Motion Simulation and Mechanism (Design with COSMOSMotion

Transcription

Motion Simulation and
Mechanism (Design
with COSMOSMotion 2007
Kuang-Hua Chang, Ph.D.
School of Aerospace and Mechanical Engineering
The University of Oklahoma
PUBLICATIONS
Schroff Development Corporation
www.schroff.com
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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
PUBLICATIONS
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.
Examination Copies:
Books received as examination copies are for review purposes only and may not
be made available for student use. Resale of examination copies is prohibited.
Electronic Files:
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only. These files may not be transferred to any other party
Mechanism
Design
with
COSMOSMotion
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 example 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 have 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
ii
Mechanism
Design
with
COSMOSMotion
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 t h e 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 have 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
encouragement 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.
Mechanism
Design
with
COSMOSMotion
iii
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 M e c h a n i c a l 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 a n d 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 have 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.
Mechanism
iv
Design
with
COSMOSMotion
Table of Contents
Preface
i
Acknowledgments
11
A b o u t the A u t h o r
iii
A b o u t the Cover Page
iii
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
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
Overview of the Lesson
3.2
T h e Spring-Mass System
3.3
3.4
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
4.2
T h e Simple P e n d u l u m E x a m p l e
4.3
4.4
Exercises
4-1
4-1
4-2
4-5
4-9
Mechanism
Design
with
COSMOSMotion
v
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
5.2
The Slider-Crank E x a m p l e
5.3
5.4
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
Exercises
6-1
6-2
6-6
6-9
Lesson 7: C a m a n d Follower
7.1
7.2
The C a m and Follower E x a m p l e
7.3
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
T h e Assistive D e v i c e
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 cams, 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 e x a m p l e s 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 components 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 e x a m p l e , 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 t h e 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 e x a m p l e , w h a t is t h e 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., t h e y 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),
which are connected by joints (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 l o o p 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 r e g a r d 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 must be conducted before dynamic behavior 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
shown in Figure 1-6. In this case, m o t i o n of t h e 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 governed 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 movable, 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 y o u r 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 time 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 mass 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
w o r k i n g . 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 m o d e l . 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 shown 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 e x a m p l e , 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 <f? to enter COSMOSMotion, a different set of
entities will be listed in the browser. In addition, an additional toolbar is a d d e d to SolidWorks, located at
the top of the graphics screen, as depicted in Figure 1-13. T h e y are the COSMOSMotion shortcut buttons
shown in Figure 1-9. This toolbar provides settings, simulation and post processing features. Especially,
the Play Simulation button
is h a n d y when y o u finish running a simulation and are ready to animate
the motion. Click some of the buttons and try to get familiar with their functions. T h e shortcut buttons in
COSMOSMotion and their functions are also s u m m a r i z e d in Table 1-1 with a few m o r e details.
tabbed dialog b o x and a w i z a r d that leads y o u through 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
model) 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 b o d y , 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 a n d material properties referring to the local coordinate
system. A m o v i n g part has a symbol (see Figure l-16a) attached, usually located at its m a s s center, as
shown 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 shown 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 . A l s o , 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 mates 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 a s s e m b l y m a t e s 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
y o u r o w n . 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 . F o r e x a m p l e , 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 joints 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 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. 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 j o i n t s 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 t h e m .
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 ground body, 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 j o i n t s r e m o v e redundant d o f s. For 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 shown in Figure 1-15 consists of three bodies (excluding the ground body),
one revolute j o i n t a n d 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 example 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 joints that r e m o v e a large n u m b e r
of constraints with joints 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 dampers, and bushings,
which symbols are s h o w n in Figure 1-19.
A m a g n i t u d e a n d 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 mates. 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 shown 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 s h o w n in F i g u r e 1-24. T hese 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 motion 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
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 dynamics 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 v e r y
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 or change the units system b y
choosing from 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 t h e n pick the units system y o u prefer, as shown 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)
are the velocities of the ball before
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
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
a s s e m b l y 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 a s s e m b l y 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 shown in F i g u r e 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 shown 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 p l a n e A s m e n t i o n e d
earlier, the ball will be thrown 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
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
shown in Figure 2-5). This b r o w s e r p r o v i d e s 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 through 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 shown 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 t h e
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 s a m e
for
Coincident3(Ground<l>,ball<l>).
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<Display State-1>), 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 t h e assembly (see Figure 2-8).
enter
Click the Motion button
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 page. 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 F i g u r e 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 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 (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 b y 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 motion joints that
are frequently encountered can be found in A p p e n d i x A. T a k e a few minutes 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 2-13. 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 from assembly mates. Y o u m a y add additional
joints to the motion 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 m o t i o n m o d e l . T h e 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 w a n t ; 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
b r o w s e r 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 shown 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 shown 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 browser 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 bounce back a
few times before the simulation ends. T h e ball did n o t fall t h r o u g h t h e 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 c h o o s e Create Trace Path (see Figure 2-23) to
bring up the Edit Trace Path dialog b o x , as s h o w n in F i g u r e 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 ground 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 shown 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
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 dynamics theory to this ballthrowing 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.
D a t a in c o l u m n C is g r a p h e d 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
shown 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 a n d 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 b o t h 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 r e v i e w 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
In this lesson, we will create a simple spring-mass system and simulate its d y n a m i c responses under
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 a s s e m b l y 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 w i t h simulation results for the three respective scenarios.
In the assembly m o d e l s , there are three assembly mates,
Coincident3(ground<l>,ball<l>),
and LimitDistancel(ground<l>,ball<l>),
as
Coincidentl(ground<l>,block<l>),
shown
in
Figure
3-2.
m
T hh ee bblock
l o c k is
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
m the graphics screen, y o u should be able to m o v e the
top of the graphics screen, and drag the b l o c k in
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 bb ll oo cc kk to
the lower
lower and
and upper
upper limits.
limits. We
We will
will take
take aa look
look at
at the
the assembly
assembly m
m aa tt ee
the
to m
m oo vv ee bb ee tt w
w ee ee nn the
LimitDistancel. 1.
LimitDistance
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 back 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<l>@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 have 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<l>).
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 mate.
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 a n d 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
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 block 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 e x p a n d 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 shown 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 mate and choose Edit Feature. Y o u should see the
definition of the assembly mate 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 a s s e m b l y 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 F i g u r e 312. Click Apply button to accept the definition.
N e x t , we will create a graph for the displacement of the
block 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 your 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 u n d e r
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 box, 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 added 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.
Pick any place in the ground 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 shown 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 your m o d e l .
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 dynamics 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 shown i n Figure 3-26, applying N e w t o n ' s S e c o n d 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 a n d 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 block 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
E q u a t i o n 3.7 can be i m p l e m e n t e d into Microsoft® Excel
spreadsheet, as shown 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 terms 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. The 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 shown 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 t h e 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 c o m p a r e y o u r calculation with that of
COSMOSMotion.
(ii)
D e r i v e 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 s y m b o l 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, expand 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 shows 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
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 shown 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 h a s 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.
Data in these three columns 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 , e v e n 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 shown 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 with those obtained from COSMOSMotion.
If a force p = 2 l b is applied to the ball as s h o w n in F i g u r e E 4 f
1, repeat b o t h (i) and (ii) of P r o b l e m 1.
5.1
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 F i g u r e 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 a s s e m b l y h a v e b e e n created for y o u . 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 b r a n c h 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.
The 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 mates (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 a d d e d 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 mate), 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 next 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
Start SolidWorks
a n d 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, expand 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 node. 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.
Take 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 node. 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 s a m e 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 y o u r
SolidWorks a s s e m b l y 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 . U s i n g 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 have 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 pick all four components 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 have 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 t u r n e d 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 pick the component.
Pick the end face of the piston, as s h o w n in Figure
5 - 2 1 . T h e 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.

Motion Simulation and Mechanism (Design with COSMOSMotion

Transcription

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