 1 . T h e part block-1 is n o w listed in the Select Component to which Force is Applied field, and block-l/DDMFace8 is listed in both the Select Location and the Select Direction fields. That is, the force will be applied to the center of the selected end face a n d in the direction that is normal to the selected face. N o w in the Insert Action-Only Force dialog box, the Select Reference Component to orient Force field is active (highlighted in red) a n d is ready for selection. We will p i c k the g r o u n d part for reference. P i c k any place in the g r o u n d part, ground-1 will n o w appear in the Select Reference Component to orient Force field.

Click the Function tab (see Figure 3-22), choose Harmonic, and enter the followings: Amplitude: 10 Frequency: 360 Phase Shift: -90 N o t e that the -90 degrees entered for Phase Shift is to convert a sine function (default) to the desired cosine function. Click the graph button (right m o s t and circled in Figure 3-22); the sinusoidal force function will appear like the one in Figure 3-23. This is indeed the cosine function p(t) = 10 cos 360t we w a n t e d to define. Close the graph a n d click Apply button to accept the force definition. Y o u should see a force symbol a d d e d to the block, as s h o w n in Figure 3-4. F r o m the browser, right click the Motion Model n o d e , a n d choose Simulation Parameters. C h a n g e the simulation duration to 0.5 seconds (in order to see a graph later that covers a larger t i m e span). N o t e that the 0.5-second duration is half the h a r m o n i c function period of the force applied to the block. F r o m the browser, right click the Motion Model n o d e again, and choose Run Simulation. After 2 to 3 seconds, the block starts m o v i n g . N o t e that in s o m e occasions, the b l o c k m a y slide out of the slope face during the simulation, as s h o w n in Figure 3-24. W h e n this h a p p e n s , simply unsuppress the assembly m a t e ; for example, Coincident3, to restricts the b l o c k to stay on the slope face.

After unsuppressing Coincident3, the planar j o i n t will b e c o m e a translational j o i n t (converted by COSMOSMotion) c o m p o s e d of t w o assembly mates, Coincident 1 and Coincident^. Please refer to the assembly file Lesson3Cwithresults.SLDASM for the translational j o i n t e m p l o y e d for this example. R e r u n a simulation if necessary. As soon as the simulation is completed, a graph like that of Figure 325 should appear. F r o m the graph, the block m o v e s along the slope face r o u g h l y for 2 in. b a c k and forth (since friction is turned off). The vibration amplitude is e n v e l o p e d by a cosine function due to the external force p(t). Also, it takes about 0.04 seconds to complete a cycle, w h i c h is u n c h a n g e d from the previous case. We will carry out calculations to verify these results later. Save y o u r model.

Figure 3-25

The D i s p l a c e m e n t Graph: Scenario 3

In this section, we will verify analysis results of Scenarios 1 and 3 obtained from COSMOSMotion. We will a s s u m e that the block is of a concentrated m a s s so that the particle d y n a m i c s theory is applicable. We will start with Scenario 1 (i.e., free vibration with gravity), and then solve the equations of m o t i o n for Scenario 3 (forced vibration, no friction). Equation

of

Motion:

Scenario

1

F r o m the free-body diagram s h o w n in Figure 3-26, applying N e w t o n ' s Second L a w a n d force equilibrium along the X-direction (i.e., along the 3 0 ° slope), we h a v e

w h e r e m is the m a s s of the block, U is the unstretched length of the spring, x is the distance b e t w e e n the m a s s center of the b l o c k and the top right end of the slope, m e a s u r e d from the top right end. T h e double dots on top of x represent the second derivative of x with respect to time. R e a r r a n g e Eq. 3.2, w e h a v e mx + kx = mgsin 0 + Uk

(3.3)

w h e r e b o t h terms on the right are time-independent. This is a second-order ordinary differential equation. It is well k n o w n that the general solution of the differential equation is

determined with initial conditions. N o t e that the m a s s of the steel b l o c k is 0.264 l b . This can be obtained from m

SolidWorks by opening the b l o c k part file, and choosing, from the p u l l - d o w n m e n u , Tools > Mass Properties. F r o m the Mass Properties dialog b o x (Figure 3-27), the m a s s of the b l o c k is 0.264 p o u n d s (pound-mass, l b ) . N o t e that there are 2 decimal points set in SolidWorks by default. Y o u m a y increase it t h r o u g h the Document Properties - Units dialog b o x (choose from p u l l - d o w n m e n u , Tools > Options). m

N o t e that the p o u n d - m a s s unit l b is n o t as c o m m o n as slug that we are m o r e familiar with. T h e corresponding force unit o f l b i s l b i n / s e c according t o N e w t o n ' s S e c o n d L a w . m

2

m

m

Equation 3.7 can be i m p l e m e n t e d into Microsoft® Excel spreadsheet, as s h o w n in Figure 3-28. C o l u m n B in the spreadsheet shows the results of Eq. 3.7, w h i c h is graphed in Figure 3-29. C o m p a r i n g Figure 3-29 with Figure 3-14, the results obtained from theory and COSMOSMotion agree very well, w h i c h m e a n s the m o t i o n m o d e l has b e e n properly defined, and COSMOSMotion gives us g o o d results. Equation

of

Motion:

Scenario

3

Refer to the free-body diagram s h o w n in Figure 3-26 again. F o r Scenario 3 we m u s t include the force p = fo cos (cot) along the X-direction for force equilibrium; i.e.,

w h e r e the right-hand side consists of constant and time-dependent terms. For the constant terms, the particular solution is identical to that of Scenario 1\ i.e., Eq. 3.5. For the time-dependent term, p = f cos (cot), the particular solution is

0

N o t e that t e r m s grouped in the first bracket of Eq. 3.12 are identical to those of Eq. 3.7; i.e., Scenario 1. The second term of Eq. 3.12 graphed in Figure 3-30 represents the contribution of the external force p(t) to the b l o c k motion. T h e graph shows that the amplitude of the b l o c k is kept within 1 in., b u t the position of the b l o c k varies in time. The vibration amplitude is enveloped by a cosine function. T h e overall solution of Scenario 3; i.e., Eq. 3.12, is a combination of graphs shown in Figures 3-29 and 3-30. In fact, Eq. 3.12 has b e e n i m p l e m e n t e d in C o l u m n C of the spreadsheet. T h e data are g r a p h e d in Figure 3 - 3 1 . C o m p a r i n g Figure 3-31 with Figure 3-25, the results obtained from theory and COSMOSMotion are very close. N o t e that the spreadsheet s h o w n in Figure 3-28 can be found at the p u b l i s h e r ' s website (filename: lesson3.xls).

Exercises: 1.

S h o w that Eq. 3.12 is the correct solution of Scenario 3 g o v e r n e d by Eq. 3.8 by simply plugging Eq. 3.12 into Eq. 3.8.

2.

R e p e a t the Scenario 3 of this lesson, except changing the external force to p(t) = 10 cos 9798. Ot l b . f

Will this external force c h a n g e the vibration amplitude of the system? Can y o u simulate this resonance scenario in COSMOSMotion! 3.

A d d a d a m p e r with d a m p i n g coefficient C = 0.01 l b sec/in. and repeat the Scenario 1 simulation f

using

COSMOSMotion.

(i)

Calculate the natural frequency of the system and compare y o u r calculation with that of COSMOSMotion.

(ii)

Derive a n d solve the equations that describe the position and velocity of the m a s s . C o m p a r e your solutions with those obtained from COSMOSMotion.

4.1

O v e r v i e w of the Lesson

In this lesson, we will create a simple p e n d u l u m m o t i o n m o d e l using COSMOSMotion. The p e n d u l u m will be released from a position slightly off the vertical line. The p e n d u l u m will then rotate freely due to gravity. In this lesson, y o u will learn h o w to create the p e n d u l u m m o t i o n model, run a d y n a m i c analysis, and visualize the analysis results. T h e d y n a m i c analysis results of the simple pendulum e x a m p l e can be verified using particle dynamics theory. Similar to Lessons 2 and 3, we will formulate the equation of m o t i o n ; calculate the angular position, velocity, and acceleration of the p e n d u l u m ; anc c o m p a r e our calculations with results obtained from COSMOSMotion. 4.2

T h e Simple P e n d u l u m E x a m p l e

Physical

Model

T h e physical m o d e l of the p e n d u l u m is c o m p o s e d of a sphere and a r o d rigidly connected, as shown in Figure 4 - 1 . T h e radius of the sphere is 10 m m . T h e length and radius of the thin r o d are 90 mm and 0.5 m m , respectively. T h e top of the rod will be connected to the wall with a revolute joint. This revolute j o i n t allows the p e n d u l u m to rotate. B o t h r o d and sphere are m a d e of A l u n i m u m . N o t e that from the SolidWorks material library the Aluminum Alloy 2014 has b e e n selected for b o t h sphere and rod. The MMGS units system is selected for this e x a m p l e (millimeter for length, N e w t o n for force, and second for time). N o t e that in the MMGS units system, the gravitational acceleration is 9,806 m m / s e c . 2

T h e p e n d u l u m will be released from an angular position of 10 degrees m e a s u r e d from the vertical position about the rotational axis of the revolute joint. The rotation angle is intentionally k e p t small so that the particle dynamics theory can be applied to verify the simulation result.

Y o u can find these files at the p u b l i s h e r ' s w e b site (http://www.schroffl.com/). We will start with Lesson4.SLDASM, in w h i c h the p e n d u l u m is fully assembled to the ground. In addition, the assembly file Lesson4withresults.SLDASM consists of a complete simulation m o d e l with simulation results.

4-3

F r o m top of the browser, click the Motion button

to

enter

COSMOSMotion.

F r o m top of the browser, click the Motion button $ to enter COSMOSMotion. Before creating any entities, always check the units system. M a k e sure that MMGS is chosen. Defining

Bodies

F r o m the browser, e x p a n d the Assembly branch (right u n d e r n e a t h the Motion Model clicking the small H button in front of it. Y o u t w o parts listed, ground-1 and pendulum-7, as Figure 4-4.

Components n o d e ) by should see s h o w n in

A l s o e x p a n d the Parts branch; y o u should see Moving Parts and Ground Parts listed. Go ahead to m o v e pendulum-1 to Moving Parts and ground-1 to Ground Parts by using the drag-and-drop method. E x p a n d the Constraints branch, a n d then the Joints branch. Y o u should see a Revolute j o i n t listed, as s h o w n in Figure 4-5 and a revolute j o i n t symbol should appear in the graphics screen (see Figure 4-3).

Setting

Gravity

We w o u l d like to m a k e sue the gravity is set up properly. F r o m the browser, right-click the Motion Model n o d e and select System Defaults. In the Options dialog b o x (Figure 4-6), enter 9806 for Acceleration (mm/sec**2) w h i c h should appear as default already, and m a k e sure the Direction is set to -7 for Y. Click OK to accept the gravity setting. Defining

and Running

Simulation

Click the Motion Model node, press the right m o u s e button and select Simulation Parameters. Enter 1.5 for simulation duration and then 300 for the n u m b e r of frames. Click the Motion Model n o d e again, press the right m o u s e button and select Run Simulation. Y o u should see the p e n d u l u m start m o v i n g b a c k and forth about the axis of the revolute joint. We will graph the position, velocity, and acceleration of the p e n d u l u m next. Displaying

Simulation

Results

The results of angular position, velocity, and acceleration of the p e n d u l u m can be directly obtained by right clicking the m o v i n g part, pendulum-7, from the browser.

The results of angular position, velocity, and acceleration of the p e n d u l u m can be directly obtained by right clicking the m o v i n g part, pendulum-7, from the browser. F r o m the browser, e x p a n d the Parts n o d e and the then Moving Parts n o d e . Right-click pendulum-7, and choose Plot > Bryant Angles > Angle 3. N o t e that the Bryant angles are also k n o w n as X-Y-ZEuler angles or Cardan angles. T h e y are simply the rotation angles of a spatial object along the 7-, and Z-axes of the reference coordinate system. Angle 3 is m e a s u r e d about the Z-axis. A graph like that of Figure 4-7 should appear. F r o m the graph, the p e n d u l u m swings about the Z-axis b e t w e e n -10 and 10 degrees, as expected (since no friction is involved). Also, it takes about 0.6 seconds to complete a cycle. N o t e that y o u can export the graph data, for e x a m p l e , by right clicking the graph and choosing Export CSV. O p e n the spreadsheet and e x a m the data. F r o m the spreadsheet, the t i m e for the p e n d u l u m to swing b a c k to its original position; i.e., -10 degrees., is 0.64 second, as s h o w n in the spreadsheet of Figure 4 - 8 . We will carry out calculations to verify these results later. Before we do that, we will graph the angular velocity and acceleration of the p e n d u l u m .

and c h o o s e Angular Acceleration > Z Component. Y o u should see graphs like those of Figures 4-9 and 410. Figure 4-9 s h o w s that the angular velocity starts at 0, w h i c h is expected. T h e angular velocity varies b e t w e e n r o u g h l y -100 a n d 100 degrees/sec. Also, the angular acceleration varies b e t w e e n roughly -1,000 and 1,000 degrees/sec . A r e these results correct? We will carry out calculations to verify if these graphs are accurate. 2

4.4

Result Verifications

In this section, we will verify the analysis results obtained from COSMOSMotion using particle dynamics theory. There are four assumptions that we h a v e to m a k e in order to apply the particle dynamics theory to this simple p e n d u l u m p r o b l e m : (i) (ii) (iii) (iv)

M a s s of the r o d is negligible (this is w h y the diameter of the p e n d u l u m r o d is very small), T h e sphere is of a concentrated m a s s , Rotation angle is small ( r e m e m b e r the initial conditions we defined?), and No friction is present.

T h e p e n d u l u m m o d e l has b e e n created to comply with these assumptions as m u c h as possible. We expect that the particle dynamics theory will give us results close to those obtained from simulation. T w o approaches will be presented to formulate the equations of m o t i o n for the p e n d u l u m : energy conservation and N e w t o n ' s law. Energy

Conservation

Referring to Figure 4 - 1 1 , the kinetic energy and potential energy of the p e n d u l u m can be written, respectively, as

T=- J 0

(4.1)

2

w h e r e J is the polar m o m e n t of inertia, i.e., J = m£ \ and U=mg/(l-<:os

6)

A c c o r d i n g to the energy conservation theory, the total mechanical energy, w h i c h is the s u m of the kinetic energy and potential energy, is a constant with respect to time; i.e.,

F r o m the free-body diagram s h o w n in Figure 4-12, the equilibrium equation of m o m e n t at the origin about the Z-axis (normal to the paper) can be written as:

N o t e that the same equation of m o t i o n has b e e n derived from t w o different approaches. T h e linear ordinary second-order differential equation can be solved analytically. Solving the Differential Equation

T h e a b o v e equations represent angular position, velocity, a n d acceleration, of the revolute joint. T h e s e equations can be i m p l e m e n t e d into, for example, Excel spreadsheet s h o w n in Figure 4 - 1 3 , for numerical solutions. C o l u m n s B, C, and D in the spreadsheet s h o w the results of Eqs. 4.9a, b, a n d c, respectively, b e t w e e n 0 and 7.5 seconds with an increments of 0.005 seconds. D a t a in these three c o l u m n s are graphed in Figures 4-14, 15, and 16, respectively. C o m p a r i n g Figures 4-14 to 16 with Figures 4-7, 4-9, and 4-10, the results obtained from theory and simulation are v e r y close. The m o t i o n m o d e l has b e e n properly defined, and COSMOSMotion gives us g o o d results. N o t e that in the calculation, the angular position of the p e n d u l u m is set to zero w h e n it aligns with the vertical axis; therefore, the p e n d u l u m swings b e t w e e n -10 a n d 10 degrees.

H o w e v e r , even t h o u g h graphs obtained from COSMOSMotion and spreadsheet calculations are alike these results are not identical. This is because that the COSMOSMotion m o d e l is not really a simple p e n d u l u m since m a s s of the rod is non-zero. If y o u reduce the diameter of the rod, the COSMOSMotion results should approach those obtained through spreadsheet calculations.

Exercises: 1.

Create a spring-damper-mass system, as s h o w n in Figure E 4 - 1 , using COSMOSMotion. N o t e that the unstretched spring length is 3 in. The radius of the ball is 0.5 in. and the material is Cast Alloy Steel (mass density: 0.2637 l b / i n ) . 3

m

2.

(i)

Find the spring length in the equilibrium condition using COSMOSMotion.

(ii)

Solve the same p r o b l e m u s i n g N e w t o n ' s laws. C o m p a r e y o u r results w i t h those obtained from COSMOSMotion.

If a force p = 2 l b is applied to the ball as s h o w n in Figure E 4 f

1, repeat b o t h (i) and (ii) of P r o b l e m 1.

5.1

O v e r v i e w of the L e s s o n

In this lesson, y o u will learn h o w to create simulation m o d e l s for a slider-crank m e c h a n i s m and conduct three analyses: kinematics, interference, and dynamics. M o r e j o i n t types will be introduced in this lesson. Y o u will learn h o w to select assembly mates to connect parts in order to create a successful m o t i o n m o d e l . We will first drive the m e c h a n i s m by rotating the crank with a constant angular velocity; therefore, conducting a kinematic analysis. After we complete a kinematic analysis, we will turn on interference checking and repeat the analysis to see if parts collide. It is very important to m a k e sure no interference exists b e t w e e n parts while the m e c h a n i s m is in motion. The final analysis will be d y n a m i c , w h e r e we will add a firing force to the piston for a d y n a m i c analysis. This lesson will start with a brief overview about the slider-crank assembly created in SolidWorks. At the e n d of this lesson, we will verify the kinematic simulation results using theory and computational m e t h o d s e m p l o y e d for m e c h a n i s m design. 5.2

The Slider-Crank Example

Physical

Model

T h e slider-crank m e c h a n i s m is essentially a four-bar linkage, as s h o w n in Figure 5 - 1 . T h e y are c o m m o n l y found in m e c h a n i c a l systems; e.g., internal combustion engine and oil-well drilling equipment. F o r the internal c o m b u s t i o n engine, the m e c h a n i s m is driven by a firing load that pushes the piston, converting the reciprocal m o t i o n into rotational m o t i o n at the crank. In the oil-well drilling equipment, a torque is applied at the crank. The rotational m o t i o n is converted to a reciprocal m o t i o n at the piston that digs into the ground. N o t e that in any case the length of the crank m u s t be smaller than that of the r o d in order to allow the m e c h a n i s m to operate. This is c o m m o n l y referred to as the G r a s h o f s law. In this example, the lengths of the crank and r o d are 3" and 8", respectively. N o t e that the units system chosen for this e x a m p l e is IPS (in-lbj-sec). All parts are m a d e of A l u m i n u m , 2014 Alloy. subassemblies).

No

friction

is

assumed between

any pair of the

components

(parts

or

SolidWorks

Parts

and Assembly

T h e slider-crank system consists of five parts and one subassembly. T h e y are bearing, crank, rod, pin, piston, and rodandpin (subassembly, consisting of r o d and pin). An exploded v i e w of the m e c h a n i s m is s h o w n in Figure 5-2. SolidWorks parts and assembly h a v e b e e n created for you. T h e y are bearing.SLDPRT, crank. SLDPRT, rod.SLDPRT, pin.SLDPRTpiston.SLDPRT, and rodandpin.SLDASM. In addition, there are three assembly files, Lesson5.SLDASM, Lesson5Awithresults.SLDASM, and LessonSBwithresults.SLDASM. Y o u can find these files at the p u b l i s h e r ' s w e b site. We will start with LessonS. SLDASM, in w h i c h all c o m p o n e n t s are properly assembled. In this a s s e m b l y the bearing is anchored (ground) and all other parts are fully constrained. We will suppress one a s s e m b l y m a t e in order to allow for m o v e m e n t . S a m e as before, the assembly file LessonSAwithresults. SLDASM and Lesson5Bwithresults.SLDASM (with firing force) consist of complete simulation m o d e l s with simulation results. Y o u m a y w a n t t o open these files to see the m o t i o n animation of the m e c h a n i s m . In these assembly files with complete simulation results, a m a t e has b e e n suppressed. Y o u can also see h o w the parts m o v e by m o v i n g the cursor to the graphics screen and press the right m o u s e button. In the m e n u option appearing next, choose Move Component, a n d drag a m o v a b l e part, for e x a m p l e drag the crank to rotate it with respect to the bearing. T h e w h o l e m e c h a n i s m will m o v e accordingly. There are eight assembly mates, including five coincident and three concentric, defined in the assembly. Y o u m a y w a n t to expand the MateGroupl branch in the b r o w s e r to see the list of mates. M o v e y o u r cursor on any of the m a t e s ; y o u should see the entities selected for the assembly m a t e highlighted in the graphics screen. T h e first three m a t e s (Concentric 1, Coincident 1, and Coincident!) assemble the crank to the fixed bearing, as s h o w n in Figure 5-3a. As a result, the crank is completely fixed. N o t e that the m a t e Coincident! orients the crank to the upright position. This m a t e will be suppressed before entering COSMOSMotion. Suppressing this m a t e will allow the crank to rotate with respect the bearing. COSMOSMotion will convert these t w o m a t e s , Concentricl and Coincident 1, to a revolute joint. T h e next t w o mates (Concentric2 and Coincident^) assemble the r o d to the crank, as shown in Figure 5-3b. U n l i k e the crank, the r o d is allowed to rotate with respect to the crank, leading to another revolute j o i n t in COSMOSMotion. The next t w o m a t e s (Concentric3 and Coincident4) assemble the piston to the pin, allowing the piston to rotate about the pin. As a result, a revolute j o i n t (or a concentric j o i n t in some cases) will be added b e t w e e n the piston and the pin. The final m a t e (CoincidentS) eliminates the rotation by m a t i n g t w o planes, Right Plane of the piston and the Top Plane of the assembly, as s h o w n in Figure 5-3c. COSMOSMotion will add a translational j o i n t b e t w e e n the piston and the ground. Since the translational j o i n t is c o m p o s e d of Coincident5 and Coincident4, Concentric3 will be carried over to COSMOSMotion as it is. Therefore, instead of a revolute joint, a cylindrical j o i n t appears in the m o t i o n model.

Simulation

Model

In this example, after suppressing Coincident COSMOSMotion converts assembly m a t e s to four joints: Concentric3 (directly carrying over from assembly m a t e ) , Revolute, Revolute2, and Translational, as s h o w n in Figure 5-4. T h e total n u m b e r of degrees of freedom of the slider-crank m e c h a n i s m can be calculated as follows: 3 (bodies) x6 (dofs/body) - 2 (revolute) - 1 (concentric) x4 (dof s/concentric) = 18-19 = -1

X 5

(dofs/revolute)

-

1

(translational)

X 5

(dofs/translational)

Apparently, there are t w o redundant d o f s e m b e d d e d in the m o t i o n m o d e l . Kinematically, this m e c h a n i s m is identical to that of the single piston engine presented in Lesson 1. In Lesson 1, instead of defining t w o revolute j o i n t s , one concentric joint, and one translational joint, the engine e x a m p l e e m p l o y s three cylindrical joints and one translational joint, resulting one free degree of freedom. Since COSMOSMotion will automatically detect a n d r e m o v e r e d u n d a n t d o f s during m o t i o n simulation, we will not m a k e any changes to the j o i n t s converted from the assembly mates. Since the m e c h a n i s m has one free degree of freedom, either rotating the crank or the r o d (about the axis of the revolute joints), or m o v i n g the piston horizontally (along the translational joint) will be sufficient to uniquely determine the position, velocity, and acceleration of any parts in the m e c h a n i s m . T h e m e c h a n i s m will b e f i r s t driven b y rotating the crank at a constant angular velocity of 360 degrees/sec. Gravity will be turned off. This will be essentially a kinematic simulation. This m o d e l will also serve for interference check. It is very important to m a k e sure no interference exists b e t w e e n parts while the m e c h a n i s m is in motion. The simulation results are included in LessonSAwithresults.SLDASM. T h e n e x t and final analysis will be d y n a m i c , w h e r e we will a d d a firing force to the piston for a d y n a m i c simulation. T h e results are included in LessonSBwithresults. SLDASM.

5.3

U s i n g COSMOSMotion Start SolidWorks

and open

assembly

file

Lesson5.SLDASM.

Before entering COSMOSMotion, we will suppress the third assembly m a t e , Coincident2. In this lesson, we will use drag-and-drop as well as right-click activated m e n u s , instead of the IntelliMotion Builder. F r o m the Assembly browser, e x p a n d the Mates branch, right click Coincident2, and choose Suppress. T h e m a t e Coincident2 will b e c o m e inactive. Save y o u r m o d e l .

Before creating any entities, always check the units system. M a k e sure IPS units system is chosen for this example. Defining

Bodies

F r o m the browser, click bearing-1 and drag and drop it to the Ground Parts n o d e . Click the first part u n d e r the Assembly Components n o d e (should be crank-1), press the Shift key, a n d click the last part listed u n d e r the Assembly Components node (should be rodandpin-1). All three c o m p o n e n t s will be selected. D r a g and drop t h e m to the Moving Parts n o d e . E x p a n d the Constraints branch, and then the Joints branch. Y o u should see that four joints, Concentric3, Revolute, Revolute2, and Translational, are listed (Figure 5-6). All j o i n t symbols should appear in the graphics screen, similar to that of Figure 5-4. E x p a n d all j o i n t s in the b r o w s e r and identify the parts they connect. T a k e a look at the j o i n t Revolute (connecting crank to bearing), w h e r e we will add a driver next. Driving

Joint

F r o m the browser, e x p a n d the Constraints n o d e and then the Joints n o d e . Right click the Revolute n o d e a n d choose Properties (see Figure 5-7). In the Edit Mate-Defined Joint dialog b o x (Figure 5-8), u n d e r the Motion tab, choose Velocity for Motion Type, choose Constant for Function, and enter 360 degrees/sec for Angular Velocity (should appear as defaults), as s h o w n in Figure 5-8. Click Apply to accept the definition. We are ready to run a simulation. Turning

Off Gravity

Running

Simulation

We will u s e all default simulation parameters for the kinematic analysis. Click the Motion Model n o d e , press the right m o u s e button and select Run Simulation. After a few seconds, y o u should see the m e c h a n i s m starts m o v i n g . T h e crank rotates 360 degrees as expected and the piston m o v e s a complete cycle, similar to that of Figure 5-10, since the default simulation duration is 1 second. Saving

and Reviewing

Results

We will create four graphs for the m e c h a n i s m : Apposition, X-velocity, a n d X-acceleration of the piston; and angular velocity of Revolute2 (between crank and rod).

Figure 5-10 M o t i o n A n i m a t i o n

F r o m the browser, e x p a n d the Parts branch and then the Moving Parts branch. Right click the piston-1 n o d e , and choose Plot > CM Position > X ( s e e Figure 5-11). T h e graph should be similar to that of Figure 5-12. N o t e that from the graph, the piston m o v e s b e t w e e n about 5 a n d 11 in. horizontally, in reference to the global coordinate system, in w h i c h the origin of the coordinate system coincides with the center point of the hole in the bearing. At the starting point, the crank is at the upright position, and the piston is located at 7.42 in. (that is, V8 -3 ) to the right of the origin of the global coordinate system. N o t e that the lengths of the crank and 2

2

r o d are 3 and 8 in., respectively. W h e n the crank rotates to 90 degrees counterclockwise, the position b e c o m e s 5 (which is 8-3). W h e n the crank rotates 270 degrees, the piston position is 11 (which is 8+3).

R e p e a t the same steps to create graphs for the velocity direction. The graphs should be similar to those of Figures 5-13 piston-1 n o d e in the browser, y o u should see there are three Position -X-piston-1, and CM Velocity-X-piston-1, as s h o w n in

and acceleration of the piston in the inand 5-14, respectively. If y o u e x p a n d the entities listed, CM Accel - X-piston-1, CM Figure 5-15.

T h e graph of the angular velocity of the j o i n t Revolute2 can be created by expanding the Constraints b r a n c h a n d then the Joints branch, right clicking Revolute2 and selecting Plot > Angular Velocity > ZComponent. The graph should be similar to that of Figure 5-16. An entity, Angular Vel - Z-Revolute2, is a d d e d u n d e r the j o i n t Revolute2 in the browser. Interference

Check

N e x t we will learn h o w to perform interference check. COSMOSMotion allows y o u to check for interference in y o u r m e c h a n i s m as the parts m o v e . Y o u can check any of the c o m p o n e n t s in your

SolidWorks assembly m o d e l for possible interference, regardless of w h e t h e r a c o m p o n e n t participates in the m o t i o n m o d e l . Using the interference detection capability, y o u can find:

(1)

All the interference that occur b e t w e e n the selected c o m p o n e n t s as the m e c h a n i s m m o v e s through a specified range of motion, or

(2)

T h e place w h e r e the first interference occurs b e t w e e n the selected c o m p o n e n t s . T h e assembly is m o v e d to the position w h e r e the interference occurred.

M a k e sure y o u h a v e completed a simulation before proceeding to the interference check. R i g h t click the Motion Model n o d e in the b r o w s e r and then select Interference Check. T h e Find Interferences Over Time dialog b o x appears (Figure 5-17). To select the parts to include in the interference check, select the Select Parts to test text field and then p i c k all four c o m p o n e n t s from the graphics screen (or from the browser). T h e Start Frame, End Frame, and Increment allow y o u to specify the m o t i o n frame u s e d as the starting position, final position, and increment in b e t w e e n for the interference check. We will u s e the default n u m b e r s ; i.e., 1, 51, a n d 2, for the Start Frame, End Frame, and Increment, respectively. Click the Find Now button (circled in Figure 5-17) to start the interference check. After pressing the Find Now button, the m e c h a n i s m starts m o v i n g , in w h i c h the crank rotates a complete cycle. At the same time, the Find Interferences Over Time dialog b o x expands. T h e list at the lower half of the dialog b o x shows all interference conditions detected. T h e frame, simulation time, parts that caused the interference, and the v o l u m e of the interference detected are listed.

Close the dialog b o x and save y o u r m o d e l . After saving the m o d e l , y o u m a y w a n t to save it again u n d e r a different n a m e and u s e it for the next simulation.

Creating

and Running

a

Dynamic Analysis

A force simulating the engine firing load (acting along the negative X-direction) will be a d d e d to the piston for a d y n a m i c simulation. It will be m o r e realistic if the force can be applied w h e n the piston starts m o v i n g to the left (negative X-direction) a n d can be applied only for a selected short period. In order to do so, we will h a v e to define m e a s u r e s that monitor the position of the piston for the firing load to be activated. Unfortunately, such a capability is n o t available in COSMOSMotion. Therefore, the force is simplified as a step function of 3 l b along the negative X-direction applied for 0.1 seconds. T h e force will be defined as a point force at the center point of the end face of the piston, as s h o w n in Figure 5 - 2 1 . f

Before we add the force, we will turn off the angular velocity driver defined at the j o i n t Revolute2 in the previous simulation. We will h a v e to delete the simulation before we can m a k e any changes to the

F r o m the browser, e x p a n d the Constraints branch, and then the Joints branch. Right click Revolute to bring up the Edit Mate-Defined Joint dialog b o x (Figure 5-22). P u l l - d o w n the Motion Type a n d choose Free. Click Apply to accept the change. N o t e that if y o u run a simulation n o w , nothing will h a p p e n since there is no m o t i o n driver or force defined (gravity has b e e n turned off). N o w we are ready to add the force. T h e force can be a d d e d from the b r o w s e r by expanding the Forces branch, right clicking the Action Only n o d e , and choosing Add Action-Only Force, as s h o w n in Figure 52 3 . In the Insert Action-Only Force dialog box, the Select Component to which Force is Applied field (see Figure 5-24) will be active (highlighted in red) and ready for y o u to p i c k the component. Pick the end face of the piston, as s h o w n in Figure 5 - 2 1 . The part piston-1 is n o w listed in the Select Component to which Force is Applied field, and piston1/DDMFacelO is listed in both the Select Location and the Select Direction fields. That is, the force will be applied to the center of the end face a n d in the direction that is n o r m a l to the face; i.e., in the positive X-direction.

N o w in the Insert Action-Only Force dialog b o x (Figure 5-24), the Select Reference Component to orient Force field is active (highlighted in red) and is ready for selection. We will p i c k the bearing y o u should see As semi appear in the Select Reference Component to orient Force field. Click the Function tab (see Figure 5-25), choose Step for function, a n d enter the followings: Initial Value: -3 Final Value: 0 Start Step Time: 0 End Step Time: 0.1 N o t e that the negative sign for the initial value is to reverse the force direction to the negative Xdirection. Click the graph button (right most, as s h o w n in Figure 5-25), the step function will appear like the o n e in Figure 5-26. N o t e that this is a s m o o t h e d step function with time extrapolated to the negative domain. T h e force varies from -3 at 0 second to 0 at 0.1 seconds. D u r i n g the simulation, the force will be activated at the beginning; i.e., 0 second. Close the graph and click Apply button to accept the force definition. Y o u should see a force symbol a d d e d to the piston, as s h o w n in Figure 5-4. Before running a simulation, we will increase the n u m b e r of frames in order to see m o r e refined results and graphs. F r o m the browser, right click the Motion Model n o d e , and choose Simulation Parameters. C h a n g e the n u m b e r of frames to 500. A c c e p t the change and then right click the Motion Model n o d e , and choose Run Simulation. The m e c h a n i s m will m o v e and the crank will m a k e several turns before reaching the e n d of the simulation duration; i.e., 1 second by default. G r a p h s created in previous simulation, such as the piston position, etc., should appear immediately at the e n d of the simulation. As s h o w n in Figure 5-27, the piston m o v e s along the.negative X-direction for about 0.15 seconds before reversing its direction. It is also evident in the velocity graph s h o w n in Figure 5-28 that the velocity changes signs at t w o instances (close to 0.15 a n d 0.48 seconds). Recall that the force w a s applied for the first 0.1 seconds. H a d the force application lasted longer, the piston could be continuously p u s h e d to the left (negative X-direction) even w h e n the piston reaches the left end and tries to m o v e to the right (due to inertia). As a result, the crank w o u l d h a v e b e e n oscillating at the left of the center of the bearing; i.e., b e t w e e n 0 a n d 180 degrees about the Z-axis, w i t h o u t m a k i n g a complete turn.

G r a p h the reaction force for the applied force at the piston by expanding the Forces branch, then the Action Only branch, right clicking the ForceAO, a n d choosing Plot. T h e reaction force that represents the actual force applied to the piston appears, as s h o w n in Figure 5-29. T h e graph shows that the force of 3 lbf w a s applied at the beginning of the simulation. T h e force gradually decreases to 0 in the 0.7-second period, w h i c h is w h a t we expected and is consistent with the force function, as seen in Figure 5-26. G r a p h the reaction force at the j o i n t Revolute (between crank and the ground) along the X-direction; y o u should see a graph like that of Figure 5-30. There are three peaks in Figure 5-30 representing w h e n the largest reaction forces occur at the joint, w h i c h occurs at close to 0.15, 0.48, a n d 0.8 seconds; i.e., w h e n the piston reverses its m o v i n g direction. The results m a k e sense.

5.4

Result Verifications

In this section, we will verify the m o t i o n analysis results using kinematic analysis theory often found in m e c h a n i s m design textbooks. N o t e that in kinematic analysis, position, velocity, a n d acceleration of given points or axes in the m e c h a n i s m , are analyzed. In kinematic analysis, forces a n d torques are not involved. All b o d i e s (or links) are a s s u m e d massless. H e n c e , m a s s properties defined for bodies are not influencing the analysis results. T h e slider-crank m e c h a n i s m is a planar kinematic analysis problem. A vector plot that represents the positions of joints of the planar m e c h a n i s m is s h o w n in Figure 5-31. The vector plot serves as the first step in c o m p u t i n g position, velocity, and accelerations of the m e c h a n i s m . T h e position equations of the system can be described by the following vector summation,

T h e real and imaginary parts of Eq. 5 . 1 , corresponding to the X and / c o m p o n e n t s of the vectors, can be written as

In Eqs. 5.2a and 5.2b, Zj, Z , and 6 are given. We are solving for Z a n d 6 . Equations 5.2a and 2

A

3

B

5.2b are non-linear. Solving t h e m directly for Z and 0 is not straightforward. Instead, we will calculate s

Z first, using trigonometric relations; i.e., 3

B

w h e r e t w o solutions ofZ represent the t w o possible configurations of the m e c h a n i s m s h o w n in Figure 53

32. N o t e that point C can be either at C or C for any given Z and 0 . 1

A

Figure 5-32 T w o Possible Configurations

Similarly, 0 has t w o possible solutions, corresponding to vector Z j . B

Taking derivatives of Eqs. 5.2a and 5.2b with respect to time, we h a v e

relatively. In Figure 3-37, the angular velocity 0

B

is the angular velocity of the r o d referring to the

ground. Therefore, it is zero w h e n the crank is in the upright position. N o t e that the accelerations of a given j o i n t in the m e c h a n i s m can be formulated by taking one m o r e derivative of Eqs. 5.5a and 5.5b with respect to time. T h e resulting t w o coupled equations can be solved, using Excel spreadsheet. This is left as an exercise.

Exercises: 1.

Derive the acceleration equations for the slider-crank m e c h a n i s m , by taking derivatives of Eqs, 5.5a a n d 5.5b with respect to time. Solve these equations for the linear acceleration of the piston and the angular acceleration of the j o i n t Revolute2, u s i n g a spreadsheet. C o m p a r e y o u r solutions with those obtained from COSMOSMotion.

2.

U s e the same slider-crank m o d e l to conduct a static analysis using COSMOSMotion. The static analysis in COSMOSMotion should give y o u equilibrium configuration(s) of the m e c h a n i s m due to gravity (turn on the gravity). S h o w the equilibrium configuration(s) of the m e c h a n i s m and use the energy m e t h o d y o u learned from S o p h o m o r e Statics to verify the equilibrium configuration(s).

3.

C h a n g e the length of the crank from 3 to 5 in. in SolidWorks. R e p e a t the kinematic analysis discussed in this lesson. In addition, change the crank length in the spreadsheet {Microsoft Excel file, lesson5.xls). Generate position and velocity graphs from b o t h COSMOSMotion and the spreadshee: Do they agree with each other? D o e s the m a x i m u m slider velocity increase due to a longer crank? Is there any interference occurring in the m e c h a n i s m ?

4.

D o w n l o a d five SolidWorks parts from the p u b l i s h e r ' s w e b site to your c o m p u t e r (folder name Exercise 5-4). (i)

U s e these five parts, i.e., bearing, crankshaft, connecting rod, piston pin, and piston (see Figure E5-1), to create an assembly like the one s h o w n in Figure E 5 - 2 . N o t e that the crankshaft m u s : orient at 45° C C W , as s h o w n in Figure E 5 - 2 .

(ii)

Create a m o t i o n m o d e l for kinematic analysis. C o n d u c t m o t i o n analysis by defining a d r i v a that drives the crankshaft at a constant angular speed of 1,000 rpm.

Figure E5-1

Five SolidWorks Parts

Figure E 5 - 2 A s s e m b l e d Configuration

6.1

O v e r v i e w of the Lesson

In this lesson we will discuss h o w to simulate m o t i o n of a spur gear train. A gear train is a set or system of gears arranged to transfer torque or energy from one part of a m e c h a n i c a l system to another. A gear train consists of driving gears that are m o u n t e d on the input shaft, driven gears m o u n t e d on the output shaft, and idler gears that interpose b e t w e e n the driving and driven gears in order to maintain the direction of the output shaft to be the same as the input shaft or to increase the distance b e t w e e n the drive and driven gears. There are different kinds of gear trains, such as simple gear train, c o m p o u n d gear train, epicylic gear train, etc., depending on h o w the gears are shaped and arranged as well as the fuctions they intend to perform. T h e gear train we are simulating in this lesson is a c o m p o u n d gear train, in w h i c h t w o or m o r e gears are u s e d to transmit torque or energy. All gears included in this lesson are spur gears; therefore, the shafts that these gears m o u n t e d on are in parallel. In COSMOSMotion, gear pair is defined as a special coupler constraint. Joint couplers allow the m o t i o n of a revolute, cylindrical, or translational j o i n t to be coupled to the m o t i o n of another revolute, cylindrical or translational joint. T h e t w o coupled j o i n t s m a y be of the same or different types. For example, a revolute j o i n t m a y be coupled to a translational joint. The coupled motion m a y also be of the same or different type. For example, the rotary m o t i o n of a revolute j o i n t m a y be coupled to the rotary m o t i o n of a cylindrical joint, or the translational m o t i o n of a translational j o i n t m a y be coupled to the rotary m o t i o n of a cylindrical joint. To create a gear pair, we will be coupling t w o revolute j o i n t s . Usually a concentric and a coincident mates will lead to a revolute joint, as seen in previous lessons. Coupling t w o revolute j o i n t s for a gear pair will be carried out in SolidWorks using the advance assembly m a t e option, w h e r e t w o axes that pass through the respective revolute j o i n t s (or gears) are picked for the gear mate. T h e gear m a t e will be m a p p e d to a gear m a t e j o i n t in COSMOSMotion. In fact, neither SolidWorks nor COSMOSMotion cares about the detailed geometry of the gear pair; i.e., if the gear teeth m e s h adequately. Y o u m a y simply uses cylinders or disks to represent the gears. No detailed tooth profile is necessary for any of the computations involved. Apparently, force and m o m e n t b e t w e e n a pair of teeth in contact will not be calculated in gear train simulations. H o w e v e r , there are other important data being calculated by COSMOSMotion, such as reaction force exerting on the driven shaft (for a d y n a m i c analysis), w h i c h is critical for m e c h a n i s m design. In any case, pitch circle diameters are essential for defining gear pair and gear trains in COSMOSMotion. Gear ratio of the gear train, w h i c h is defined by the ratio of the angular velocities of the output a n d input gears, is determined by the pitch circle diameters of the individual gear pairs in the gear train. A l t h o u g h cylinders or disks are sufficient to m o d e l gears in SolidWorks, we will u s e m o r e realistic gears throughout this lesson. All gears in the e x a m p l e are s h o w n with detailed geometry, including teeth. In addition, detailed parts, including shafts, bearing, screws a n d aligning pins are included for a realistic gear train system, as s h o w n in Figure 6 - 1 . In this gear train simulation, we will focus m o r e on graphical

animation, less on computations of physical quantities. We will a d d a m o t i o n driver to drive the input shaft. 6.2

T h e G e a r Train E x a m p l e

Physical

Model

T h e gear train e x a m p l e we are using for this lesson is part of a gearbox designed for an experimental lunar rover. The gear train is located in a gear b o x w h i c h is part of the transmission system of the rover, driven by a m o t o r p o w e r e d by solar energy. The p u r p o s e of the gear train is to convert a high-speed rotation a n d small torque generated by the m o t o r to a low speed rotation and large torque output in order to drive the wheels of the rover. The gear train consists of four spur gears m o u n t e d on three parallel shafts, as s h o w n in Figure 6 - 1 .

T h e four spur gears form t w o gear pairs: Pinion 1 and Gear 7, and Pinion 2 and Gear 2, as depicted in Figure 6-1 a n d 6-2. N o t e that Pinion 1 is the driving gear that connects to the m o t i o n driver; e.g., a motor. T h e m o t o r rotates in a clockwise direction, therefore, driving Pinion 1. Gear 1 is the driven gear of the first gear pair, w h i c h is m o u n t e d on the same shaft as Pinion 2. B o t h rotate in a counterclockwise direction. Gear 2 is driven by Pinion 2, and rotates in a clockwise direction. N o t e that the diameters of the pitch circles of the four gears are: 50, 120, 60, and 125 m m , respectively; a n d the n u m b e r s of teeth are 2 5 , 6 0 , 2 4 , and 50, respectively. Therefore, the circular pitch P the diametral pitch P , a n d m o d u l e m of the first gear pair are, respectively C9

d

n u m b e r of teeth of the four respective gears. T h e gear ratio of the gear train s h o w n in Figure 1 is 1:5; i.e., the angular velocity is r e d u c e d 5 times at the output. Theoretically, the torque output will increase 5 times if there is no loss due to; e.g., friction. N o t e that we will use MMGS units system for this lesson. SolidWorks

Parts

and Assembly

In this lesson, SolidWorks parts of the gear train h a v e b e e n created for you. There are six files created, gbox housing.SLDPRT, gbox input.SLDPRT, gboxjniddle.SLDPRT, gbox_output.SLDPRT, Lesson6.SLDASM, and Lesson6withresults.SLDASM. Y o u can find these files at the p u b l i s h e r ' s w e b site (http://www.schroffl.com/). We will start with Lesson6.SLDASM, in w h i c h the gears are a s s e m b l e d to the housing. In addition, the assembly file Lesson6withresults.SLDASM consists of a complete simulation m o d e l with simulation results. N o t e that the h o u s i n g part in SolidWorks w a s converted directly from Pro/ENGINEER part. T h e three gear parts in SolidWorks w e r e converted from respective Pro/ENGINEER assemblies. There w e r e nine, nine, and six distinct parts within the three gear assemblies, respectively. These three Pro/ENGINEER assemblies (and associated parts) w e r e first converted to SolidWorks as assemblies. Parts in each assembly w e r e then m e r g e d into a single gear part in SolidWorks. T h e detailed part a n d assembly conversions as well as m e r g i n g multiple parts into a single part in SolidWorks can be found in A p p e n d i x C. In the SolidWorks assembly m o d e l s Lesson6.SLDASM (and Lesson6withresults.SLDASM), there are nine a s s e m b l y m a t e s . T h e first three m a t e s , Concentric1, Coincidentl, and Coincident2 assemble the input gear to the housing. T h e input gear is fully constrained. N o t e that before entering COSMOSMotion, we will suppress Coincident2 in order to allow rotational degree of freedom for the input gear about the Z-axis (see Figures 6-3a, b, and c). Similarly, the next three mates, Concentric2, Coincident^ a n d Coincident4 assemble the m i d d l e gear to the housing. Again, we will suppress Coincident4 to allow the m i d d l e gear to rotate about the Z-axis (see Figures 6-3d, e and f). T h e third set of mates, Concentric3, Coincident5, and Coincident6 does the same for the output gear (see Figures 6-3g, h a n d i). Similarly, Coincident6 will be suppressed to allow for rotation. N o t e that the three suppressed m a t e s are created to properly orient the three gears, so that the gear teeth m e s h well b e t w e e n pairs.

As m e n t i o n e d earlier, one important factor for the animation to " l o o k right" is to m e s h the gear teeth properly. Y o u m a y w a n t to use the Front v i e w and z o o m in to the tooth m e s h areas to check if the t w o pairs of gears m e s h well (see Figure 6-4). T h e y should m e s h well, w h i c h is accomplished by the three coincident mates that will be suppressed before entering COSMOSMotion. N o t e that the tooth profile is represented by straight lines, instead of m o r e popular ones such as involutes, j u s t for simplicity.

Figure 6-4 Gear Teeth Properly M e s h e d If y o u turn on the axis display (View > Axes), axes that pass through the center of the gears about the Z-axis are defined for each gear. These axes are necessary for creating gear m a t e s . Simulation

Model

T h e gear h o u s i n g will be defined as the ground part. All three gears will rotate with respect to their respective axes. T h e four gears will be m e s h e d into t w o gear pairs; Pinion 1 with Gear 7, a n d Pinion 2 with Gear 2, as discussed earlier. In SolidWorks, gear pairs are created by selecting t w o axes of respective gears (or cylinders) u s i n g Advanced Mates capability. Before the gear m a t e s can be created, we will suppress the three coincident mates that help properly orient the gears; i.e., Coincident2, Coincident4 a n d Coincident6, in order to allow desired gear rotation motion. W h e n these m a t e s are suppressed, revolute joints will be created b e t w e e n the h o u s i n g and the three gear parts in COSMOSMotion, as s h o w n in Figure 65. T h e revolute j o i n t b e t w e e n the h o u s i n g and the input gear will be driven at a constant angular velocity of 360 degrees/sec. We will basically conduct a kinematic analysis for this example.

6.3

U s i n g COSMOSMotion Start SolidWorks and open the

assembly file Lessond. SLDASM.

N o t e that w h e n y o u o p e n the assembly, y o u will see a m e s s a g e w i n d o w , as s h o w n in Figure 6-6, indicating that SolidWorks is u n a b l e to locate gbox input, sldasm. SolidWorks is trying to locate the assembly from w h i c h the input gear part w a s created. Since the input gear assembly and its associated parts are not available in the Lesson 6 folder, SolidWorks is unable to locate it. It is fine to click No and not to locate gbox_input.sldasm. N o t locating the assembly file for the input gear part will n o t affect the m o t i o n simulation in this lesson. After clicking No, SolidWorks will ask y o u to locate the m i d d l e gear assembly and output gear assembly. C h o o s e No for both. The assembly files that SolidWorks is looking for are actually located in the subfolder u n d e r Lesson 6 as well as the A p p e n d i x C folder. Y o u m a y choose Yes from the m e s s a g e w i n d o w and locate the missing files in one of these t w o folders. Before entering COSMOSMotion there are t w o things n e e d to be done. First, we will suppress three assembly m a t e s , Coincident2, Coincident4 and Coincident6. Second, we will create t w o gear m a t e s for the t w o gear pairs, respectively. F r o m the Assembly browser, e x p a n d the Mates branch, right-click Coincident2, and choose Suppress. T h e m a t e Coincident2 will b e c o m e inactive. R e p e a t the same to suppress Coincident4 and Coincident6. Save y o u r m o d e l . N e x t , turn on the axis v i e w by choosing from the p u l l - d o w n m e n u , View > Axes. All three axes, one for each gear, will appear in the graphics screen. W e will create t w o gear mates. C h o o s e f r o m the p u l l - d o w n m e n u Insert > Mate. In the Mate dialog b o x (overlapping with the browser), the Mate Selections field will be active (in red), and is ready for y o u to pick entities. Pick the axes of the input and m i d d l e gears from the graphics screen. C h o o s e Advanced Mates, click Gear, and enter 50mm and 120mm for Ratio, as s h o w n in Figure 6-7. Click the c h e c k m a r k button on top to accept the m a t e definition, and click the same button one m o r e time to close the dialog b o x . N o t e that if the axes of the t w o gears are pointing in the opposite direction, y o u will h a v e to click Reverse (right b e l o w the Ratio text field in the Mate dialog b o x ) to correct the rotation direction. In this example, all three axes are pointing in the same direction. Therefore, do not choose Reverse. R e p e a t the same steps to define the second gear mate. This time, p i c k the axes of the m i d d l e and output gears, and enter 60mm a n d 125mm for Ratio. T w o n e w m a t e s , Gear Mate 1 (gbox_input, gbox_middle) and GearMate2(gbox_middle,gbox_output), are n o w listed u n d e r Mates.

N o w we are r e a d y to enter COSMOSMotion. Click the Motion button

enter

COSMOSMotion.

N o w we are r e a d y to enter COSMOSMotion. Click the Motion button

#

enter COSMOSMotion.

Similar to previous lessons, we will u s e the browser, and basic drag-and-drop and right-clicl^ m e t h o d s to create a n d simulate the gear train motion in this lesson. Before creating any entities, always check the units system. M a k e sure the units system chosen is Defining Bodies MMGS. F r o m the browser, expand the Assembly Components branch. Y o u should see four parts listed, gbox housing-1, gboxjnput-l, gboxmiddle1, a n d gbox_output-l, as s h o w n in Figure 6-8. A l s o e x p a n d the Parts branch; y o u should see Moving Parts a n d Ground Parts listed. Go ahead to m o v e gboxjiousing-l to Ground Parts and m o v e the three gears to Moving Parts by using the dragand-drop m e t h o d . E x p a n d the Constraints branch, a n d then the Joints branch. Y o u should see t w o gear m a t e s and three revolute joints listed, as shown in Figure 6-9. In addition, y o u should see the revolute j o i n t symbols appear in the graphics screen, similar to those of Figure 6-5. E x p a n d all joints in the b r o w s e r a n d identify the parts they connect. Take a look at the j o i n t Revolute2 (connecting the input gear to the gear housing), w h e r e we will a d d a driver next. N o t e that y o u m a y see a different revolute j o i n t connecting the input gear to the gear housing. M a k e sure y o u pick the right one. Driving

Joint

F r o m the browser, e x p a n d the Constraints n o d e and then the Joints n o d e . Right-click the Revolute2 n o d e and choose Properties. In the Edit Mate-Defined Joint dialog b o x (Figure 6-10), u n d e r the Motion tab (default), choose Rotate Z for Motion On, choose Velocity for Motion Type, choose Constant for Function, and enter 360 degrees/sec for Angular Velocity (should appear as defaults). Click Apply to accept the definition. A m o t i o n driver symbol should appear at Revolute2, as s h o w n in Figure 6-5. We are ready to run a simulation. We will u s e all default simulation parameters.

Running

Simulation

Click the Motion Model n o d e , press the right m o u s e button and select Run Simulation. After a few seconds, y o u should see the gears start turning. T h e input gear rotates 360 degrees as expected since the default simulation duration is 7 second. Saving

and Reviewing

Results

We will graph the angular velocity of the output gear. F r o m the browser, e x p a n d the Parts branch and then the Moving Parts branch. Right-click the ghox_output-l n o d e , and choose Plot > Angular Velocity > Z Component (Figure 6-11). T h e graph should appear and is similar to that of Figure 6-12, w h i c h shows that the output velocity is a constant of 72 degrees/sec. N o t e that this m a g n i t u d e is one fifth of the input velocity since the gear ratio is 7:5. B o t h the input (Pinion 7) and output gears (Gear 2) rotate in the same direction. COSMOSMotion gives g o o d results. Save your m o d e l .

Exercises: 1.

T h e same gear train will be u s e d for this exercise. Create a constant torque for the input gear (gboxinput.SLDPRT) about the Z-axis. Turn on friction for all three axles (Steel-Dry/Steel-Dry). Define and r u n a 2-second d y n a m i c simulation for the gear train. (i)

W h a t is the m i n i m u m torque that is required to rotate the input gear, and therefore, the entire gear train?

(ii)

If the torque applied to the input gear is 100 mm N, w h a t is the output angular velocity of the gear train at the end of the 2-second simulation? Verify the simulation result using y o u r o w n calculation.

(iii)

Create a graph for the reaction m o m e n t b e t w e e n gears of the first gear pair {GearMatel) due to the 100 mm N torque. W h a t is the reaction m o m e n t obtained from simulation?

7.1

O v e r v i e w of the Lesson

In this lesson, we will learn c a m and follower, or cam-follower. A cam-follower is a device for converting rotary m o t i o n into linear motion. T h e simplest form of a c a m is a rotating disc w i t h a variable radius, so that its profile is n o t circular b u t oval or egg-shaped. W h e n the disc rotates, its edge (or side face) p u s h e s against a follower (or c a m follower), w h i c h m a y be a small w h e e l at the end of a lever or the end of the lever or r o d itself. The follower will thus rise and fall at exactly the same a m o u n t as the variation in radius. By profiling a c a m appropriately, a desired cyclic pattern of straight-line motion, in terms of position, velocity, a n d acceleration, can be produced. We will learn to create a m o t i o n m o d e l and simulate the control of opening and closing of an inlet or exhaustive valve, usually found in internal c o m b u s t i o n engines, using cam-follower connections. In a design such as that of Figure 7 - 1 , the drive for the camshaft is taken from the crankshaft t h r o u g h a timing chain, w h i c h k e e p s the c a m s synchronized with the m o v e m e n t of the piston so that the valves are o p e n e d or closed at a precise instant. T h e m e c h a n i s m w e will b e w o r k i n g with consists o f bushings, camshaft, pushrod, rocker, valve, valve guide and spring, as s h o w n in Figure 7 - 1 . T h e cam-follower connects the camshaft and the pushrod. W h e n the c a m on the camshaft p u s h e s the p u s h r o d u p , the rocker rotates and p u s h e s the valve on the other side d o w n w a r d . T h e spring surrounding the v a l v e gets compressed, and opens up the inlet for air to flow into the combustion chamber. 7.2

The Cam and Follower Example

Physical

Model

T h e camshaft and the rocker will rotate about the axes of their respective revolute j o i n t s connecting t h e m to their respective bearings (defined as g r o u n d b o d y ) . The camshaft is driven by a m o t o r of constant velocity of 600 r p m (or 10 rev/sec). T h e profile of the c a m consists of t w o circular arcs of 0.25 and 0.5 in. radii, respectively, as s h o w n in Figure 7-2. T h e lower arc is concentric with the shaft, a n d the center of the u p p e r arc is 0.52 in. above the center of the shaft. W h e n the camshaft rotates, the c a m m o u n t e d on the shaft p u s h e s the p u s h r o d up by up to 0.27 in. (that is, 0.52+0.25-0.5 = 0.27). As a result, the rocker will rotate and p u s h the valve at the other e n d d o w n w a r d at a frequency of 10 times/sec. T h e valve will m o v e again up to 0.27 in. d o w n w a r d since the p u s h r o d and the valve are positioned at an equal distance from the rotation axis of the rocker. W h e n the camshaft rotates w h e r e the larger circular arc (0.5 in. radius) of

the c a m is in contact with the follower (in this example, the pushrod), the p u s h r o d has r o o m to m o v e d o w n w a r d . At this point, the rocker will rotate b a c k since the spring is being uncompressed. As a result, the valve will m o v e u p , a n d therefore, close the inlet. T h e valve will be o p e n for about 120 degree p e r cycle, b a s e d on the c a m design shown in Figure 7-2. T h e unit system chosen for this e x a m p l e is IPS and all parts are m a d e up of steel. SolidWorks

Parts

and Assembly

T h e cam-follower system consists of seven parts, b u s h i n g (two), valve guide, camshaft, pushrod, rocker, and valve, as s h o w n in Figure 7 - 1 . In addition, there are t w o assembly files, Lesson7.SLDASM and Lesson7withresults.SLDASM that you m a y d o w n l o a d f r o m the p u b l i s h e r ' s w e b site. We will start with Lesson 7. SLDASM, in w h i c h the parts are adequately assembled. In this assembly the first bushing is anchored (ground) and the second busing and the valve guide are fully constrained. These three parts will be assigned as g r o u n d parts. The r e m a i n i n g four parts will be defined as m o v a b l e parts in COSMOSMotion. Same as before, the assembly file Lesson 7withresults. SLDASM contains a complete simulation m o d e l with simulation results. Y o u m a y w a n t to open the assembly to see the m o t i o n animation of the m e c h a n i s m . In the assembly w h e r e a m o t i o n m o d e l is completely defined, a m a t e has b e e n suppressed to allow m o v e m e n t b e t w e e n components. Y o u can also see h o w the parts m o v e by right clicking in the graphics screen, choosing Move Component, and dragging any m o v a b l e parts; for e x a m p l e the camshaft to rotate with respect to the second bushing. The w h o l e m e c h a n i s m will m o v e accordingly. There are eighteen assembly m a t e s , including four coincident, three concentric, seven distance, t w o parallel, o n e tangent, and one cam-mate-tangent, as listed in the b r o w s e r (see Figure 7-3). Y o u m a y w a n t to e x p a n d the Mates b r a n c h in the b r o w s e r to r e v i e w the list of a s s e m b l y mates. M o v e the cursor over any of the m a t e s ; y o u should see the entities selected for the assembly m a t e highlighted in the graphics screen. As mentioned earlier, the first bushing, bushing, s h o w n in the b r o w s e r is anchored to the assembly. T h e second bushing (bushing<2>) and the valve guide (valve guide) w e r e fully assembled to bushing. T h e first three mates, Coincident 1, Distance 1, and Distance2, w e r e e m p l o y e d to assemble bushing<2> to bushing. A n d the n e x t three distance m a t e s assemble the valve guide to bushing.

N o t e that the distance mates are essentially coincident m a t e with distance b e t w e e n entities. T h e distance mates w e r e created to properly position the second bushing with respect to the first bushing. All three parts will be defined as the g r o u n d part in COSMOSMotion. T h e n e x t t w o m a t e s , Concentric 1 and Coincident!, assemble the rocker {rocker) to the first b u s h i n g (hushing), allowing a rotation degree of freedom about the Z-axis, as s h o w n in Figures 7-4a and b. COSMOSMotion will m a p a revolute j o i n t b e t w e e n the rocker and the first bushing. T h e n e x t part assembled is the p u s h r o d (pushrod). T h e p u s h r o d w a s a s s e m b l e d to the rocker using Tangent/, Distance6, and Coincident3 mates, as s h o w n in Figures 7-4c, d, and e, respectively. As a result, the p u s h r o d is allowed to m o v e vertically at a distance of 1.25 in. from the Right plane of the first b u s h i n g (Distanced), at the same t i m e , maintaining t a n g e n c y b e t w e e n the top of the cylindrical surface of the p u s h r o d and the socket surface of the rocker.

(c) Pushrod: T a n g e n t l

(d) Pushrod: Distance6

(e) Pushrod: Coincident3

Figure 7-4 A s s e m b l y M a t e s Defined for the M e c h a n i s m

T h e next part is the camshaft (cam_shaft). T h e camshaft w a s first assembled to the second b u s h i n g (bushing<2>), and then to the pushrod. Concentric2 aligns the camshaft and the second bushing. Coincident4 mates the center plane of the camshaft to that of pushrod, as shown in Figures 7-4f and g. As a result, the camshaft is allowed to rotate about the Z-axis. In addition, the CamMateTangentl defines a c a m a n d follower b e t w e e n the c a m surface of the camshaft a n d the cylindrical surface at the b o t t o m of the pushrod. N o t e that all surrounding surfaces on the c a m and follower m u s t be selected for the cam-follower joint. In this case, four surfaces are selected for the c a m ( m o u n t e d on the camshaft) and one surface is included on the follower, as s h o w n in Figure 74h. N o t e that the assembly should h a v e overall one degree of freedom at this point. Y o u m a y either rotate the camshaft, the rocker, or m o v e the p u s h r o d vertically to see the relative m o t i o n of the assembly. U s e

Apparently, this result implies that there are r e d u n d a n t d o f s created in the system. This is fine since COSMOSMotion filters out the r e d u n d a n t d o f s . Y o u m a y w a n t to check the r e d u n d a n c y by choosing, from the pulld o w n m e n u , COSMOSMotion > Show Simulation Panel, as discussed i n A p p e n d i x A . Y o u m a y w a n t t o r e v i e w A p p e n d i x A for m o r e information about defining j o i n t s a n d calculating degrees of freedom. T h e final m o t i o n m o d e l is s h o w n in Figure 7-6, w h e r e the Z-rotation of the concentric joint, Concentric2, b e t w e e n the camshaft and the second b u s h i n g is driven by a constant angular velocity of

3,600 degrees/sec; i.e., 600 rpm, about the Z-axis of the global coordinate system. In addition, a spring surrounding the valve will be created in order to provide a vertical force to p u s h the rocker u p , therefore, close the valve. The spring has a spring constant of 10 lbf/in and an unstretched length of 1.25 in. T h e spring is created b e t w e e n the b o t t o m face of the rocker a n d top face of the valve guide. 7.3

Using COSMOSMotion Start SolidWorks and o p e n assembly file Lesson 7. SLDASM. F r o m the browser, click the Motion button

if

1

to enter COSMOSMotion.

Again, always check the units system. M a k e sure that IPS units system is chosen for this example. Defining

Bodies

F r o m the browser, e x p a n d the Assembly Components branch. Y o u should see seven entities listed, Bushing-1, Bushing-2, cam_shaft-1, pushrod-1, rocker-7, valve guide-1, and valve-1, as s h o w n in Figure 7-7. A l s o expand the Parts branch; y o u should see Moving Parts and Ground Parts listed. We will m o v e Bushing-1, Bushing-2, a n d valve guide-1 to Ground Parts and the r e m a i n i n g four parts to Moving Parts b y using the drag-and-drop m e t h o d . F r o m the browser, click Bushing-1. Press the Ctrl k e y and click Bushing-2 and valve guide-1. All three parts should be selected. D r a g a n d drop t h e m to the Ground Parts n o d e . R e p e a t the same to select the r e m a i n i n g four parts u n d e r the Assembly Component branch. D r a g and drop t h e m to the Moving Parts n o d e . E x p a n d the Constraints branch, and then the Joints branch. Y o u should see that ten j o i n t s are listed (see Figure 7-5). All joint symbols should appear in the graphics screen, similar to that of Figure 7-6. E x p a n d all joints in the browser and identify the parts they connect. T a k e a look at the j o i n t Coincident2 (connecting camshaft to Bushing-2), w h e r e we will add a driver next.

Driving

Joint

R i g h t click the Concentric2 n o d e a n d choose Properties (see Figure 7-8). In the Edit Mate-Defined Joint dialog b o x (Figure 7-9), u n d e r the Motion tab (default), choose Rotate Z for Motion On, choose Velocity for Motion Type, choose Constant for Function, and enter 3600 degrees/sec for Angular Velocity, as s h o w n in Figure 7-9. Click Apply to accept the definition. Defining

Spring

F r o m the browser, e x p a n d the Forces branch, right click the Spring n o d e a n d choose Add Translational Spring (see Figure 7-10). In the Input Spring dialog b o x (Figure 7-11), the Select 1st Component field should be highlighted in red and ready for y o u to pick. Rotate the v i e w a n d pick the b o t t o m face of the rocker (see Figure 7-12), the Select 2nd Component field should n o w highlight in red, and rocker-1/DDMFace 19 should appear in the Select Point on 1st Component field, w h i c h indicates that the spring will be connected to the center point of the face selected. In case y o u p i c k e d a w r o n g entity, simply select the entire text in the respective text field in the dialog b o x , and press the Delete k e y to delete the text. T h e text field will turn b a c k to red and will be ready for y o u to p i c k another entity. Rotate the v i e w back, and then p i c k the top face in the valve guide, as s h o w n in Figure 7-12. N o w , valve guide-1 and valve guide-l/DDMFace20 should appear in the Select 2nd Component field a n d Select Point on 2nd Component field, respectively. Also, a spring should appear in the graphics screen, connecting the center points of the t w o faces. Enter the followings: Stiffness:

10

Length: 1.25 (Note that y o u h a v e to deselect the Design b o x to the right before entering this value) Force: 0 Coil Diameter: 0.75 Number of coils: 8 Wire Diameter: 0.1 Click Apply to accept the spring definition and close the Insert Spring dialog b o x . Defining

and Running

Simulation

Click the Motion Model n o d e , press the right m o u s e button and select Simulation Parameters. Enter 0.5 for simulation duration a n d 500 for the n u m b e r of frames. Click the Motion Model n o d e again, press the right m o u s e button and select Run Simulation. Y o u should see that the camshaft starts rotating, the p u s h r o d is m o v i n g up a n d d o w n , w h i c h drives the rocker,

and then the valve. T h e camshaft rotates 5 times in the 0.5-second simulation duration. We will graph the position, velocity, and acceleration of the valve next.

As s h o w n in Figure 7-14, the flat portion on top indicates that the valve stays completely closed, w h i c h spans about 0.066 seconds, approximately 240 degrees of the camshaft rotation in a complete cycle. Therefore, the valve will open for about 0.034 seconds per cycle, roughly 120 degrees. Graph the 7-velocity and 7-acceleration of the valve by choosing Plot > CM Velocity (and CM Acceleration) > Y Component. The graphs of the velocity a n d acceleration are s h o w n in Figures 7-15 and 16, respectively. As s h o w n in Figure 7-15, there are t w o velocity spikes per cycle, representing that the valve is p u s h e d d o w n w a r d (negative velocity) for opening and is being pulled b a c k (positive velocity) for closing, respectively. T h e valve stays closed with zero velocity. Figure 7-16 reveals h i g h accelerations w h e n the valve is p u s h e d and pulled. N o t e that such a high acceleration is due to high-speed rotation at the camshaft. This high acceleration could p r o d u c e large inertial force on the valve, yielding high contact force b e t w e e n the top of the valve and the socket surface in the rocker. We w o u l d like to check the reaction force b e t w e e n the top of the valve and the rocker. The

graph of the reaction force can be created by expanding Constraints and Joints branches, right clicking Concentric2 (between the valve a n d the rocker), a n d choosing Plot > Reaction Force > Y Component. T h e reaction force graph (Figure 7-17) shows that the reaction force b e t w e e n the top of the valve a n d the socket face of the rocker is about 0.4 l b , w h i c h is insignificant. N o t e that this small reaction force can f

be attributed to the small m a s s of the valve. If y o u open the valve part and acquire its m a s s (from pulld o w n m e n u , choose Tools > Mass Properties), the m a s s of the valve is 0.03 l b . Therefore, the inertia for the v a l v e at the p e a k accelerations is about 0.03 \b x5,600 i n / s e c = 168 l b i n / s e c = 168/386 l b = 0.44 lbf, w h i c h is consistent to peaks found in Figure 7-17. If y o u are n o t quite sure about w h y this 386 is factored in for force calculation, please refer to A p p e n d i x B for m a s s and force unit conversions. Save your m o d e l . m

2

m

2

m

f

Exercises: 1.

R e d e s i g n the c a m by reducing the small arc radius from 0.25 to 0.2 and reducing the center distance of the small arc from 0.52 to 0.40, as s h o w n in Figure E 7 - 1 . R e p e a t the d y n a m i c analysis a n d check reaction force b e t w e e n t h e valve and the rocker. D o e s this redesigned c a m alter the reaction force?

2.

If we change the Parallel! m a t e b e t w e e n the Right plane of the valve and the Right plane of the first b u s h i n g to a distance m a t e , will t h e m e c h a n i s m m o v e ? W h a t other changes m u s t be m a d e in order to create a valid and m o v a b l e m e c h a n i s m similar to that w a s presented in this lesson?

8.1

O v e r v i e w of the Lesson

This is an application lesson. We will apply w h a t we learned in previous lessons to a real-world application. This application involves designing a device that can be m o u n t e d on a wheelchair to m i m i c soccer ball-kicking action w h i l e b e i n g operated by a child sitting on the wheelchair with limited mobility and h a n d strength. Such a device will provide m o r e incentive and realistic experience for children with physical disabilities to participate in soccer g a m e s . This e x a m p l e w a s extracted from an undergraduate student design project that w a s carried out in conjunction with a local children hospital. This device w a s intended primarily to be u s e d in the s u m m e r c a m p sponsored by the children hospital. The focus of this lesson is slightly different from previous ones. Instead of focusing on discussing h o w to use COSMOSMotion to create m o t i o n entities, we will focus on h o w to use COSMOSMotion to support design. In order to n a r r o w d o w n the design options to be m o r e m a n a g e a b l e , we will assume all major c o m p o n e n t s are designed w i t h dimensions determined. M o r e specifically, we will u s e COSMOSMotion to help choose a spring, as well as determine if the required operating force is acceptable. Since the users of this device are children with limited physical h a n d strength, the operating force m u s t be m i n i m i z e d in order to m a k e the device useful. T h e examples we h a v e discussed in previous lessons are simple e n o u g h so that some of the simulation results can be verified by h a n d calculations (for example, using a spreadsheet). H o w e v e r , m o s t of the real-world applications, including the e x a m p l e of this lesson, are too complicate to verify by h a n d calculations. W h e n we are dealing w i t h such applications, t w o principles are helpful in leading to successful simulations. First, the simulation m o d e l y o u created has to be physically meaningful and is as consistent to the physical conditions as possible. Second, very often y o u will h a v e to m a k e assumptions in order to simplify the p r o b l e m s so that the simulations can be carried out. This is b e c a u s e that the simulation m o d e l s m u s t c o m p l y w i t h the ability of the software y o u are using. In order to effectively u s e the simulations to support design, y o u will h a v e to understand the physical p r o b l e m s very well; in the m e a n time, be familiar with the capabilities and limitations of the software y o u are using. Since m o s t of y o u will be often learning the software as y o u are tackling simulation and/or design p r o b l e m s , it is strongly r e c o m m e n d e d that y o u e m p l o y the principle of spiral d e v e l o p m e n t to incrementally build up y o u r simulation m o d e l . In another w o r d , y o u m a y w a n t to start from a simplified m o d e l with simple scenarios by m a k i n g adequate assumptions to y o u r simulation m o d e l . M a k e the simplified m o d e l w o r k s first, then relax the assumptions and add m o t i o n entities to m a k e y o u r m o d e l closer to the real situation. R e p e a t the process until y o u reach a simulation m o d e l a n d simulation scenarios that answer y o u questions a n d help y o u m a k e design decisions. In each step, m a k e sure that the simulation m o d e l does w h a t y o u expect it to do before bringing it to the next level. In this lesson, we will e m p l o y the spiral d e v e l o p m e n t principle. We will assume that all c o m p o n e n t s and their physical dimensions are determined. The design is essentially n a r r o w e d d o w n to the selection of

a spring, including both spring constant and free length, and to ensure that the required force is small e n o u g h for a child to easily operate the device. We will try our best to check and hopefully verify the simulation m o d e l in each step. N o t e that COSMOSMotion is very sensitive to s o m e of the conditions and parameters, such as the initial condition (that is, the handle bar orientation), spring constant, etc. S o m e of the conditions simulated are physically meaningful a n d yet COSMOSMotion gives unrealistic simulation results due to its limitations. Again, COSMOSMotion is not foolproof. O n e cannot blindly accept the simulation results. W h e n a result is determined unrealistic after r e v i e w i n g animation, graphs, etc., the best w a y to p r o c e e d is to c o m p o s e a simpler simulation m o d e l and/or try a different ( m o r e idealized) scenario until the simulation result is physically meaningful b a s e d on y o u r educated j u d g m e n t . Y o u will see trialsand-errors in this lesson and m a n y other real-world applications in the future. 8.2

T h e Assistive Device

Physical

Model

This assistive device for soccer g a m e s consists of five major c o m p o n e n t s : the clamper, handle bar, plate, kicking-rod, and spring, as illustrated in Figure 8-1. In reality these five c o m p o n e n t s will be assembled first and c l a m p e d to the lower frame of the wheelchair for use.

The h a n d l e b a r is m o u n t e d to the plate at the pivot pin of the plate and linked to the m i d d l e pin of the kicking rod. T h e kicking r o d is inserted into the t w o lower brackets m o u n t e d on the plate. W h e n the handle (on top of the handle bar) is pulled backward, the handle bar rotates about the pivot pin; therefore, drives the kicking r o d to m o v e forward along the longitudinal direction through the link b e t w e e n the b o t t o m slot of the handle bar and the middle pin of the kicking rod. T h e forward m o v e m e n t of the kicking r o d produces m o m e n t u m to " k i c k " the soccer ball. A spring is a d d e d b e t w e e n the u p p e r bracket and the handle bar to restore the handle bar to its neutral position after pulling. The spring also helps the user to pull the handle b a r with a lesser force.

T h e focus of this lesson is to u s e COSMOSMotion to simulate the position a n d velocity of the kicking r o d for a given force that can be comfortably p r o v i d e d by a child with limited physical strength. Lots of factors contribute to the operating force of the m e c h a n i s m . For example, one of the critical parameters is the location of the pivot pin. T h e lower the pivot pin is located the lesser force is required to operate the m e c h a n i s m . H o w e v e r , the purpose of this lesson is not necessarily to determine the final design of the device, b u t illustrate t h e process of using COSMOSMotion to assist the design. Therefore, as m e n t i o n e d earlier, t h e scope of t h e design has b e e n n a r r o w e d d o w n to the selection of the spring and to determine if the force is small e n o u g h for a child to operate the device. SolidWorks

Parts

and Assembly

T h e a s s e m b l y of the m e c h a n i s m consists of eight parts and one subassembly. T h e s e parts are handle.SLDPRT, plate. SLDPRT, rod.SLDPRT, foot.SLDPRT, clamper. SLDPRT, joint.SLDPRT, collar. SLDPRT, and wheelchair.SLDPRT. The s u b a s s e m b l y is kickingjrod.SLDASM w h i c h consists of rod.SLDPRT m& foot.SLDPRT. In addition, there are six assembly files, Lesson8. SLDASM, Lesson8TaskOne.SLDASM, Lesson8TaskTwo.SLDASM, Lesson8TaskThreeNoFriction.SLDASM, Lesson8TaskThreeSmallFriction. SLDASM, mdLesson8TaskThreeLargeFriction. SLDASM. Y o u can d o w n l o a d these files from p u b l i s h e r ' s w e b site. S a m e as before, the assembly files, with the exception of Lesson8.SLDASM, consist of complete simulation m o d e l s with simulation results u n d e r respective simulation scenarios. Y o u m a y w a n t to open these files to see the motion animations of the m e c h a n i s m . In these assembly files, a m a t e (Anglel) has b e e n suppressed. Y o u can also see h o w the parts m o v e by right clicking in the graphics screen, choosing Move Component, and dragging any m o v a b l e parts; for example dragging the h a n d l e to drive the kicking rod. There are fifteen assembly m a t e s , including four coincident, three concentric, four distance, t w o parallel, and one angle, defined in the assembly, as listed in the b r o w s e r (see Figure 8-2). Y o u m a y w a n t to e x p a n d the Mates b r a n c h in the b r o w s e r to see these assembly m a t e s . M o v e y o u r cursor over any of the m a t e s ; y o u should see the entities chosen for the assembly m a t e highlighted in the graphics screen. T h e first nine mates assemble the clamper to the wheelchair, the j o i n t to the clamper a n d the wheelchair, and then the plate to the joint part. N o t e that t h e j o i n t is a SolidWork part that connects the plate a n d the c l a m p e r rigidly. T h e s e nine m a t e s are pretty standard. All these parts are fully constrained and are fixed to the wheelchair. T h e n e x t t w o m a t e s , Concentric3 a n d Distance4, assemble the h a n d l e bar to the plate at the pivot pin, allowing the h a n d l e bar to rotate at the pivot pin, as s h o w n in Figure 8-3a. COSMOSMotion will convert these m a t e s to a revolute joint. T h e distance m a t e provides an adequate clearance between the h a n d l e bar and the plate, as s h o w n in Figure 8-3b.

T h e n e x t three m a t e s , CamMateTangentl, Coincident3, a n d Coincident4, assemble the k i c k i n g r o d to the plate and the h a n d l e bar. First, the m i d d l e pin of the kicking r o d is a s s e m b l e d to the inner surface of the b o t t o m slot of the h a n d l e b a r using CamMateTangentl, as s h o w n in Figure 8-3c. As a result, the pin can only m o v e within the slot, w h i c h is desirable. Second Coincident3 m a t e s the b o t t o m face of the kicking r o d to the inner b o t t o m face of the first lower bracket of the plate, as s h o w n in Figure 8-3d. Similarly Coincident4 m a t e s the rear face of the kicking r o d to the inner side face of the first lower bracket of the plate, as s h o w n in Figure 8-3e. These t w o m a t e s restrict the kicking r o d to slide along the longitudinal direction, w h i c h will be converted to a translational j o i n t by COSMOSMotion. T h e final m a t e , Anglel, orients the vertical plane of the h a n d l e bar {Right Plane) respect to that of the plate {Right Plane). This m a t e will help determine an initial condition for m o t i o n simulations. N o t e that the Anglel m a t e to orient the handle, it will has to be suppressed to allow the handle bar to rotate

B a s e d on the geometry of the m e c h a n i s m and dimensions of its constituent c o m p o n e n t s , the kicking r o d is able to travel a total of 12.2 in. along the longitudinal direction (Z-direction). T h e kicking r o d can m o v e 6.82 in. forward (positive Z-direction with respect tot the m i d d l e pin) until its m i d d l e pin b e c o m e s in contact with the inner face at the lower end of the slot, as s h o w n in Figure 8-4a. Similarly, the kicking r o d m o v e s 5.34 in. b a c k w a r d until the side face of the handle bar b e c o m e s in contact w i t h the front end face of the first lower bracket, as s h o w n in Figure 8-4b. At the same time, the handle will travel a total of 18.6 in., 9.98 b a c k w a r d and 8.6 in. forward, as s h o w n in Figures 8-4c and 8-4d, respectively. N o t e that these m e a s u r e m e n t s shown in Figure 8-4 can be obtained by using the Measure option in SolidWorks. To access the Measure option, simply choose from the p u l l - d o w n m e n u Tools > Measure. Simulation

Model

In this m o t i o n m o d e l , the only m o v i n g parts are the handle bar and the kicking rod. After suppressing the m a t e Angle1, COSMOSMotion will add a revolute j o i n t to the m o t i o n m o d e l b e t w e e n the h a n d l e bar and the plate at the pivot pin, as shown in Figure 8-5. The h a n d l e bar is allowed to rotate about the X-axis of the global coordinate system at the pivot pin. In addition, a translational j o i n t is created by COSMOSMotion b e t w e e n the kicking r o d and the first lower bracket. This j o i n t constrains the kicking rod to translate along the longitudinal direction; i.e., the Z-direction. T h e third and final j o i n t is the CamMateTangent b e t w e e n the outer surface of the m i d d l e pin and the inner surface of the slot at the b o t t o m of the handle bar. This j o i n t restricts the pin to m o v e inside the slot. In addition to joints, a spring is a d d e d b e t w e e n the u p p e r bracket of the plate and the h o o k on the side of the handle bar. This spring, as s h o w n in Figure 8-5, is added to restore the handle b a r to a neutral position after pulling. Since the free spring length is set to a slightly larger value so that the handle bar will be oriented at a negative 5~/0-degree angle (about the X-axis). Therefore, the user will h a v e to p u s h the handle forward before pulling it b a c k to kick the ball. A larger spring free length will p u s h the h a n d l e leaning further b a c k w a r d (toward the user), providing additional pulling force that helps the users to pull b a c k the handle bar. N o t e that the pulling action will p u s h the kicking r o d forward (positive Z-direction) to " k i c k " the soccer ball. There is one contact constraint a d d e d to the m o t i o n m o d e l . T h e contact constraint is defined b e t w e e n the outer side face of the handle bar and the front end face of the first lower bracket. This contact constraint will prevent the handle bar from m o v i n g further b a c k w a r d and penetrating t h r o u g h the brackets. In this contact constraint, a restitution coefficient of 0.5 is assumed. Finally, an impulse force of 5-65 l b in a time span of 1.0 second will be added to the handle bar along the Z-direction, as shown in Figure 8-5, to simulate the operating force. N o t e that the impulse force m u s t first p u s h the handle b a r about 10 degrees forward before pulling it back, as illustrated in Figure 8-6. f

In this example, we will turn on the gravity, w h i c h is acting in the negative 7-direction (vertically d o w n w a r d ) ; i.e., the default setting. We will first a s s u m e no friction in any joints. This assumption will greatly simplify the simulation m o d e l a n d help set up the m o t i o n m o d e l correctly. We will u s e this m o d e l to choose a spring, including the selection of spring constant and free length. T h e simulation results of this non-friction m o d e l h a v e b e e n created in the assembly files Lesson8TaskOne.SLDASM and Lesson8TaskTwo. SLDASM. T h e friction force will be turned on for both the revolute and translational joints to determine the required force for operating the m e c h a n i s m . In addition, the operating force, m o d e l e d as an impulse force will be a d d e d to the m e c h a n i s m . N o t e that the friction is not a d d e d to the CamMateTangent j o i n t b e t w e e n the m i d d l e pin and the slot since such a capability is not currently supported by COSMOSMotion. Results of these simulations can be found in Lesson8TaskThreeNoFriction.SLDASM, Lesson8TaskThreeSmallFriction.SLDASM, and Lesson8TaskThreeLargeFriction.SLDASM. 8.3

U s i n g COSMOSMotion

In this example, we will start with a valid simulation m o d e l defined in the assembly Lesson8.SLDASM. T h e unit system is IPS. W h e n y o u open this assembly file, y o u should see a properly assembled m o d e l with fifteen m a t e s , as s h o w n in Figure 8-2, w h e r e the last constraint, Angle1, should h a v e b e e n suppressed. N o t e that the m a t e angle is set to positive 10 degrees for the time being, and the handle b a r is leaning forward (toward the Z-direction), as s h o w n in Figure 8-7. N o t e that this angle is w h a t we a s s u m e for T a s k O n e simulations. If y o u enter COSMOSMotion and e x p a n d the Parts a n d Constraints branches in the browser, y o u should see the existing m o t i o n entities, as s h o w n in Figure 8-8. There are four parts u n d e r the Ground Parts branch. O n l y h a n d l e bar and kicking r o d are m o v a b l e . In addition, there are three j o i n t s defined, CamMateTangentl, Revolute, and Translational, as discussed earlier. In the Contact branch u n d e r the Constraints, there is o n e contact joint, Contact 3D, defined to prevent the kicking rod from penetrating into the brackets. D u e to the contact constraint and the restitution coefficient defined, the handle bar will b o u n c e b a c k w h e n it hits the front edge of the first lower bracket.

There are three major tasks we will carry out in this design. In T a s k O n e we will run simulation to check the function of the 3D contact constraint. We h o p e to ensure that all joints are adequately defined, and the restitution coefficient we a s s u m e d in the contact constraint gives us reasonable results. In T a s k T w o , we will add the spring. We will adjust the spring constant and its free length until we reach an equilibrium configuration that we can w o r k with. N o t e that a desired free length should bring the handle b a r b a c k w a r d a negative 5-10 degree angle ( a b o u t the X-axis). After the spring is determined, we will add an operating force at the handle in Task Three. N o t e that the force will first p u s h the handle b a r forward about 10 degrees (positive, a b o u t the X-axis) before pulling it b a c k w a r d in order to provide e n o u g h travel distance for the kicking rod, and hopefully, sufficient m o m e n t u m to kick the ball. In T a s k Three, we will start with a non-friction case, a n d then turn on friction in both the revolute and translational joints. F r o m the friction cases, we will determine if the operating force is sufficient to p u s h the handle forward about 10 degrees before pulling it backward. We will vary the friction coefficients to simulate different scenarios and then determine the m a g n i t u d e of the operating forces accordingly. The m a g n i t u d e of the force will answer the critical question: if the design is acceptable. We h o p e to k e e p the m a x i m u m force m a g n i t u d e under 20 lbf. Task

One:

Determining

Contact

Constraints

We will carry out simulations for the m o t i o n m o d e l defined in Lesson8.SLDASM. In the assembly, the handle is leaning forward 10 degrees (see Figure 8-7), the contact j o i n t Contact 3D is defined, and the gravity is turned on. Y o u m a y w a n t to o p e n the Contact3D constraint by right clicking Contact3D from the b r o w s e r and choosing Properties. In the Edit 3D Contact dialog box, y o u should see that the plate a n d handle are included in the first and second containers, respectively, as s h o w n in Figure 8-9. If y o u choose the Contact tab, y o u should see that the Coefficient of Restitution is 0.5, as s h o w n in Figure 8-10. N o t e that no friction is i m p o s e d for this constraint. Close the dialog b o x by clicking the Apply button.

A l s o , we w o u l d like to m a k e sure that the gravity is set up properly. F r o m the browser, right click the Motion Model n o d e and select System Defaults. In the Options dialog b o x (Figure 8-11), y o u should see the acceleration is 386.22 i n / s e c , and the Direction is set to -1 for Y. Click OK to accept the gravity setting. 2

Click the Motion Model n o d e from the browser, press the right m o u s e button a n d select Simulation Parameters. Enter 2 for simulation duration a n d the 200 for the n u m b e r of frames, as s h o w n in Figure 8-

12. M a k e sure the Use Precise Geometry for 3D Contacts is selected in order for COSMOSMotion to detect contact during simulation. Click the Motion Model n o d e again, press the right m o u s e button and select Run Simulation. Y o u should see that the h a n d l e bar start m o v i n g forward and the kicking r o d m o v i n g b a c k w a r d due to gravity. W h e n the handle b a r and the first lower bracket is in contact, the handle b a r b o u n c e s b a c k slightly due to the contact constraint we defined. Next, we will graph the position and velocity of the kicking r o d a l o n g the Z-direction. F r o m the browser, e x p a n d the Parts n o d e and then the Moving Parts n o d e . Right click kickingjrod7, a n d choose Plot > CM Position > Z, and Plot > CM Velocity > Z Component. T w o graphs like those of Figures 8-13 and 8-14 should appear. N o t e that the vertical scales of the graphs h a v e b e e n adjusted for clarity. T h e position graph shows that the m a s s center of the kicking r o d w a s located at Z = 21.6 in. initially. T h e m a s s center m o v e s to the right to Z = 17.8 in., w h e r e the handle bar is in contact with the first lower bracket. The handle bar, therefore the kicking rod, b o u n c e s back, and the center m a s s of the kicking r o d reaches to Z = 18.6 in. before it slides to the right again due to gravity. After about 1.5 seconds, the kicking r o d rests and stays in contact with the bracket. T h e velocity graph (Figure 8-14) shows that the b o u n c i n g velocity is half of the i n c o m i n g velocity in the opposite direction. This is certainly due to the 0.5 restitution coefficient defined at the contact constraint. F r o m these t w o graphs, w e conclude that the m o t i o n m o d e l has b e e n defined correctly. Save y o u r m o d e l . Y o u m a y w a n t to save the m o d e l u n d e r different n a m e and u s e it for T a s k T w o simulations.

Task

Two: Adding Spring

In Task T w o , we will add a spring to the m e c h a n i s m . We will adjust the spring constant and its free length until we reach an equilibrium configuration that we can w o r k with. N o t e that the free length we specify will h a v e to bring the handle b a r b a c k w a r d about 5-10 degrees (that is, negative 5-10 degrees a b o u t the X-axis).

Delete the simulation result. F r o m the browser, right click the Spring n o d e and choose Add Translational Spring, the Insert Spring dialog b o x will appear (Figure 8-15). Pick the center hole of the u p p e r bracket and the h o o k of the handle bar, as shown in Figure 8-16. Enter the followings: Stiffness: 30 Length: 5 Force: 0 Coil Diameter: 1 Number of coils: 10 Wire Diameter: 0.25

N o t e that the actual distance b e t w e e n the hole and the h o o k under the current configuration is about 4.34 in., w h i c h can be obtained by clicking the Design b o x to the right of the Length field. T h e n u m b e r we enter, 5, is larger than the actual distance. Again, the purpose of entering a larger free spring length is to m a k e the handle bar lean b a c k w a r d at equilibrium. Click the Apply button to accept the spring. In the current configuration, the spring is c o m p r e s s e d since the h a n d l e is leaning 10 degrees forward. R u n a simulation. Y o u should see that the handle bar start m o v i n g b a c k w a r d a n d the kicking r o d m o v i n g forward due to the stretching of the spring. W h e n the simulation is completed, the position a n d velocity graphs of the kicking r o d will appear, similar to Figures 8-17 and 8-18. B o t h the position and velocity graphs reveal a sinusoidal type curve. This is due to the fact that no friction has b e e n applied to the joints. Also, the handle bar is not colliding with the bracket. The graphs s h o w that the period of one vibration is j u s t u n d e r 0.5 seconds.

N o w we will add a graph to s h o w the rotation angle of the handle b a r . Delete the simulation result. F r o m the browser, right click the handle-1 a n d choose Plot > Bryant Angles > Angle7; i.e., about the Xaxis. R e r u n the simulation, the angle graph should appear, similar to Figure 8-19. T h e graph shows that the h a n d l e b a r is oscillating b e t w e e n 10 and -9 degrees. T h e angle of the handle b a r at equilibrium (assuming friction is added to dissipate energy) will be roughly the average of 10 and - 9 ; i.e., less than 1 degree, w h i c h is far less than the desired angle (negative 5-10 degrees). Delete the simulation result, change the free length to 5.5 in., and rerun the simulation. The angle graph s h o w n in Figure 8-20 indicates that the handle bar oscillates b e t w e e n 10 and -25 degrees, and the m e a n angle is about -7 degrees, w h i c h is desired.

N o t e that a softer spring will increase the oscillation angle. If the spring constant is too small, say 2 lbf/in, the handle b a r m a y reach a dead lock position w i t h the m i d d l e pin of the kicking rod, similar to w h a t w a s s h o w n in Figure 8-4a, w h i c h is not desirable. On the other hand, if the spring is too stiff, the

force required to p u s h the h a n d l e bar forward m a y be excessive. Currently, the spring constant is set to 30 lbf/in. This parameter will be revisited later in T a s k Three. Save y o u m o d e l before m o v i n g to T a s k Three. Task

Three:

Determining

the

Operating Force

In Task Three, we will determine the operating force. T h e force m u s t be small e n o u g h to allow children w i t h limited physical strength to operate the m e c h a n i s m . We will add a force at the handle, a n d use simulation results to determine the required operating force. T h e force to be determined is supposed to p u s h the h a n d l e forward about 10 degrees, as s h o w n in Figure 8-6, and then pull it b a c k w a r d to p u s h out the kicking rod. Then, we will turn on friction at both translational and revolute joints, and determine the operating force again. We will adjust the friction coefficient (assuming different physical conditions) in order to determine a range of the operating force. In the simulation, we will start with a configuration w h e r e the handle bar is set to -7 degrees; i.e., in its neutral position, as determined in T a s k T w o . Save the m o d e l under a different n a m e , say Task3. Delete the simulation result, and go b a c k to SolidWorks assembly m o d e e

by clicking clicking the the Assembly Assembly buttons buttons % on on top top of of the the browser. browser. First unsuppress the m a t e AngleL Anglel. Then, right click the Anglel m a t e and choose Edit Feature. In the Anglel w i n d o w (Figure 8-21), change the angle to 7, click the Flip direction button (to deselect it), a n d click the c h e c k m a r k button on top to accept the definition. The handle b a r should rotate to a 7-degree position b a c k w a r d in the graphics screen, as s h o w n in Figure 82 2 . This is the initial configuration for T a s k Three simulations. N e x t we will create a force at the handle. T h e force can be a d d e d from the b r o w s e r by e x p a n d i n g the Forces branch, right clicking the Action Only n o d e , a n d choosing Add Action-Only Force. In the Insert Action-Only Force dialog box, the Select Component to which Force is Applied field (see Figure 8-23) is active (highlighted in red) and ready for y o u to pick the entities. Rotate the m o d e l a n d p i c k the face of the handle, as s h o w n in Figure 8-24. T h e part handle-1 is now listed in the Select Component to which Force is Applied field, a n d handle- 1/DDMFace 10 is listed in both the Select Location a n d the Select Direction fields.

Figure 8-21

N o w the Select Reference Component to orient Force field is active for selection. We will click the ground button to the right 01 the h e l d . A l t e r that, y o u should see Assem5 (representing the ground) appear in the text field. A force symbol will appear in the graphics screen pointing d o w n w a r d , w h i c h is not w h a t we want. We will h a v e to change the force direction. N o w the Select Reference Component to orient Force field is active for selection. We will click the ground button • to the right of the field. After that, y o u should see Assem5 (representing the ground) appear in the text field. A force symbol will appear in the graphics screen pointing d o w n w a r d , w h i c h is not w h a t we want. We will h a v e to change the force direction. Select all the text in the Select Direction field (press the let m o u s e button and drag to select all text), and press the Delete k e y to delete the current selection. Pick the end face of the foot, as s h o w n in Figure 8-24, to orient the force along the negative Z-direction. T h e arrow of the force symbol should n o w point to the negative Z-direction, w h i c h is n o r m a l to the face we picked.

Click the graph button (right most, as circled in Figure 8-25), the function graph will appear like the one in Figure 8-26. Note that internally COSMOSMotion will create a smooth spline function using the data entered. Close the graph a n d click Apply button to accept the force definition. R u n a simulation. T h e result graphs will appear at the e n d of the 2-second simulation. T h e angle graph (Figure 8-27) shows that the h a n d l e bar starts at an orientation angle of -7 degrees as expected, and swing forward to a 13degree angle, w h i c h is desirable, due to the forward force. T h e handle then m o v e s b a c k w a r d to about 26 degrees, and then oscillates.

T h e position graph in Figure 8-28 s h o w s that the m a s s center of the kicking r o d starts at about 24 in. It then travels to about 21.2 (backward) a n d then to about 26.8 in. forward due to the pulling force and stretch of the spring. T h e overall distance that the kicking r o d travels is about 5.6 in., w h i c h seems to be sufficient to produce e n o u g h m o m e n t u m to k i c k the ball. Figure 8-29 shows that the velocity of the kicking r o d reaches about 27 in/sec w h e n the r o d is p u s h e d near the foremost position. This velocity will p r o d u c e a m o m e n t u m of about 310 lbf-sec at 0.5 seconds, as s h o w n in Figure 8-30. To create a m o m e n t u m graph y o u m a y simply right click kicking_rod-l from the browser and choose Plot > Translational Momentum > Z Component. N o t e that the velocity and m o m e n t u m are proportional, with the m a s s of the kicking r o d as the scaling factor. T h e m a x i m u m force required to operate the device is determined to be 5 l b ( m a x i m u m force value entered), assuming no friction at any joints. E v e n t h o u g h the force data we entered s h o w a polyline in Figure 8-26, the actual force e m p l o y e d for simulation in COSMOSMotion is a spline curve generated f

Save y o u m o d e l . We will turn on friction and continue determining the required operating force. We will turn on friction at both the revolute and the translational joints. Friction for the CamMateTangent j o i n t is currently unavailable in COSMOSMotion. Delete the simulation result from the browser. E x p a n d the Constraints a n d then the Joints branch. R i g h t click Revolute a n d choose Properties. In the Edit Mate-Defined Joint dialog b o x (Figure 8-33), choose the Friction tab, click the Use Friction, and choose Aluminum Greasy for both Material 1 and Material 2. The Coefficient (mu) will show 0.03. Enter Joint dimensions, Radius: 0.26 and Length: 0.31. Click Apply button to accept the definition. N o t e that the dimensions entered are the diameter of the pivot pin and the thickness of the handle b a r w h e r e the j o i n t is located.

Similarly, turn on the friction for the translational joint. Enter 7.25, 7, a n d 7, for Length, Width, and Height, respectively, as s h o w n in Figure 8-34. N o t e that the length dimension entered is the sum of both the lower brackets; i.e., 7 and 0.25 in. for the first and second lower brackets, respectively. The width and height of the inner square of the brackets is 7 and 7 in., respectively. R u n a simulation a n d check the angle of the h a n d l e bar. E v e n t h o u g h the friction coefficient is small (ju = 0.03) for both joints, the handle bar hardly m o v e s . Therefore, the force m a g n i t u d e m u s t be increased. We will follow in general the overall force pattern, and increase the force m a g n i t u d e to p u s h the handle bar forward. Delete the simulation result. E x p a n d the Forces a n d then the Action Only n o d e s from the browser. Right click the ForceAO n o d e a n d choose Properties. In the Edit Action-Only Force dialog box, choose the Function tab (see Figure 8-25), and enter the followings:

Click the graph button, the function will appear like the one in Figure 8-35. The m a x i m u m force is n o w 12 lbf. N o t e that the first half of the force (negative part) is increased m o r e than twice, and the positive portion remains the same. T h e positive part of the force is k e p t the same since the spring will contribute partially to the pulling force. T h e overall force pattern is similar to that of Figure 8-26. The force data entered are results of a few trials-and-errors.

T h e m o m e n t u m graph (Figure 8-37) shows that w h e n the rod is p u s h e d near the foremost position the m o m e n t u m of the kicking rod is about 230 l b s e c , w h i c h is less than the previous non-friction case. After reviewing the graphs, the 7 2 - l b force seems to be acceptable. H o w e v e r , this small operating force, 12 lbf, is due to a very small friction force; i.e., friction coefficient jU = 0.03. This result also indicates that the spring constant 30 lbf/in seems to be adequate. Next, we will increase the friction coefficient by changing the material from Aluminum Greasy to Aluminum Dry. r

f

Delete the simulation result. E x p a n d the Constraints a n d then the Joints branch. R i g h t click Revolute and choose Properties. In the Edit Mate-Defined Joint dialog box, choose the Friction tab, a n d choose Aluminum Dry for both Material 1 and Material 2. The Coefficient (mu) will show 0.20. R e p e a t the s a m e for the translational joint. R u n a simulation. The handle b a r is hardly m o v e d . That is, the force will h a v e to be increased again. Delete the simulation results. R i g h t click the ForceAO n o d e to enter the force data. N o t e that after several attempts, a force that is large e n o u g h to m o v e the handle bar, therefore the kicking rod, is about 65 lbf. M o r e specifically, the force data entered are:

Click the graph button, the function will appear like the one in Figure 8-38. Even though the m a x i m u m p u s h i n g force is n o w 65 lb . the pulling force (positive portion) remains the same, A r e : running a simulation, the angle and m o m e n t u m graphs appear as in Figures 8-39 and 8-40, respectively B o t h seem to be reasonable. H o w e v e r , the large operating force, 65 lb , raises a flag. The m e c h a n i s m requires too large a force for a child to operate. f

f

N o t e that the simulation engine, ADAMS/Solver, is very sensitive to the force data entered. Y o u may encounter p r o b l e m s while carrying out some of the simulations in T a s k Three. W h e n this happens, simply c h a n g e the m a x i m u m force data, e.g., 65, to a slightly different value, e.g., 63, until a simulation can be completed. Save y o u r m o d e l .

8.4

Result Discussion

Apparently, the biggest concern raised in the simulations is the large operating force. The friction coefficient ju = 0.20, provided by COSMOSMotion for Aluminum-Aluminum contact without lubrication, seems to be physically reasonable. A l t h o u g h this friction coefficient represents an extreme case since in reality some lubricant w o u l d be added to the joints to reduce friction resistance. Nevertheless, the force is still too large. As revealed in simulations; i.e., Task Three, the m a x i m u m operating force increases from 5 lbf for non-friction, 12 lbf for small friction (ju = 0.03) to 65 lbf for large friction (ju = 0.20). R e d u c i n g the friction force at joints, especially the translational j o i n t b e t w e e n the kicking r o d and the t w o lower brackets on the plate, is critical for a successful device. Y o u can easily confirm that the translational j o i n t contributes significantly to the friction encountered in the m e c h a n i s m by conducting separate simulations w h e r e friction is only present in one of the t w o joints. T h e flag raised by the simulation has b e e n observed in the physical device, as s h o w n in Figure 8 - 4 1 , built by students following the design created in SolidWorks and COSMOSMotion. The physical device confirms that the contact b e t w e e n the kicking r o d and the t w o brackets produces a large friction force, resulting in a large operating force to operate the device. F o r children with limited physical strength, such a device is unattractive. In order to reduce the friction, four bearings are a d d e d to the device, as s h o w n in Figure 8-42. T w o are a d d e d to the top surface of the kicking rod, and t w o are underneath the kicking rod. W i t h the bearings, the friction is significantly reduced. Therefore, a smaller force is required to operate the device. T h e actual operating force is less than 20 lbf.

8.5

C o m m e n t s on COSMOSMotion Capabilities a n d Limitations

U s i n g COSMOSMotion does answer critical questions a n d help the design process, as demonstrated in this example. H o w e v e r , from this e x a m p l e , a n u m b e r of limitations in COSMOSMotion h a v e also b e e n encountered. K n o w i n g these limitations will help y o u u s e COSMOSMotion m o r e effectively. First, the simulation engine, ADAMS/Solver, w h i c h solves the equations of m o t i o n for the m e c h a n i s m , is n o t stable. Sometimes w h e n y o u rerun the same simulation, y o u could see slightly different results. This p r o b l e m is m o r e vivid w h e n we ran the same simulation using different computers.

Moreover, the simulation engine p r o d u c e d results, such as the velocity or m o m e n t u m (see Figures 8-37 and 8-40), with spikes, w h i c h is not quite realistic. S o m e of the spikes disappear or b e c o m e smaller w h e n we rerun the same simulation. Second, friction is n o t supported for a CamMateTangent joint. Therefore, an attempt w a s m a d e to add a 3D contact j o i n t b e t w e e n the m i d d l e pin and the slot of the handle bar. A n u m b e r of restitution coefficients w e r e used, including 0.5, 0.75, etc. Yet, adding a 3D contact j o i n t significantly slow d o w n the motion of the handle bar and the kicking r o d since lots of contact are encountered b e t w e e n the outer surface of the m i d d l e pin and the inner surface of the slot w h e n the m e c h a n i s m is in motion. M o r e contact causes m o r e energy dissipation. H o w e v e r , the s l o w - d o w n is w a y too m u c h to grant a physically reasonable simulation. In addition, m o r e spikes appear in graphs, such as in velocity. H o w e v e r , the biggest issue with adding the 3D contact is that the simulation engine b e c o m e s extremely sensitive to the initial orientation angle of the handle bar and the m a g n i t u d e of the operating force. For some simulations, the solution engine encountered p r o b l e m s , for example, force imbalance at certain time steps during the simulation, and terminated the simulation prematurely. Overall COSMOSMotion is an excellent tool with lots of nice features and capabilities for support of m e c h a n i s m design and analysis. H o w e v e r , as m e n t i o n e d in this b o o k n u m e r o u s times, no software is foolproof. Before creating a simulation m o d e l , y o u always w a n t to formulate y o u r design questions and set up y o u r simulation m o d e l a n d scenarios gearing t o w a r d answering these specific questions. Y o u will h a v e to e x a m the simulation results very carefully and challenge yourself about the validity of the results since if y o u d o n ' t s o m e b o d y else will do, usually in a less friendly w a y .

APPENDIX A: DEFINING JOINTS Degrees of F r e e d o m Understanding degrees of freedom is critical in creating successful motion model. The free degrees of freedom of the m e c h a n i s m represent the n u m b e r of independent parameters required to specify the position, velocity, and acceleration of each rigid b o d y in the system for any given time. A completely unconstrained b o d y in space has six degrees of freedom, three translational and three rotational. If y o u add a joint; e.g., a revolute j o i n t to the b o d y , y o u restrict its m o v e m e n t to rotation about an axis, and the free degrees of freedom of the b o d y are r e d u c e d from six to one. F o r a given m o t i o n m o d e l , y o u can determine its n u m b e r of degrees of freedom using the G r u e b l e r ' s count. T h e m e c h a n i s m ' s Gruebler count is calculated using the m e c h a n i s m ' s total n u m b e r of bodies. As m e n t i o n e d above, each m o v a b l e b o d y introduces six degrees of freedom. Joints added to the m e c h a n i s m constrain the system, or r e m o v e d o f s . M o t i o n inputs, i.e., m o t i o n drivers, r e m o v e additional d o f s . COSMOSMotion uses the following equation to calculate the G r u e b l e r ' s count: (A.1) w h e r e D is the Gruebler count representing the total free degrees of freedom of the m e c h a n i s m , M is the n u m b e r of bodies excluding the g r o u n d b o d y , TV is the n u m b e r of d o f s restricted by all joints, and O is the n u m b e r of the m o t i o n inputs in the system. F o r kinematic analysis, the G r u e b l e r ' s count m u s t be equal to or less than 0. The ADAMS/Solver recognizes and deactivates redundant constraints during m o t i o n simulation. For a kinematic analysis, if y o u create a m o d e l w i t h a G r u e b l e r ' s count greater than 0 and try to simulate it, the simulation will not r u n and an error m e s s a g e will appear. If the G r u e b l e r ' s count is less than zero, the solver will automatically r e m o v e redundancies, if possible. F o r example, y o u m a y apply this formula to a door m o d e l that is supported by t w o hinges m o d e l e d as revolute joints. Since a revolute j o i n t r e m o v e s five d o f s , the G r u e b l e r ' s count b e c o m e s :

T h e calculated degrees o f f r e e d o m result i s - 4 , w h i c h include f i v e redundant d o f s . Redundancy R e d u n d a n c i e s are excessive d o f s . W h e n a j o i n t constrains the m o d e l in exactly the same w a y as another j o i n t (like the door example), the m o d e l contains excessive d o f s , also k n o w n as redundancies. A j o i n t b e c o m e s excessive w h e n it does n o t introduce any further restriction on a body's motion. It is important that y o u eliminate redundancies from y o u r m o t i o n m o d e l while carrying out d y n a m i c analyses. If y o u do not r e m o v e redundancies, y o u m a y n o t get accurate values w h e n y o u check j o i n t reactions or load reactions. For example, if y o u m o d e l a door using t w o revolute j o i n t s for the hinges, the second revolute j o i n t does not contribute to constraining the door's motion. COSMOSMotion detects the redundancies and ignores one of the resolute j o i n t s in its analysis. The o u t c o m e m a y be incorrect in reaction results, yet the

m o t i o n is correct. For complete and accurate reaction forces, it is critical that y o u eliminate redundancies from your mechanism. F o r a kinematic simulation w h e r e y o u are interested in displacement, velocity, and acceleration, redundancies in y o u r m o d e l do not alter the performance of the m e c h a n i s m . Y o u can eliminate or reduce the redundancies in y o u r m o d e l by carefully choosing joints. These j o i n t s m u s t be able to restrict the same d o f s , b u t not duplicate each other, introducing redundancies. After y o u decide w h i c h joints y o u w a n t t o use, y o u can use the G r u e b l e r ' s count t o calculate the d o f s and check redundancies. Y o u m a y also ask COSMOSMotion to calculate the G r u e b l e r ' s count for you. Y o u can simply click the Show simulation control button on top of the graphics screen to bring up the dialog box, as s h o w n in Figure A1. N o t e that the DOF field in the dialog b o x will show the G r u e b l e r ' s count if a simulation has b e e n completed. If not, Y o u m a y click the Calculate button to ask COSMOSMotion to calculate the actual dof. In the m e s s a g e window appearing next (Figure A-2), COSMOSMotion identifies redundant dofs a n d recalculates the dof for the simulation model.

Before y o u select a j o i n t to add to y o u r m o d e l , y o u should k n o w w h a t m o v e m e n t y o u w a n t to restrain for the b o d y and w h a t m o v e m e n t y o u w a n t to allow. T h e following table describes the c o m m o n l y e m p l o y e d j o i n t types in COSMOSMotion and the degrees of freedom they r e m o v e .

T h e following provides m o r e details about the j o i n t s listed in the table above. Revolute

Joint

A revolute joint, as depicted in Figure A - 3 , allows the rotation of one rigid b o d y w i t h respect to another rigid b o d y about a c o m m o n axis. T h e origin of the revolute j o i n t can be located a n y w h e r e along the axis about w h i c h the bodies can rotate with respect to each other. T h e j o i n t origin is assigned by COSMOSMotion w h e n y o u enter COSMOSMotion from SolidWorks. Orientation of the revolute j o i n t defines the direction of the axis about w h i c h the bodies can rotate with respect to each other. T h e rotational axis of the revolute j o i n t is parallel to the orientation vector a n d passes t h r o u g h the origin.

Translational

Joint

A translational j o i n t allows one rigid b o d y to translate along a vector with respect to a second rigid body, as illustrated in Figure A - 4 . T h e rigid bodies m a y only translate, not rotate, w i t h respect to each other. T h e location of the origin of a translational j o i n t with respect to its rigid bodies does n o t affect the m o t i o n of the j o i n t but does affect the reaction loads on the joint. T h e location of the j o i n t origin determines w h e r e the j o i n t symbol is located. T h e orientation of the translational j o i n t determines the direction of the axis along w h i c h the bodies can slide with respect to each other (axis of translation). T h e direction of the m o t i o n of the translational j o i n t is parallel to the orientation vector and passes t h r o u g h the origin. Cylindrical

Joint

A cylindrical j o i n t allows b o t h relative rotation and relative translation of one b o d y with respect to another b o d y , as s h o w n in Figure A - 5 . T h e origin of the cylindrical j o i n t can be located a n y w h e r e along the axis about w h i c h the bodies rotate or slide with respect to each other. Orientation of the cylindrical j o i n t defines the direction of the axis about w h i c h the bodies rotate or slide along with respect to each other. T h e rotational/translational axis of the cylindrical j o i n t is parallel to the orientation vector a n d passes t h r o u g h the origin.

Spherical

Joint

A spherical j o i n t allows free rotation about a c o m m o n point of one b o d y with respect to another body, as depicted in Figure A - 6 . The origin location of the spherical j o i n t determines the point about w h i c h the bodies pivot freely with respect to each other.

A universal j o i n t allows the rotation of one b o d y to be transferred to the rotation of another b o d y , as shown in Figure A - 7 . This j o i n t is particularly useful to transfer rotational m o t i o n around corners, or to transfer rotational m o t i o n b e t w e e n t w o connected shafts that are permitted to b e n d at the connection point (such as the drive shaft on an automobile). T h e origin location of the universal j o i n t represents the connection point of the t w o bodies. T h e t w o shaft axes identify the center lines of the t w o bodies connected by the universal joint. N o t e that COSMOSMotion uses rotational axes parallel to the rotational axes y o u identify b u t passing t h r o u g h the origin of the universal joint.

A screw j o i n t r e m o v e s one degree of freedom. It constrains one b o d y to rotate as it translates w i t h respect to another body, as s h o w n in Figure A - 8 . W h e n defining a screw joint, y o u can define the pitch. T h e pitch is the a m o u n t of translational displacement of the t w o bodies for each full rotation of the first body. The displacement of the first b o d y

relative to the second b o d y is a function of the b o d y ' s rotation about the axis of rotation. For every full rotation, the displacement of the first b o d y along the translation axis with respect to the s e c o n d b o d y is equal to the value of the pitch. V e r y often, the screw j o i n t is u s e d with a cylindrical joint. T h e cylindrical j o i n t r e m o v e s t w o translational and t w o rotational degrees of freedom. T h e screw j o i n t r e m o v e s one m o r e degree of freedom by constraining the translational m o t i o n to be proportional to the rotational motion. Planar

Joint

A planar j o i n t allows a plane on one b o d y to slide and rotate in the plane of another body, as shown in Figure A - 9 . T h e orientation vector of the planar j o i n t is perpendicular to the j o i n t ' s plane of motion. T h e rotational axis of the planar joint, w h i c h is normal to the j o i n t ' s plane of motion, is parallel to the orientation vector.

Figure A - 9 Planar Joint S y m b o l Fixed

Figure A - 1 0 F i x e d Joint S y m b o l

Joint

A fixed j o i n t locks t w o bodies together so they cannot m o v e w i t h respect to each other. T h e fixed j o i n t symbol is s h o w n in Figure A - 1 0 .

M a p p e d SolidWorks

Mates

After y o u bring an assembly from SolidWorks to COSMOSMotion a n d assign c o m p o n e n t s to g r o u n d part and m o v i n g parts, COSMOSMotion automatically m a p s assembly m a t e s to joints. In m o s t cases, these j o i n t s w o r k well for the m o t i o n simulation. A selected set of the m a p p e d SolidWorks m a t e s , w h i c h is c o m m o n l y e m p l o y e d in assembly, is given in the next table for your reference.

Therefore, from Eqs. B.2 and B . 3 , we h a v e 7 l b = 386 l b f

2

m

i n / s e c , and the force in l b

2

m

i n / s e c unit

is 386 times smaller than that of l b that we are m o r e u s e d to. W h e n y o u apply a 7 l b force to the same f

f

2

m a s s block, it will accelerate 386 i n / s e c , as s h o w n in Figure B - l b . On the other hand, we h a v e the m a s s unit, 7 l b

2

m

1/386 l b s e c / i n . It m e a n s that a 1 l b m a s s b l o c k f

m

2

2

is 386 times smaller than that of a 7 l b s e c / i n block. Therefore, a 1 l b s e c / i n b l o c k will w e i g h 386 l b f

f

2

f

on earth. W h e n applying a 1 lbf force to the m a s s block, it will accelerate at a 7 i n / s e c rate, as illustrated in Figure B - l c .

APPENDIX C: IMPORTING Pro/ENGINEER PARTS AND ASSEMBLIES F r o m time to time w h e n y o u use COSMOSMotion for simulations, y o u m a y encounter the n e e d for importing solid m o d e l s from other C A D software, such as Pro/ENGINEER. SolidWorks provides an excellent capability that support importing solid m o d e l s from a b r o a d range of software and formats, including Parasolid, A C I S , I G E S (Initial Graphics E x c h a n g e Standards), S T E P (STandard for E x c h a n g e of Product data), SolidEdge, Pro/ENGINEER, etc. For a complete list of supported software and formats in SolidWorks, please refer to Figure C - 1 . Y o u m a y access this list by choosing File > Open from the pull-down m e n u , a n d pull d o w n the Files of type in the File Open dialog box. In this appendix, we will focus on importing Pro/ENGINEER parts and assemblies. Hopefully, m e t h o d s and principles y o u learn from this appendix will be applicable to importing solid m o d e l s from other software and formats. SolidWorks provides capabilities for importing both part and assembly. Users can choose t w o options in importing solid m o d e l . T h e y are Option 1: importing solid features a n d Option 2: importing j u s t geometry. Importing solid features m a y bring y o u a parametric solid m o d e l that j u s t like a SolidWorks part that y o u will be able to modify. On the other hand, if y o u choose to import geometry only, y o u will end up with an imported feature that y o u cannot c h a n g e since all solid features are l u m p e d into a single imported geometry without any solid features nor dimensions. Importing g e o m e t r y is relatively straightforward. In general, SolidWorks does a g o o d j o b in bringing in Pro/ENGINEER part as a single imported geometry. In fact, several other translators, such as IGES and S T E P , support such geometric translations well. I G E S and S T E P are especially useful w h e n there is no direct translation from one C A D to another. Importing solid m o d e l s w i t h solid features is a lot m o r e challenging, in w h i c h solid features e m b e d d e d in the part geometry, such as holes, chamfers, etc., m u s t be identified first. In addition, sketches that w e r e e m p l o y e d for generating the solid features m u s t be recovered and the feature types, for instance revolve, extrude, sweep, etc., m u s t be identified. W i t h virtually infinite n u m b e r of possibilities in creating solid features, it is almost certain that y o u will encounter p r o b l e m s while importing solid models with feature conversion. Therefore, if y o u do n o t anticipate m a k i n g design changes in SolidWorks. it is highly r e c o m m e n d that y o u import parts as a single geometric feature. We will discuss the approaches of importing parts, and then importing assemblies. In each case, e will try both options; i.e., importing solid features v s . importing geometry. We will use the gear train e x a m p l e e m p l o y e d in Lesson 6 as the test case a n d as an example for illustrations.

sketches in the graphics screen by clicking their n a m e s listed in the browser. In addition, the b a c k plate (Extrudel in the browser) is recognized incorrectly. Certainly, SolidWorks is capable of importing s o m e parts correctly and completely, especially, w h e n the solid features are relatively simple (but n o t this gear h o u s i n g part). If y o u take a closer look at any of the successful solid features, for e x a m p l e ExtrudeS, y o u will see that the sketches (for example Sketch3 of ExtrudeS) of the solid features do not h a v e complete dimensions. Usually a (—) symbol is placed in front of the sketch, indicating that the sketch is not fully defined. Apparently, this translation is not satisfactory. Unfortunately, this translation represents a typical scenario y o u will encounter for the majority of the parts. In m a n y cases, it m a y take only a small effort to repair or re-create wrong or unrecognized solid features. H o w e v e r , w h e n y o u translate an assembly with m a n y parts, the effort could be substantial. Option

2:

Importing

Geometry

Importing geometry is m o r e straightforward and has a higher successful rate than that of importing solid features. R e p e a t the same steps to open the gear housing part, gboxjiousingprt. In the Pro/ENGINEER to SolidWorks Converter dialog b o x (Figure C-8), choose Import geometry directly (default), a n d then Kniting (default) in order to import solid m o d e l s instead of j u s t surface m o d e l s . N o t e that if y o u choose BREP (Boundary Representation), only b o u n d a r y surfaces will be imported. Click OK.

T h e conversion process will start. After about a m i n u t e or two, the converted m o d e l will appear in the graphics screen, as shown in Figure C-9. In addition, an entity Importedl will appear in the browser (Figure C-9). As m e n t i o n e d earlier, there will be no parametric solid feature with dimensions and sketch converted if y o u choose Option 2. However, the geometry converted seems to be accurate. All the geometric features in Pro/ENGINEER shown in Figure C-3 were included in this imported feature. This translation is successful. Since we do not anticipate m a k i n g any change to the gear housing, this imported part is satisfactory. T h e gear housing part, gbox housing, sldprt, e m p l o y e d in Lesson 6 w a s created by u s i n g Option 2.

We will import the input gear assembly (gbox_input.asm) s h o w n in Figure C-10 using b o t h options. We will try Option 1 first; i.e.. importing solid features. As s h o w n in Figure C-10 {Pro/ENGINEER Model Tree w i n d o w ) , there are 11 parts (and several d a t u m features) in this assembly. SolidWorks will try to import this assembly as well as the 11 parts from Pro/ENGINEER.

Importing geometry is also m o r e straightforward for assembly and has a higher rate of success. R e p e a t the same steps to open the input gear assembly, gbox input.asm. In the Pro/ENGINEER to SolidWorks Converter dialog b o x (Figure C - l 3), choose Use body import for all parts (default), and then Kniting (default) in order to import solid m o d e l s . C h o o s e Overwrite for If same name SolidWorks file is found, and choose Import material properties and Import sketch/curve entities. Click Import. T h e conversion process will begin.

After about a m i n u t e or t w o , the converted assembly will appear in the graphics screen, as s h o w n in Figure C - l 4 . T h e assembly a n d all 11 parts s e e m to be correctly imported. If y o u expand any of the part branch, for example, the gear (wheel_gbox_pinion_ls), y o u will see an imported feature listed, as

depicted in Figure C-14. Again, there is no solid feature converted in any of the parts. In addition, the Mates branch is empty. Since we do n o t anticipate m a k i n g any change to this input gear assembly, this imported assembly is satisfactory, except it does not have any assembly mates. Assemble all 11 parts (may be m o r e for some cases) will take a non-trivial effort. Since we do not anticipate m a k i n g change in h o w these parts are assembled, we will m e r g e all 11 parts into a single part. In SolidWorks, y o u can j o i n t w o or m o r e parts to create a n e w part in an assembly. T h e m e r g e operation r e m o v e s surfaces that intrude into each other's space, and m e r g e s the parts into a single solid v o l u m e . We will insert a n e w part into the assembly and m e r g e all 11 parts into that n e w part. C h o o s e from the pull-down m e n u Insert > Component > New Part. In the Save As dialog b o x , enter gbox Jnput for part n a m e , and click Save. SolidWorks is expecting y o u to select a plane or a flat face to place a sketch for the n e w part. Click a plane or planar face on a component, for e x a m p l e pick the assembly Front plane from the browser, the Front plane will appear in the graphics screen (Figure C-15). T h e n e w part gboxinput will appear in the browser. In the n e w part, a sketch opens on the selected plane. Close the sketch. B e c a u s e we are creating a j o i n e d part, we do not n e e d a sketch. Next, we will select all 11 parts a n d m e r g e t h e m into the n e w part. F r o m the browser, click the first part wheel box_shaftinput, press the Shift key, and then click the last part, screw_setjip_6*6<2>. All 11 parts will be selected. F r o m the p u l l - d o w n m e n u , choose Insert > Features > Join. T h e Join w i n d o w will appear (overlapping with the browser) as s h o w n in Figure C-16. In the Join w i n d o w , all 11 parts are listed. All y o u h a v e to do is to click the c h e c k m a r k on top to accept the parts. Save the assembly (and the part), and then close the w h o l e assembly. N o w open the part gbox Jnput. M a k e sure y o u open gbox input, sldprt instead of gboxJnput. sldasm. T h e part gbox input will appear in the graphics screen. In addition, all entities b e l o n g to this part will be listed in the browser, as s h o w n in Figure C-17. N o t e that there is an arrow symbol -> to the right of the root entity, gbox Jnput. This symbol indicates that these entities enclosed in this part refer to other parts or assembly. N o t e that the Joinl branch has the same symbol. E x p a n d the Joinl branch, y o u will see 11 parts listed, all with arrows, pointing to the actual parts currently in the same folder. W h e n the link is broken; i.e., w h e n the referring parts are r e m o v e d from the folder, a question m a r k symbol will be added to the arrow. T h e three gear parts, gbox Jnput. sldprt, gboxjniddle.sldprt, and gbox output, sldprt, e m p l o y e d for Lesson 6 w e r e created following the approach discussed. O n e axis in each part that passes t h r o u g h the center hole of the gear w a s created simply by intersecting t w o planes, for e x a m p l e , Top a n d Right planes for the axis in gbox Jnput. sldprt, as s h o w n in Figure C-18. T h e s e axes are necessary for creating gear pairs, as discussed in Lesson 6.