Kinematics, Dynamics, and Design of Machinery

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ISBN: 9780471244172 | 0471244171
Cover: Paperback
Copyright: 10/24/2003

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* The book introduces spatial mechanisms using both vectors and matrices, which introduces the topic from two vantage points. * Comprehensive and authoritative coverage. * Several real-world problems are included to show how to apply the basic principles in a realistic setting.

CHAPTER 1 INTRODUCTION

(59)

1.1 Historic Perspective

(1)

1.2 Kinematics

(1)

1.3 Design: Analysis and Synthesis

(1)

1.4 Mechanisms

(4)

1.5 Planar Linkages

(2)

1.6 Visualization

(2)

1.7 Constraint Analysis

(7)

1.8 Constraint Analysis of Spatial Linkages

(5)

1.9 Idle Degrees of Freedom

(2)

1.10 Overconstrained Linkages

(4)

1.11 Uses of the Mobility Criterion

(1)

1.12 Inversion

(1)

1.13 Reference Frames

(1)

1.14 Motion Limits

(1)

1.15 Actuation

(5)

1.16 Coupler-Driven Linkages

(1)

1.17 Motion Limits for Slider-Crank Mechanism

(2)

1.18 Interference

(4)

1.19 Practical Design Considerations

(10)

1.19.1 Revolute Joints

(2)

1.19.2 Prismatic Joints

(1)

1.19.3 Higher Pairs

(1)

1.19.4 Cams vs. Linkages

(1)

1.19.5 Actuation

(6)

Problems

(6)

CHAPTER 2 GRAPHICAL POSITION, VELOCITY, AND ACCELERATION ANALYSIS FOR MECHANISMS WITH REVOLUTE JOINTS OR FIXED SLIDES

(36)

2.1 Introduction

(1)

2.2 Graphical Position Analysis

(1)

2.3 Planar Velocity Polygons

(3)

2.4 Graphical Acceleration Analysis

(2)

2.5 Graphical Analysis of a Four-Bar Mechanism

(7)

2.6 Graphical Analysis of a Slider-Crank Mechanism

(2)

2.7 The Velocity Image Theorem

(3)

2.8 The Acceleration Image Theorem

(5)

2.9 Solution by Inversion

(5)

Problems

(7)

CHAPTER 3 LINKAGES WITH ROLLING AND SLIDING CONTACTS AND JOINTS ON MOVING SLIDERS

(49)

3.1 Introduction

(1)

3.2 Reference Frames

(2)

3.3 General Velocity and Acceleration Equations

(6)

3.3.1 Velocity Equations

(3)

3.3.2 Acceleration Equations

101

(1)

3.3.3 Chain Rule for Positions, Velocities, and Accelerations

101

(3)

3.4 Special Cases for the Velocity and Acceleration Equations

104

(2)

3.4.1 Points P and Q Fixed to B

104

(1)

3.4.2 P and Q Are Coincident

105

(1)

3.4.3 P and Q Are Coincident and in Rolling Contact

105

(1)

3.5 Linkages with Rotating Sliding Joints

106

(5)

3.6 Rolling Contact

111

(10)

3.6.1 Basic Kinematic Relationships for Rolling Contact

112

(6)

3.6.2 Modeling Rolling Contact Using a Virtual Linkage

118

(3)

3.7 Cam Contact

121

(7)

3.7.1 Direct Approach to the Analysis of Cam Contact

121

(3)

3.7.2 Analysis of Cam Contact Using Equivalent Linkages

124

(4)

3.8 General Coincident Points

128

(8)

3.8.1 Velocity Analyses Involving General Coincident Points

130

(1)

3.8.2 Acceleration Analyses Involving General Coincident Points

130

(6)

Problems

136

(9)

CHAPTER 4 INSTANT CENTERS OF VELOCITY

145

(26)

4.1 Introduction

145

(1)

4.2 Definition

145

(1)

4.3 Existence Proof

146

(1)

4.4 Location of an Instant Center from the Directions of Two Velocities

147

(1)

4.5 Instant Center at a Revolute Joint

148

(1)

4.6 Instant Center of a Curved Slider

148

(1)

4.7 Instant Center of a Prismatic Joint

148

(1)

4.8 Instant Center of a Rolling Contact Pair

149

(1)

4.9 Instant Center of a General Cam-Pair Contact

149

(1)

4.10 Centrodes

150

(3)

4.11 The Kennedy-Aronholdt Theorem

153

(2)

4.12 Circle Diagram as a Strategy for Finding Instant Centers

155

(1)

4.13 Using Instant Centers: The Rotating-Radius Method

156

(8)

4.14 Finding Instant Centers Using Drafting Programs

164

(1)

Problems

165

(6)

CHAPTER 5 ANALYTICAL LINKAGE ANALYSIS

171

(86)

5.1 Introduction

171

(1)

5.2 Position, Velocity, and Acceleration Representations

172

(3)

5.2.1 Position Representation

172

(1)

5.2.2 Velocity Representation

172

(2)

5.2.3 Acceleration Representation

174

(1)

5.2.4 Special Cases

175

(1)

5.2.5 Mechanisms to Be Considered

175

(1)

5.3 Analytical Closure Equations for Four-Bar Linkages

175

(9)

5.3.1 Solution of Closure Equations for Four-Bar Linkages When Link 2 Is the Driver

176

(3)

5.3.2 Analysis When the Coupler (Link 3) Is the Driving Link

179

(1)

5.3.3 Velocity Equations for Four-Bar Linkages

179

(2)

5.3.4 Acceleration Equations for Four-Bar Linkages

181

(3)

5.4 Analytical Equations for a Rigid Body after the Kinematic Properties of Two Points Are Known

184

(3)

5.5 Analytical Equations for Slider-Crank Mechanisms

187

(13)

5.5.1 Solution to Position Equations When θ2 Is Input

190

(2)

5.5.2 Solution to Position Equations When r1 Is Input

192

(1)

5.5.3 Solution to Position Equations When θ3 Is Input

193

(1)

5.5.4 Velocity Equations for Slider-Crank Mechanism

194

(1)

5.5.5 Acceleration Equations for Slider-Crank Mechanism

195

(5)

5.6 Analytical Equations for the Slider-Crank Inversion

200

(11)

5.6.1 Solution to Position Equations When θ2 Is Input

202

(2)

5.6.2 Solution to Position Equations When &theta3 Is Input

204

(1)

5.6.3 Solution to Position Equations When r3 Is Input

204

(1)

5.6.4 Velocity Equations for the Slider-Crank Inversion

205

(2)

5.6.5 Acceleration Equations for the Slider-Crank Inversion

207

(4)

5.7 Analytical Equations for an RPRP Mechanism

211

(7)

5.7.1 Solution of Closure Equations When θ2 Is Known

212

(1)

5.7.2 Solution of Closure Equations When r4 Is Known

213

(2)

5.7.3 Solution of Closure Equations When r3 Is Known

215

(1)

5.7.4 Velocity and Acceleration Equations for an RPRP Mechanism

216

(2)

5.8 Analytical Equations for an RRPP Mechanism

218

(5)

5.8.1 Solution When θ2 Is Known

219

(1)

5.8.2 Solution When r1 Is Known

220

(1)

5.8.3 Solution When r3 Is Known

221

(2)

5.9 Analytical Equations for Elliptic Trammel

223

(5)

5.9.1 Analysis When θ3 Is Known

224

(1)

5.9.2 Analysis When r1 Is Known

225

(3)

5.10 Analytical Equations for the Oldham Mechanism

228

(5)

5.10.1 Analysis When θ2 Is Known

229

(1)

5.10.2 Analysis When r2 Is Known

230

(3)

5.11 Closure or Loop-Equation Approach for Compound Mechanisms

233

(10)

5.11.1 Handling Points Not on the Vector Loops

236

(1)

5.11.2 Solving the Position Equations

237

(6)

5.12 Closure Equations for Mechanisms with Higher Pairs

243

(5)

5.13 Notational Differences: Vectors and Complex Numbers

248

(3)

Problems

251

(6)

CHAPTER 6 PLANAR LINKAGE DESIGN

257

(72)

6.1 Introduction

257

(3)

6.2 Two-Position Double-Rocker Design

260

(3)

6.2.1 Graphical Solution Procedure

260

(1)

6.2.2 Analytical Solution Procedure

261

(2)

6.3 Motion Generation

263

(20)

6.3.1 Introduction

263

(1)

6.3.2 Two Positions

263

(3)

6.3.3 Three Positions with Selected Moving Pivots

266

(1)

6.3.4 Synthesis of a Crank with Chosen Fixed Pivots

266

(2)

6.3.5 Design of Slider-Cranks and Elliptic Trammels

268

(2)

6.3.6 Order Problem and Change of Branch

270

(6)

6.3.7 Analytical Approach to Rigid-Body Guidance

276

(7)

6.4 Function Generation

283

(11)

6.4.1 Function Generation Using a Four-Bar Linkage

285

(2)

6.4.2 Design Procedure When y = y(x) Is to Be Generated

287

(1)

6.4.3 Selection of Design Positions

288

(1)

6.4.4 Summary of Solution Procedure for Four-Bar Linkage and Three Precision Points

289

(4)

6.4.5 Graphical Approach to Function Generation

293

(1)

6.5 Synthesis of Crank-Rocker Linkages for Specified Rocker Amplitude

294

(14)

6.5.1 Extreme Rocker Positions and Simple Analytical Solution

294

(1)

6.5.2 The Rocker Amplitude Problem: Graphical Approach

295

(5)

6.5.3 Transmission Angle

300

(1)

6.5.4 Alternative Graphical Design Procedure Based on Specification of ο2-ο4

301

(3)

6.5.5 Analytical Design Procedure Based on Specification of ο2-ο4

304

(3)

6.5.6 Use of Analytical Design Procedure for Optimization

307

(1)

6.6 Path Synthesis

308

(12)

6.6.1 Design of Six-Bar Linkages Using Coupler Curves

309

(6)

6.6.2 Motion Generation for Parallel Motion Using Coupler Curves

315

(3)

6.6.3 Four-Bar Cognate Linkages

318

(2)

References

320

(1)

Problems

321

(8)

CHAPTER 7 SPECIAL MECHANISMS

329

(33)

7.1 Special Planar Mechanisms

329

(11)

7.1.1 Introduction

329

(1)

7.1.2 Approximate Straight-Line Mechanisms

329

(3)

7.1.3 Exact Straight-Line Mechanisms

332

(1)

7.1.4 Pantographs

333

(7)

7.2 Spherical Linkages

340

(7)

7.2.1 Introduction

340

(3)

7.2.2 Gimbals

343

(1)

7.2.3 Universal Joints

343

(4)

7.3 Constant-Velocity Couplings

347

(2)

7.3.1 Geometric Requirements of Constant Velocity Couplings

347

(1)

7.3.2 Practical Constant-Velocity Couplings

347

(2)

7.4 Automotive Steering and Suspension Mechanisms

349

(5)

7.4.1 Introduction

349

(1)

7.4.2 Steering Mechanisms

349

(4)

7.4.3 Suspension Mechanisms

353

(1)

7.5 Indexing Mechanisms

354

(5)

7.5.1 Geneva Mechanisms

354

(5)

References

359

(1)

Problems

360

(2)

CHAPTER 8 PROFILE CAMDESIGN

362

(59)

8.1 Introduction

362

(1)

8.2 Cam-Follower Systems

363

(1)

8.3 Synthesis of Motion Programs

364

(2)

8.4 Analysis of Different Types of Follower Displacement Functions

366

(1)

8.5 Uniform Motion

367

(1)

8.6 Parabolic Motion

368

(5)

8.7 Harmonic Follower-Displacement Programs

373

(2)

8.8 Cycloidal Follower-Displacement Programs

375

(1)

8.9 General Polynomial Follower-Displacement Programs

376

(5)

8.10 Determining the Cam Profile

381

(36)

8.10.1 Graphical Cam Profile Layout

381

(10)

8.10.2 Analytical Determination of Cam Profile

391

(26)

References

417

(1)

Problems

417

(4)

CHAPTER 9 SPATIAL LINKAGE ANALYSIS

421

(37)

9.1 Spatial Mechanisms

421

(7)

9.1.1 Introduction

421

(1)

9.1.2 Velocity and Acceleration Relationships

422

(6)

9.2 Robotic Mechanisms

428

(1)

9.3 Direct Position Kinematics of Serial Chains

429

(9)

9.3.1 Introduction

429

(2)

9.3.2 Concatenation of Transformations

431

(4)

9.3.3 Homogeneous Transformations

435

(3)

9.4 Inverse Position Kinematics

438

(1)

9.5 Direct and Inverse Velocity Problems

438

(7)

9.5.1 Introduction

438

(1)

9.5.2 Direct Rate Kinematics

439

(5)

9.5.3 Inverse Velocity Problem

444

(1)

9.6 Closed-Loop Linkages

445

(3)

9.7 Lower Pair Joints

448

(4)

9.8 Motion Platforms

452

(2)

9.8.1 Mechanisms Actuated in Parallel

452

(1)

9.8.2 The Stewart Platform

452

(2)

9.8.3 The 3-2-1 Platform

454

(1)

References

454

(1)

Problems

454

(4)

CHAPTER 10 SPUR GEARS

458

(38)

10.1 Introduction

458

(1)

10.2 Spur Gears

459

(1)

10.3 Condition for Constant-Velocity Ratio

460

(1)

10.4 Involutes

461

(3)

10.5 Gear Terminology and Standards

464

(3)

10.5.1 Terminology

464

(1)

10.5.2 Standards

465

(2)

10.6 Contact Ratio

467

(4)

10.7 Involutometry

471

(3)

10.8 Internal Gears

474

(1)

10.9 Gear Manufacturing

475

(4)

10.10 Interference and Undercutting

479

(3)

10.11 Nonstandard Gearing

482

(5)

10.12 Cartesian Coordinates of an Involute Tooth Generated with a Rack

487

(7)

10.12.1 Coordinate Systems

487

(4)

10.12.2 Gear Equations

491

(3)

References

494

(1)

Problems

494

(2)

CHAPTER 11 HELICAL, BEVEL, AND WORM GEARS

496

(34)

11.1 Helical Gears

496

(17)

11.1.1 Helical Gear Terminology

497

(4)

11.1.2 Helical Gear Manufacturing

501

(1)

11.1.3 Minimum Tooth Number to Avoid Undercutting

501

(2)

11.1.4 Helical Gears with Parallel Shafts

503

(6)

11.1.5 Crossed Helical Gears

509

(4)

11.2 Worm Gears

513

(4)

11.2.1 Worm Gear Nomenclature

514

(3)

11.3 Involute Bevel Gears

517

(11)

11.3.1 Tredgold's Approximation for Bevel Gears

519

(1)

11.3.2 Additional Nomenclature for Bevel Gears

520

(1)

11.3.3 Crown Bevel Gears and Face Gears

521

(2)

11.3.4 Miter Gears

523

(1)

11.3.5 Angular Bevel Gears

524

(1)

11.3.6 Zerol Bevel Gears

524

(1)

11.3.7 Spiral Bevel Gears

525

(1)

11.3.8 Hypoid Gears

526

(2)

References

528

(1)

Problems

528

(2)

CHAPTER 12 GEAR TRAINS

530

(29)

12.1 Gear Trains

530

(1)

12.2 Direction of Rotation

530

(1)

12.3 Simple Gear Trains

531

(3)

12.3.1 Simple Reversing Mechanism

533

(1)

12.4 Compound Gear Trains

534

(6)

12.4.1 Concentric Gear Trains

537

(3)

12.5 Planetary Gear Trains

540

(14)

12.5.1 Planetary Gear Nomenclature

542

(2)

12.5.2 Analysis of Planetary Gear Trains Using Equations

544

(6)

12.5.3 Analysis of Planetary Gear Trains Using the Tabular Method

550

(4)

References

554

(1)

Problems

554

(5)

CHAPTER 13 STATIC FORCEANALYSIS OF MECHANISMS

559

(49)

13.1 Introduction

559

(1)

13.2 Forces, Moments, and Couples

560

(2)

13.3 Static Equilibrium

562

(1)

13.4 Free-Body Diagrams

562

(3)

13.5 Graphical Force Analysis

565

(8)

13.6 Analytical Approach to Force Analysis

573

(5)

13.6.1 Transmission Angle in a Four-Bar Linkage

575

(3)

13.7 Friction Considerations

578

(8)

13.7.1 Friction in Cam Contact

579

(1)

13.7.2 Friction in Slider Joints

579

(2)

13.7.3 Friction in Revolute Joints

581

(5)

13.8 In-Plane and Out-of-Plane Force Systems

586

(4)

13.9 Conservation of Energy and Power

590

(5)

13.10 Virtual Work

595

(2)

13.11 Gear Loads

597

(7)

13.11.1 Spur Gears

597

(2)

13.11.2 Helical Gears

599

(2)

13.11.3 Worm Gears

601

(2)

13.11.4 Straight Bevel Gears

603

(1)

Problems

604

(4)

CHAPTER 14 DYNAMIC FORCEANALYSIS

608

(21)

14.1 Introduction

608

(2)

14.2 Problems Soluble via Particle Kinetics

610

(8)

14.2.1 Dynamic Equilibrium of Systems of Particles

610

(5)

14.2.2 Conservation of Energy

615

(1)

14.2.3 Conservation of Momentum

615

(3)

14.3 Dynamic Equilibrium of Systems of Rigid Bodies

618

(6)

14.4 Flywheels

624

(22)

Problems

646

CHAPTER 15 SHAKING FORCESAND BALANCING

629

(33)

15.1 Introduction

629

(1)

15.2 Single-Plane (Static) Balancing

630

(3)

15.3 Multiplane (Dynamic) Balancing

633

(6)

15.4 Balancing Reciprocating Masses

639

(7)

15.4.1 Expression for Lumped Mass Distribution

640

(3)

15.4.2 Analytical Approach to Balancing a Slider-Crank Mechanism

643

(3)

15.5 Expressions for Inertial Forces

646

(3)

15.6 Balancing Multicylinder Machines

649

(8)

15.6.1 Balancing a Three-Cylinder In-Line Engine

653

(2)

15.6.2 Balancing an Eight-Cylinder V Engine

655

(2)

References

657

(1)

Problems

657

(5)

INDEX

662

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Kinematics, Dynamics, and Design of Machinery

Summary

Table of Contents

Supplemental Materials

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Kinematics, Dynamics, and Design of Machinery

Summary

Table of Contents

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