Machine Analysis with Computer Applications for Mechanical Engineers

JAMES DOANE Frontier-Kemper Constructors, Indiana, USA

Preface xv

Acknowledgments xvii

About the companion website xix

1 Introductory Concepts 1

1.1 Introduction to Machines 1

1.2 Units 6

1.3 Machines and Mechanisms 10

1.4 Linkage Mechanisms 14

1.5 Common Types of Linkage Mechanisms 16

1.6 Gears 21

1.7 Cams 27

1.8 Solution Methods 28

1.9 Methods of Problem Solving 30

1.10 Review and Summary 31

Problems 31

Further Reading 33

2 Essential Kinematics Concepts 34

2.1 Introdction 34

2.2 Basic Concepts of Velocity and Acceleration 35

2.3 Translational Motion 35

2.4 Rotation about a Fixed Axis 36

2.5 General Plane Motion 41

2.6 Computer Methods 53

2.7 Review and Summary 58

Problems 58

Further Reading 65

3 Linkage Position Analysis 66

3.1 Introduction 66

3.2 Mobility 67

3.3 Inversion 72

3.4 Grashof’s Criterion 72

3.5 Coupler Curves 74

3.6 Cognate Linkages 76

3.7 Transmission Angle 79

3.8 Geometrical Method of Position Analysis 80

3.9 Analytical Position Analysis 92

3.10 Toggle Positions 100

3.11 Computer Methods for Position Analysis 100

3.12 Review and Summary 103

Problems 103

Further Reading 107

4 Linkage Velocity and Acceleration Analysis 108

4.1 Introduction 108

4.2 Finite Displacement: Approximate Velocity Analysis 109

4.3 Instantaneous Centers of Rotation 111

4.4 Graphical Velocity Analysis 119

4.5 Analytical Velocity Analysis Methods 125

4.6 Graphical Acceleration Analysis Methods 130

4.7 Analytical Acceleration Analysis Methods 134

4.8 Kinematic Analysis of Linkage Mechanisms with Moving Slides 135

4.9 Review and Summary 147

Problems 147

Further Reading 153

5 Linkage Synthesis 154

5.1 Introduction 154

5.2 Synthesis 155

5.3 Two-Position Graphical Dimensional Synthesis 156

5.4 Three-Position Graphical Dimensional Synthesis 162

5.5 Approximate Dwell Linkage Mechanisms 167

5.6 Quick Return Mechanisms 169

5.7 Function Generation 176

5.8 Review and Summary 182

Problems 182

Further Reading 189

6 Computational Methods for Linkage Mechanism Kinematics 190

6.1 Introduction 190

6.2 Matrix Review 190

6.3 Position Equations 196

6.4 Velocity Analysis 206

6.5 Acceleration Equations 209

6.6 Dynamic Simulation Using Autodesk Inventor 210

6.7 Review and Summary 211

Problems 212

Further Reading 214

7 Gear Analysis 215

7.1 Introduction 215

7.2 Involute Curves 216

7.3 Terminology 219

7.4 Tooth Contact 228

7.5 Analysis of Spur Gears 234

7.6 Analysis of Parallel Helical Gears 239

7.7 Analysis of Crossed Helical Gears 242

7.8 Analysis of Bevel Gears 246

7.9 Analysis of Worm Gearing 249

7.10 Review and Summary 252

Problems 252

Further Reading 254

8 Gear Trains 255

8.1 Introduction 255

8.2 Simple Gear Trains 256

8.3 Compound Gear Trains 258

8.4 Reverted Compound Gear Trains 262

8.5 Gear Trains with Different Types of Gears 264

8.6 Planetary Gear Trains 266

8.7 Differentials 273

8.8 Computer Methods for Gear Train Design 274

8.9 Review and Summary 274

Problems 275

Further Reading 279

9 Cams 280

9.1 Introduction 280

9.2 Types of Cams and Followers 281

9.3 Basic Concepts of Cam Geometry and Cam Profiles 283

9.4 Common Cam Functions 285

9.5 Using Cam Functions for Specific Applications 295

9.6 Application of Cam Functions for Double-Dwell Mechanisms 299

9.7 Application of Cam Functions for Single-Dwell Mechanisms 301

9.8 Application of Cam Functions for Critical Path Motion 308

9.9 Cam Geometry 310

9.10 Determining Cam Size 312

9.11 Design of Cam Profiles 316

9.12 Computer Methods for Cam Design 322

9.13 Review and Summary 322

Problems 323

Reference 327

10 Vibration Theory 328

10.1 Introduction 328

10.2 System Components 329

10.3 Frequency and Period 333

10.4 Undamped Systems 333

10.5 Torsional Systems 344

10.6 Damped Systems 346

10.7 Logarithmic Decrement 353

10.8 Forced Vibration: Harmonic Forcing Functions 356

10.9 Response of Undamped Systems to General Loading 372

10.10 Review and Summary 381

Problems 381

Further Reading 386

11 Dynamic Force Analysis 387

11.1 Introduction 387

11.2 Superposition Method of Force Analysis 388

11.3 Matrix Method Force Analysis 399

11.4 Sliding Joint Forces 405

11.5 Energy Methods of Force Analysis: Method of Virtual Work 410

11.6 Force Analysis for Slider–Crank Mechanisms Using Lumped Mass 412

11.7 Gear Forces 416

11.8 Computer Methods 418

11.9 Review and Summary 418

Problems 419

Further Reading 421

12 Balancing of Machinery 422

12.1 Introduction 422

12.2 Static Balancing 423

12.3 Dynamic Balancing 431

12.4 Vibration from Rotating Unbalance 437

12.5 Balancing Slider–Crank Linkage Mechanisms 439

12.6 Balancing Linkage Mechanisms 447

12.7 Flywheels 448

12.8 Measurement Devices 455

12.9 Computer Methods 458

12.10 Review and Summary 459

Problems 459

References 464

Further Reading 464

13 Applications of Machine Dynamics 465

13.1 Introduction 465

13.2 Cam Response for Simple Harmonic Functions 465

13.3 General Response Using Laplace Transform Method 469

13.4 System Response Using Numerical Methods 479

13.5 Advanced Cam Functions 482

13.6 Forces Acting on the Follower 492

13.7 Computer Applications of Cam Response 494

13.8 Internal Combustion Engines 494

13.9 Common Arrangements of Multicylinder Engines 499

13.10 Flywheel Analysis for Internal Combustion Engines 504

13.11 Review and Summary 506

Problems 506

References 507

Further Reading 507

Appendix A – Center of Mass 509

Appendix B – Moments of Inertia 512

Appendix C – Fourier Series 521

Index 529