Machines and Mechanisms

385 Pages·2011·9.74 MB·English

by  David H. Myszka

MACHINES AND MECHANISMS
APPLIED KINEMATIC ANALYSIS
Fourth Edition
David H. Myszka
University of Dayton
Prentice Hall
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Library ofCongress Cataloging-in-Publication Data
Myszka,David H.
Machines and mechanisms :applied kinematic analysis / David H.Myszka.—4th ed.
p.cm.
Includes bibliographical references and index.
ISBN-13:978-0-13-215780-3
ISBN-10:0-13-215780-2
1. Machinery,Kinematics of. 2. Mechanical movements. I. Title.
TJ175.M97 2012
621.8'11—dc22
2010032839
10 9 8 7 6 5 4 3 2 1
ISBN 10: 0-13-215780-2
ISBN 13:978-0-13-215780-3
PREFACE
The objective of this book is to provide the techniques 6. Every chapter concludes with at least one case study.
necessary to study the motion ofmachines.A focus is placed on Each case illustrates a mechanism that is used on
the application ofkinematic theories to real-world machinery. industrial equipment and challenges the student to
It is intended to bridge the gap between a theoretical study of discuss the rationale behind the design and suggest
kinematics and the application to practical mechanisms. improvements.
Students completing a course ofstudy using this book should 7. Both static and dynamic mechanism force analysis
be able to determine the motion characteristics ofa machine. methods are introduced.
The topics presented in this book are critical in machine design
8. Every major concept is followed by an example
process as such analyses should be performed on design con-
problem to illustrate the application ofthe
cepts to optimize the motion ofa machine arrangement.
concept.
This fourth edition incorporates much of the feedback
received from instructors and students who used the first three 9. Every Example Problem begins with an introduction
editions.Some enhancements include a section introducing ofa real machine that relies on the mechanism being
special-purpose mechanisms;expanding the descriptions of analyzed.
kinematic properties to more precisely define the property; 10. Numerous end-of-chapter problems are consistent
clearly identifying vector quantities through standard boldface with the application approach ofthe text.Every
notation; including timing charts; presenting analytical concept introduced in the chapter has at least one
synthesis methods;clarifying the tables describing cam fol- associated problem.Most ofthese problems include
lower motion;and adding a standard table used for selection of the machine that relies on the mechanism being
chain pitch.The end-of-chapter problems have been reviewed. analyzed.
In addition,many new problems have been included. 11. Where applicable,end-of-chapter problems are
It is expected that students using this book will have a provided that utilize the analytical methods and are
good background in technical drawing,college algebra,and best suited for programmable devices (calculators,
trigonometry. Concepts from elementary calculus are spreadsheets,math software,etc.).
mentioned,but a background in calculus is not required.
Also, knowledge of vectors, mechanics, and computer Initially,I developed this textbook after teaching mech-
application software,such as spreadsheets,will be useful. anisms for several semesters and noticing that students did
However,these concepts are also introduced in the book. not always see the practical applications of the material.To
The approach of applying theoretical developments to this end,I have grown quite fond ofthe case study problems
practical problems is consistent with the philosophy of and begin each class with one.The students refer to this as
engineering technology programs.This book is primarily the “mechanism of the day.”I find this to be an excellent
oriented toward mechanical- and manufacturing-related opportunity to focus attention on operating machinery.
engineering technology programs.It can be used in either Additionally, it promotes dialogue and creates a learning
associate or baccalaureate degree programs. community in the classroom.
Following are some distinctive features ofthis book: Finally, the purpose of any textbook is to guide the
students through a learning experience in an effective
1. Pictures and sketches ofmachinery that contain manner.I sincerely hope that this book will fulfill this inten-
mechanisms are incorporated throughout the text. tion.I welcome all suggestions and comments and can be
2. The focus is on the application ofkinematic theories to reached at [email protected].
common and practical mechanisms.
3. Both graphical techniques and analytical methods are ACKNOWLEDGMENTS
used in the analysis ofmechanisms.
I thank the reviewers of this text for their comments and
4. An examination copy ofWorking Model®,a commer-
suggestions: Dave Brock, Kalamazoo Valley Community
cially available dynamic software package (see Section 2.3
College; Laura Calswell,University of Cincinnati; Charles
on page 32 for ordering information),is extensively used
Drake, Ferris State University; Lubambala Kabengela,
in this book.Tutorials and problems that utilize this
University of North Carolina at Charlotte; Sung Kim,
software are integrated into the book.
Piedmont Technical College; Michael J. Rider, Ohio
5. Suggestions for implementing the graphical techniques Northern University; and Gerald Weisman, University of
on computer-aided design (CAD) systems are included Vermont.
and illustrated throughout the book. DaveMyszka
iii
CONTENTS
1 Introduction to Mechanisms and 2 Building Computer Models of
Kinematics 1 Mechanisms Using Working Model®
Software 31
Objectives 1
1.1 Introduction 1 Objectives 31
1.2 Machines and Mechanisms 1 2.1 Introduction 31
1.3 Kinematics 2 2.2 Computer Simulation ofMechanisms 31
1.4 Mechanism Terminology 2 2.3 Obtaining Working Model Software 32
1.5 Kinematic Diagrams 4 2.4 Using Working Model to Model a Four-Bar
Mechanism 32
1.6 Kinematic Inversion 8
2.5 Using Working Model to Model a Slider-
1.7 Mobility 8
Crank Mechanism 37
1.7.1 Gruebler’s Equation 8
Problems 41
1.7.2 Actuators and Drivers 12
Case Studies 42
1.8 Commonly Used Links and Joints 14
1.8.1 Eccentric Crank 14
3 Vectors 43
1.8.2 Pin-in-a-Slot Joint 14
1.8.3 Screw Joint 15 Objectives 43
1.9 Special Cases ofthe Mobility Equation 16 3.1 Introduction 43
1.9.1 Coincident Joints 16 3.2 Scalars and Vectors 43
1.9.2 Exceptions to the Gruebler’s
3.3 Graphical Vector Analysis 43
Equation 18
3.4 Drafting Techniques Required in Graphical
1.9.3 Idle Degrees ofFreedom 18
Vector Analysis 44
1.10 The Four-Bar Mechanism 19
3.5 CAD Knowledge Required in Graphical Vector
1.10.1 Grashof’s Criterion 19 Analysis 44
1.10.2 Double Crank 20
3.6 Trigonometry Required in Analytical Vector
1.10.3 Crank-Rocker 20 Analysis 44
1.10.4 Double Rocker 20 3.6.1 Right Triangle 44
1.10.5 Change Point Mechanism 20 3.6.2 Oblique Triangle 46
1.10.6 Triple Rocker 20 3.7 Vector Manipulation 48
1.11 Slider-Crank Mechanism 22 3.8 Graphical Vector Addition (+7) 48
1.12 Special Purpose Mechanisms 22 3.9 Analytical Vector Addition (+7):Triangle
1.12.1 Straight-Line Mechanisms 22 Method 50
1.12.2 Parallelogram Mechanisms 22 3.10 Components ofa Vector 52
1.12.3 Quick-Return Mechanisms 23 3.11 Analytical Vector Addition (+7):Component
1.12.4 Scotch Yoke Mechanism 23 Method 53
1.13 Techniques ofMechanism Analysis 23 3.12 Vector Subtraction (-7) 55
1.13.1 Traditional Drafting Techniques 24 3.13 Graphical Vector Subtraction (-7) 55
1.13.2 CAD Systems 24 3.14 Analytical Vector Subtraction (-7):Triangle
1.13.3 Analytical Techniques 24 Method 57
1.13.4 Computer Methods 24 3.15 Analytical Vector Subtraction (-7):
Problems 25 Component Method 59
Case Studies 29 3.16 Vector Equations 60
iv
Contents v
3.17 Application ofVector Equations 62 5.2 Time Ratio 109
3.18 Graphical Determination ofVector 5.3 Timing Charts 110
Magnitudes 63 5.4 Design ofSlider-Crank Mechanisms 113
3.19 Analytical Determination ofVector 5.4.1 In-Line Slider-Crank Mechanism 113
Magnitudes 66
5.4.2 Offset Slider-Crank Mechanism 114
Problems 67
5.5 Design ofCrank-Rocker Mechanisms 115
Case Studies 71
5.6 Design ofCrank-Shaper Mechanisms 117
5.7 Mechanism to Move a Link Between Two
4 Position and Displacement
Positions 118
Analysis 72
5.7.1 Two-Position Synthesis with a Pivoting
Objectives 72 Link 118
5.7.2 Two-Position Synthesis ofthe Coupler
4.1 Introduction 72
ofa Four-Bar Mechanism 118
4.2 Position 72
5.8 Mechanism to Move a Link Between Three
4.2.1 Position ofa Point 72
Positions 119
4.2.2 Angular Position ofa Link 72
5.9 Circuit and Branch Defects 119
4.2.3 Position ofa Mechanism 73
Problems 120
4.3 Displacement 73
Case Studies 121
4.3.1 Linear Displacement 73
4.3.2 Angular Displacement 73
6 Velocity Analysis 123
4.4 Displacement Analysis 74
4.5 Displacement:Graphical Analysis 74 Objectives 123
4.5.1 Displacement ofa Single Driving 6.1 Introduction 123
Link 74 6.2 Linear Velocity 123
4.5.2 Displacement ofthe Remaining Slave 6.2.1 Linear Velocity ofRectilinear
Links 75 Points 123
4.6 Position:Analytical Analysis 79 6.2.2 Linear Velocity ofa General
4.6.1 Closed-Form Position Analysis Equations Point 124
for an In-Line Slider-Crank 81 6.2.3 Velocity Profile for Linear
4.6.2 Closed-Form Position Analysis Motion 124
Equations for an Offset Slider- 6.3 Velocity ofa Link 125
Crank 84
6.4 Relationship Between Linear and Angular
4.6.3 Closed-Form Position Equations for a Velocities 126
Four-Bar Linkage 87
6.5 Relative Velocity 128
4.6.4 Circuits ofa Four-Bar Linkage 87
6.6 Graphical Velocity Analysis:Relative Velocity
4.7 Limiting Positions:Graphical Analysis 87
Method 130
4.8 Limiting Positions:Analytical Analysis 91
6.6.1 Points on Links Limited to Pure
4.9 Transmission Angle 93 Rotation or Rectilinear
4.10 Complete Cycle:Graphical Position Translation 130
Analysis 94 6.6.2 General Points on a Floating
Link 132
4.11 Complete Cycle:Analytical Position
Analysis 96 6.6.3 Coincident Points on Different
Links 135
4.12 Displacement Diagrams 98
6.7 Velocity Image 137
4.13 Coupler Curves 101
6.8 Analytical Velocity Analysis:Relative Velocity
Problems 101
Method 137
Case Studies 108
6.9 Algebraic Solutions for Common
Mechanisms 142
5 Mechanism Design 109
6.9.1 Slider-Crank Mechanism 142
Objectives 109 6.9.2 Four-Bar Mechanism 142
5.1 Introduction 109 6.10 Instantaneous Center ofRotation 142
vi Contents
6.11 Locating Instant Centers 142 7.13.1 Graphical Differentiation 202
6.11.1 Primary Centers 143 7.13.2 Numerical Differentiation 204
6.11.2 Kennedy’s Theorem 144 Problems 206
6.11.3 Instant Center Diagram 144 Case Studies 213
6.12 Graphical Velocity Analysis:Instant Center
Method 149 8 Computer-Aided Mechanism
Analysis 215
6.13 Analytical Velocity Analysis:Instant Center
Method 152
Objectives 215
6.14 Velocity Curves 155
8.1 Introduction 215
6.14.1 Graphical Differentiation 157
8.2 Spreadsheets 215
6.14.2 Numerical Differentiation 159
8.3 User-Written Computer Programs 221
Problems 161
8.3.1 Offset Slider-Crank Mechanism 221
Case Studies 168
8.3.2 Four-Bar Mechanism 221
Problems 222
7 Acceleration Analysis 170
Case Study 222
Objectives 170
7.1 Introduction 170 9 Cams:Design and Kinematic
7.2 Linear Acceleration 170 Analysis 223
7.2.1 Linear Acceleration ofRectilinear
Objectives 223
Points 170
9.1 Introduction 223
7.2.2 Constant Rectilinear Acceleration 171
9.2 Types ofCams 223
7.2.3 Acceleration and the Velocity
Profile 171 9.3 Types ofFollowers 224
7.2.4 Linear Acceleration ofa General 9.3.1 Follower Motion 224
Point 173 9.3.2 Follower Position 224
7.3 Acceleration ofa Link 173 9.3.3 Follower Shape 225
7.3.1 Angular Acceleration 173 9.4 Prescribed Follower Motion 225
7.3.2 Constant Angular Acceleration 173 9.5 Follower Motion Schemes 227
7.4 Normal and Tangential Acceleration 174 9.5.1 Constant Velocity 228
7.4.1 Tangential Acceleration 174 9.5.2 Constant Acceleration 228
7.4.2 Normal Acceleration 175 9.5.3 Harmonic Motion 228
7.4.3 Total Acceleration 175 9.5.4 Cycloidal Motion 230
7.5 Relative Motion 177 9.5.5 Combined Motion Schemes 236
7.5.1 Relative Acceleration 177 9.6 Graphical Disk Cam Profile Design 237
7.5.2 Components ofRelative 9.6.1 In-Line Knife-Edge Follower 237
Acceleration 179 9.6.2 In-Line Roller Follower 238
7.6 Relative Acceleration Analysis:Graphical 9.6.3 Offset Roller Follower 239
Method 181
9.6.4 Translating Flat-Faced
7.7 Relative Acceleration Analysis:Analytical Follower 240
Method 188 9.6.5 Pivoted Roller Follower 241
7.8 Algebraic Solutions for Common 9.7 Pressure Angle 242
Mechanisms 190
9.8 Design Limitations 243
7.8.1 Slider-Crank Mechanism 190
9.9 Analytical Disk Cam Profile
7.8.2 Four-Bar Mechanism 191 Design 243
7.9 Acceleration ofa General Point on a Floating
9.9.1 Knife-Edge Follower 244
Link 191
9.9.2 In-Line Roller Follower 246
7.10 Acceleration Image 196
9.9.3 Offset Roller Follower 249
7.11 Coriolis Acceleration 197
9.9.4 Translating Flat-Faced
7.12 Equivalent Linkages 201 Follower 249
7.13 Acceleration Curves 202 9.9.5 Pivoted Roller Follower 250
Contents vii
9.10 Cylindrical Cams 251 11.4 Belt Drive Kinematics 305
9.10.1 Graphical Cylindrical Cam Profile 11.5 Chains 308
Design 251 11.5.1 Types ofChains 308
9.10.2 Analytical Cylindrical Cam Profile 11.5.2 Chain Pitch 309
Design 251
11.5.3 Multistrand Chains 309
9.11 The Geneva Mechanism 252
11.5.4 Sprockets 310
Problems 254
11.6 Chain Drive Geometry 310
Case Studies 258
11.7 Chain Drive Kinematics 311
Problems 313
10 Gears:Kinematic Analysis and
Case Studies 315
Selection 260
Objectives 260 12 Screw Mechanisms 316
10.1 Introduction 260
Objectives 316
10.2 Types ofGears 261
12.1 Introduction 316
10.3 Spur Gear Terminology 262
12.2 Thread Features 316
10.4 Involute Tooth Profiles 264
12.3 Thread Forms 316
10.5 Standard Gears 266
12.3.1 Unified Threads 317
10.6 Relationships ofGears in Mesh 268 12.3.2 Metric Threads 317
10.6.1 Center Distance 268 12.3.3 Square Threads 317
10.6.2 Contact Ratio 269 12.3.4 ACME Threads 317
10.6.3 Interference 270 12.4 Ball Screws 317
10.6.4 Undercutting 271 12.5 Lead 317
10.6.5 Backlash 272
12.6 Screw Kinematics 318
10.6.6 Operating Pressure Angle 273
12.7 Screw Forces and Torques 322
10.7 Spur Gear Kinematics 273
12.8 Differential Screws 324
10.8 Spur Gear Selection 275
12.9 Auger Screws 325
10.8.1 Diametral Pitch 276
Problems 325
10.8.2 Pressure Angle 276
Case Studies 328
10.8.3 Number ofTeeth 276
10.9 Rack and Pinion Kinematics 281
13 Static Force Analysis 330
10.10 Helical Gear Kinematics 282
Objectives 330
10.11 Bevel Gear Kinematics 285
13.1 Introduction 330
10.12 Worm Gear Kinematics 286
13.2 Forces 330
10.13 Gear Trains 288
13.3 Moments and Torques 330
10.14 Idler Gears 290
13.4 Laws ofMotion 333
10.15 Planetary Gear Trains 290
13.5 Free-Body Diagrams 333
10.15.1 Planetary Gear Analysis by
Superposition 291 13.5.1 Drawing a Free-Body Diagram 333
10.15.2 Planetary Gear Analysis by 13.5.2 Characterizing Contact Forces 333
Equation 293 13.6 Static Equilibrium 335
Problems 295 13.7 Analysis ofa Two-Force Member 335
Case Studies 299 13.8 Sliding Friction Force 341
Problems 343
11 Belt and Chain Drives 302
Case Study 345
Objectives 302
14 Dynamic Force Analysis 346
11.1 Introduction 302
11.2 Belts 302 Objectives 346
11.3 Belt Drive Geometry 304 14.1 Introduction 346
viii Contents
14.2 Mass and Weight 346 14.5 Inertial Force 352
14.3 Center ofGravity 347 14.6 Inertial Torque 357
14.4 Mass Moment ofInertia 348 Problems 363
14.4.1 Mass Moment ofInertia ofBasic Case Study 366
Shapes 348
Answers to Selected Even-Numbered
14.4.2 Radius ofGyration 350
Problems 367
14.4.3 Parallel Axis Theorem 350
References 370
14.4.4 Composite Bodies 351
Index 371
14.4.5 Mass Moment ofInertia—
Experimental Determination 352
CHAPTER
ONE
INTRODUCTION TO MECHANISMS
AND KINEMATICS
of different drivers.This information sets guidelines for the
OBJECTIVES required movement of the wipers.Fundamental decisions
must be made on whether a tandem or opposed wipe pat-
Upon completion ofthis chapter,the student will
tern better fits the vehicle. Other decisions include the
be able to:
amount of driver- and passenger-side wipe angles and the
1. Explain the need for kinematic analysis of
location of pivots.Figure 1.1 illustrates a design concept,
mechanisms.
incorporating an opposed wiper movement pattern.
2. Define the basic components that comprise a
Once the desired movement has been established,an
mechanism.
assembly of components must be configured to move the
3. Draw a kinematic diagram from a view ofa complex wipers along that pattern.Subsequent tasks include analyz-
machine. ing other motion issues such as timing of the wipers and
4. Compute the number ofdegrees offreedom ofa whipping tendencies. For this wiper system, like most
mechanism. machines,understanding and analyzing the motion is neces-
5. Identify a four-bar mechanism and classify it according sary for proper operation.These types of movement and
to its possible motion. motion analyses are the focus ofthis textbook.
Another major task in designing machinery is deter-
6. Identify a slider-crank mechanism.
mining the effect of the forces acting in the machine.These
forces dictate the type of power source that is required to
1.1 INTRODUCTION operate the machine.The forces also dictate the required
strength of the components.For instance,the wiper system
Imagine being on a design and development team.The team must withstand the friction created when the windshield is
is responsible for the design of an automotive windshield coated with sap after the car has been parked under a tree.
wiper system.The proposed vehicle is a sports model with This type of force analysis is a major topic in the latter
an aerodynamic look and a sloped windshield.Ofcourse,the portion ofthis text.
purpose of this wiper system is to clean water and debris
from the windshield, giving clear vision to the driver.
Typically,this is accomplished by sweeping a pair of wipers 1.2 MACHINES AND MECHANISMS
across the glass.
One ofthe first design tasks is determining appropriate Machinesare devices used to alter,transmit,and direct forces
movements of the wipers.The movements must be suffi- to accomplish a specific objective.A chain saw is a familiar
cient to ensure that critical portions of the windshield are machine that directs forces to the chain with the objective of
cleared.Exhaustive statistical studies reveal the view ranges cutting wood.A mechanism is the mechanical portion of a
FIGURE 1.1 Proposed windshield wiper movements.
1