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Contents

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 ? 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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