Kinematics, Dynamics, and Design of Machinery

• Presents the traditional approach to the design and analysis of kinematic problems and shows how GCP can be used to solve the same problems more simply
• Provides a new and simpler approach to cam design
• Includes an increased number of exercise problems
• Accompanied by a website hosting a solutions manual, teaching slides and MATLAB® programs

Kenneth Waldron is Professor at the University of Technology, Sydney and Professor Emeritus of Stanford University. He has taught subjects in machine design and engineering mechanics over a career spanning more than forty years. He has also conducted research in kinematics of machinery, robotics, biomechanics and machine dynamics. He has received a number of awards including the American Society of Mechanical Engineers (ASME) Machine Design, Leonardo da Vinci and Ruth and Joel Spira Outstanding Design Educator Awards, and the Robotics Industries Association Joseph Engelberger Award.
Professor Waldron has served as the Technical Editor of the ASME Transactions Journal of Machine Design. He served two terms as President of IFToMM, the International Federation for the Promotion of Machine and Mechanism Science, as well as holding many offices within ASME.
Professor Waldron is excited by the many new developments in the field and the challenge of keeping this book up to date.

Gary Kinzel is an emeritus professor in the Department of Mechanical and Aerospace Engineering at The Ohio State University. He received his PhD from Purdue in 1973. After graduation, he worked for six years at Battelle and was a regular faculty member at Ohio State until he retired in 2011. His research was in design, education, and manufacturing. He has more than 150 research publications, has coauthored two books, has one patent, and has supervised to completion the research of more than one hundred graduate students. He taught courses in machine design, kinematics, stress analysis and form synthesis and received ten research and teaching awards, including the OSU Alumni Teaching Award, the ASME Ruth and Joel Spira Outstanding Design Educator Award, and the ASEE Ralph Coates Roe Award.

Sunil Agrawal has authored more than 175 archival journal papers, 225 refereed conference papers, 2 books, and 13 US patents. His work is well cited by the research community and can be viewed at Google Scholar at (scholar.google.com/citations). He has graduated 20 PhD and 25 MS students. Currently, there are 10 PhD students working under his guidance.

Preface xiii

1 Introduction 1

1.1 Historical Perspective, 1

1.2 Kinematics, 3

1.3 Design: Analysis and Synthesis, 4

1.4 Mechanisms, 4

1.5 Planar Linkages, 6

1.6 Visualization, 9

1.7 Constraint Analysis, 12

1.8 Constraint Analysis of Spatial Linkages, 18

1.9 Idle Degrees of Freedom, 22

1.10 Overconstrained Linkages, 24

1.11 Uses of the Mobility Criterion, 28

1.12 Inversion, 28

1.13 Reference Frames, 29

1.14 Motion Limits, 30

1.15 Continuously Rotatable Joints, 31

1.16 Coupler-Driven Linkages, 35

1.17 Motion Limits for Slider-Crank Mechanisms, 35

1.18 Interference, 38

1.19 Practical Design Considerations, 41

References, 44

Problems, 45

2 Techniques in Geometric Constraint Programming 59

2.1 Introduction, 59

2.2 Geometric Constraint Programming, 60

2.3 Constraints and Program Structure, 61

2.4 Initial Setup for a GCP Session, 64

2.5 Drawing a Basic Linkage Using GCP, 66

2.6 Troubleshooting Graphical Programs Developed Using GCP, 79

References, 80

Problems, 81

Appendix 2A Drawing Slider Lines, Pin Bushings, and Ground Pivots, 85

2A.1 Slider Lines, 85

2A.2 Pin Bushings and Ground Pivots, 87

Appendix 2B Useful Constructions When Equation Constraints Are Not Available, 88

2B.1 Constrain Two Angles to Be Integral Multiples of Another Angle, 89

2B.2 Constrain a Line to Be Half the Length of Another Line, 89

2B.3 Construction for Scaling, 90

2B.4 Construction for Square Ratio v2/r, 91

2B.5 Construction for Function x ˆ yz=r, 91

3 Planar Linkage Design 93

3.1 Introduction, 93

3.2 Two-Position Double-Rocker Design, 96

3.3 Synthesis of Crank-Rocker Linkages for Specified Rocker Amplitude, 100

3.4 Motion Generation, 114

3.5 Path Synthesis, 133

References, 148

Problems, 150

4 Graphical Position, Velocity, and Acceleration Analysis for Mechanisms with Revolute Joints or Fixed Slides 169

4.1 Introduction, 169

4.2 Graphical Position Analysis, 170

4.3 Planar Velocity Polygons, 171

4.4 Graphical Acceleration Analysis, 173

4.5 Graphical Analysis of a Four-Bar Mechanism, 175

4.6 Graphical Analysis of a Slider-Crank Mechanism, 183

4.7 Velocity Image Theorem, 186

4.8 Acceleration Image Theorem, 189

4.9 Solution by Geometric Constraint Programming, 194

References, 205

Problems, 205

5 Linkages with Rolling and Sliding Contacts, and Joints on Moving Sliders 221

5.1 Introduction, 221

5.2 Reference Frames, 222

5.3 General Velocity and Acceleration Equations, 223

5.4 Special Cases for the Velocity and Acceleration Equations, 228

5.5 Linkages with Rotating Sliding Joints, 230

5.6 Rolling Contact, 235

5.7 Cam Contact, 243

5.8 General Coincident Points, 250

5.9 Solution by Geometric Constraint Programming, 257

Problems, 263

6 Instant Centers of Velocity 279

6.1 Introduction, 279

6.2 Definition, 280

6.3 Existence Proof, 280

6.4 Location of an Instant Center from the Directions of Two Velocities, 281

6.5 Instant Center at a Revolute Joint, 282

6.6 Instant Center of a Curved Slider, 282

6.7 Instant Center of a Prismatic Joint, 282

6.8 Instant Center of a Rolling Contact Pair, 282

6.9 Instant Center of a General Cam-Pair Contact, 282

6.10 Centrodes, 283

6.11 The Kennedy-Aronhold Theorem, 285

6.12 Circle Diagram as a Strategy for Finding Instant Centers, 287

6.13 Using Instant Centers to Find Velocities: The Rotating-Radius Method, 287

6.14 Finding Instant Centers Using Geometric Constraint Programming, 295

References, 300

Problems, 300

7 Computational Analysis of Linkages 315

7.1 Introduction, 315

7.2 Position, Velocity, and Acceleration Representations, 316

7.3 Analytical Closure Equations for Four-Bar Linkages, 319

7.4 Analytical Equations for a Rigid Body after the Kinematic Properties of Two Points Are Known, 326

7.5 Analytical Equations for Slider-Crank Mechanisms, 329

7.6 Other Four-Bar Mechanisms with Revolute and Prismatic Joints, 338

7.7 Closure or Loop Equation Approach for Compound Mechanisms, 341

7.8 Closure Equations for Mechanisms with Higher Pairs, 347

7.9 Notational Differences: Vectors and Complex Numbers, 352

Problems, 354

8 Special Mechanisms 361

8.1 Special Planar Mechanisms, 361

8.2 Spherical Mechanisms, 374

8.3 Constant-Velocity Couplings, 381

8.4 Automotive Steering and Suspension Mechanisms, 382

8.5 Indexing Mechanisms, 387

References, 392

Problems, 392

9 Computational Analysis of Spatial Linkages 395

9.1 Spatial Mechanisms, 395

9.2 Robotic Mechanisms, 401

9.3 Direct Position Kinematics of Serial Chains, 403

9.4 Inverse Position Kinematics, 410

9.5 Rate Kinematics, 410

9.6 Closed-Loop Linkages, 416

9.7 Lower-Pair Joints, 418

9.8 Motion Platforms, 421

References, 423

Problems, 423

10 Profile Cam Design 431

10.1 Introduction, 431

10.2 Cam-Follower Systems, 432

10.3 Synthesis of Motion Programs, 434

10.4 Analysis of Different Types of Follower-Displacement Functions, 436

10.5 Determining the Cam Profile, 448

References, 482

Problems, 482

11 Spur Gears 489

11.1 Introduction, 489

11.2 Spur Gears, 490

11.3 Condition for Constant-Velocity Ratio, 491

11.4 Involutes, 492

11.5 Gear Terminology and Standards, 494

11.6 Contact Ratio, 497

11.7 Involutometry, 501

11.8 Internal Gears, 504

11.9 Gear Manufacturing, 505

11.10 Interference and Undercutting, 508

11.11 Nonstandard Gearing, 510

11.12 Cartesian Coordinates of an Involute Tooth Generated with a Rack, 514

References, 520

Problems, 520

12 Helical, Bevel, and Worm Gears 523

12.1 Helical Gears, 523

12.2 Worm Gears, 536

12.3 Involute Bevel Gears, 540

References, 547

Problems, 547

13 Gear Trains 549

13.1 General Gear Trains, 549

13.2 Direction of Rotation, 549

13.3 Simple Gear Trains, 550

13.4 Compound Gear Trains, 552

13.5 Planetary Gear Trains, 558

13.6 Harmonic Drive Speed Reducers, 570

References, 572

Problems, 572

14 Static Force Analysis of Mechanisms 579

14.1 Introduction, 579

14.2 Forces, Moments, and Couples, 580

14.3 Static Equilibrium, 581

14.4 Free-Body Diagrams, 582

14.5 Solution of Static Equilibrium Problems, 585

14.6 Transmission Angle in a Four-Bar Linkage, 587

14.7 Friction Considerations, 590

14.8 In-Plane and Out-of-Plane Force Systems, 597

14.9 Conservation of Energy and Power, 601

14.10 Virtual Work, 605

14.11 Gear Loads, 607

Problems, 613

15 Dynamic Force Analysis of Mechanisms 623

15.1 Introduction, 623

15.2 Problems Solvable Using Particle Kinetics, 625

15.3 Dynamic Equilibrium of Systems of Rigid Bodies, 633

15.4 Flywheels, 639

Problems, 641

16 Static and Dynamic Balancing 645

16.1 Introduction, 645

16.2 Single-Plane (Static) Balancing, 646

16.3 Multi-Plane (Dynamic) Balancing, 649

16.4 Balancing Reciprocating Masses, 654

16.5 Expressions for Inertial Forces, 661

16.6 Balancing Multi-Cylinder Machines, 663

16.7 Static Balancing of Mechanisms, 671

16.8 Reactionless Mechanisms, 675

References, 676

Problems, 676

17 Integration of Computer Controlled Actuators 685

17.1 Introduction, 685

17.2 Computer Control of the Linkage Motion, 686

17.3 The Basics of Feedback Control, 687

17.4 Actuator Selection and Types, 688

17.5 Hands-On Machine-Design Laboratory, 694

References, 696

Problems, 696

Index 699

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