SAEED BENJAMIN NIKU, PHD, P.E., is a Professor of Mechanical Engineering at California Polytechnic State University, San Luis Obispo, California. He has taught courses in mechanics, robotics, design, and creativity.

Preface xv

About the Companion Website xix

1 Fundamentals 1

1.1 Introduction 1

1.2 What is a Robot? 2

1.3 Classification of Robots 3

1.4 What is Robotics? 3

1.5 History of Robotics 3

1.6 Advantages and Disadvantages of Robots 4

1.7 Robot Components 5

1.8 Robot Degrees of Freedom 7

1.9 Robot Joints 9

1.10 Robot Coordinates 9

1.11 Robot Reference Frames 11

1.12 Programming Modes 12

1.13 Robot Characteristics 13

1.14 Robot Workspace 13

1.15 Robot Languages 14

1.16 Robot Applications 17

1.17 Other Robots and Applications 23

1.18 Collaborative Robots 28

1.19 Social Issues 29

1.20 Summary 30

References 30

Problems 32

2 Kinematics of Serial Robots: Position Analysis 35

2.1 Introduction 35

2.2 Robots as Mechanisms 35

2.3 Conventions 37

2.4 Matrix Representation 37

2.4.1 Representation of a Point in Space 37

2.4.2 Representation of a Vector in Space 38

2.4.3 Representation of a Frame at the Origin of a Fixed-Reference Frame 40

2.4.4 Representation of a Frame Relative to a Fixed Reference Frame 41

2.4.5 Representation of a Rigid Body 42

2.5 Homogeneous Transformation Matrices 45

2.6 Representation of Transformations 46

2.6.1 Representation of a Pure Translation 46

2.6.2 Representation of a Pure Rotation about an Axis 47

2.6.3 Representation of Combined Transformations 50

2.6.4 Transformations Relative to the Current (Moving) Frame 52

2.6.5 Mixed Transformations Relative to Rotating and Reference Frames 53

2.7 Inverse of Transformation Matrices 54

2.8 Forward and Inverse Kinematics of Robots 59

2.9 Forward and Inverse Kinematic Equations: Position 60

2.9.1 Cartesian (Gantry, Rectangular) Coordinates 60

2.9.2 Cylindrical Coordinates 61

2.9.3 Spherical Coordinates 63

2.9.4 Articulated Coordinates 65

2.10 Forward and Inverse Kinematic Equations: Orientation 65

2.10.1 Roll, Pitch, Yaw (RPY) Angles 65

2.10.2 Euler Angles 68

2.10.3 Articulated Joints 70

2.11 Forward and Inverse Kinematic Equations: Position and Orientation 70

2.12 Denavit-Hartenberg Representation of Forward Kinematic Equations of Robots 70

2.13 The Inverse Kinematic Solution of Robots 84

2.13.1 General Solution for Articulated Robot Arms 86

2.14 Inverse Kinematic Programming of Robots 89

2.15 Dual-Arm Cooperating Robots 91

2.16 Degeneracy and Dexterity 92

2.16.1 Degeneracy 92

2.16.2 Dexterity 93

2.17 The Fundamental Problem with the Denavit-Hartenberg Representation 93

2.18 Design Projects 95

2.18.1 Stair-Climbing Robot 96

2.18.2 A 3-DOF Robot 96

2.18.3 A 3-DOF Mobile Robot 98

2.19 Summary 99

References 99

Problems 99

3 Robot Kinematics with Screw-Based Mechanics 111

3.1 Introduction 111

3.2 What is a Screw? 111

3.3 Rotation about a Screw Axis 112

3.4 Homogenous Transformations about a General Screw Axis 115

3.5 Successive Screw-Based Transformations 119

3.6 Forward and Inverse Position Analysis of an Articulated Robot 120

3.7 Design Projects 127

3.8 Summary 127

Additional Reading 128

Problems 128

4 Kinematics Analysis of Parallel Robots 133

4.1 Introduction 133

4.2 Physical Characteristics of Parallel Robots 134

4.3 The Denavit-Hartenberg Approach vs. the Direct Kinematic Approach 139

4.4 Forward and Inverse Kinematics of Planar Parallel Robots 140

4.4.1 Kinematic Analysis of a 3-RPR Planar Parallel Robot 141

4.4.2 Kinematic Analysis of a 3-RRR Planar Parallel Robot 143

4.5 Forward and Inverse Kinematics of Spatial Parallel Robots 147

4.5.1 Kinematic Analysis of a Generic 6-6 Stewart-Gough Platform 147

4.5.2 Kinematic Analysis of a Generic 6-3 Stewart-Gough Platform 152

4.5.3 Kinematic Analysis of a 3-Axis RSS-Type Parallel Robot 154

4.5.4 Kinematic Analysis of a 4-Axis RSS-Type Parallel Robot 160

4.5.5 Kinematic Analysis of a 3-Axis PSS-Type Parallel Robot 167

4.6 Other Parallel Robot Configurations 169

4.7 Design Projects 169

4.8 Summary 170

References 170

Problems 170

5 Differential Motions and Velocities 173

5.1 Introduction 173

5.2 Differential Relationships 173

5.3 The Jacobian 174

5.4 Differential versus Large-Scale Motions 176

5.5 Differential Motions of a Frame versus a Robot 177

5.6 Differential Motions of a Frame 178

5.6.1 Differential Translations 178

5.6.2 Differential Rotations about Reference Axes 178

5.6.3 Differential Rotation about a General Axis q 179

5.6.4 Differential Transformations of a Frame 181

5.7 Interpretation of the Differential Change 182

5.8 Differential Changes between Frames 183

5.9 Differential Motions of a Robot and Its Hand Frame 185

5.10 Calculation of the Jacobian 185

5.11 How to Relate the Jacobian and the Differential Operator 188

5.12 The Inverse Jacobian 191

5.13 Calculation of the Jacobian with Screw-Based Mechanics 197

5.14 The Inverse Jacobian for the Screw-Based Method 206

5.15 Calculation of the Jacobians of Parallel Robots 206

5.15.1 The Jacobian of a Planar 3-RRR Parallel Robot 207

5.15.2 The Jacobian of a Generic 6-6 Stewart-Gough Parallel Robot 208

5.16 Design Projects 210

5.16.1 The 3-DOF Robot 210

5.16.2 The 3-DOF Mobile Robot 210

5.17 Summary 210

References 211

Problems 211

6 Dynamic and Force Analysis 219

6.1 Introduction 219

6.2 Lagrangian Mechanics: A Short Overview 220

6.3 Effective Moments of Inertia 229

6.4 Dynamic Equations for Multiple-DOF Robots 229

6.4.1 Kinetic Energy 229

6.4.2 Potential Energy 234

6.4.3 The Lagrangian 234

6.4.4 Robot’s Equations of Motion 234

6.5 Static Force Analysis of Robots 239

6.6 Transformation of Forces and Moments between Coordinate Frames 242

6.7 Design Project 244

6.8 Summary 244

References 244

Problems 245

7 Trajectory Planning 247

7.1 Introduction 247

7.2 Path vs. Trajectory 247

7.3 Joint-Space vs. Cartesian-Space Descriptions 248

7.4 Basics of Trajectory Planning 249

7.5 Joint-Space Trajectory Planning 252

7.5.1 Third-Order Polynomial Trajectory Planning 252

7.5.2 Fifth-Order Polynomial Trajectory Planning 255

7.5.3 Linear Segments with Parabolic Blends 257

7.5.4 Linear Segments with Parabolic Blends and Via Points 259

7.5.5 Higher-Order Trajectories 260

7.5.6 Other Trajectories 263

7.6 Cartesian-Space Trajectories 263

7.7 Continuous Trajectory Recording 267

7.8 Design Project 268

7.9 Summary 269

References 269

Problems 269

8 Motion Control Systems 273

8.1 Introduction 273

8.2 Basic Components and Terminology 273

8.3 Block Diagrams 274

8.4 System Dynamics 274

8.5 Laplace Transform 278

8.6 Inverse Laplace Transform 281

8.6.1 Partial Fraction Expansion When F(s) Involves Only Distinct Poles 281

8.6.2 Partial Fraction Expansion When F(s) Involves Repeated Poles 282

8.6.3 Partial Fraction Expansion When F(s) Involves Complex Conjugate Poles 283

8.7 Transfer Functions 285

8.8 Block Diagram Algebra 288

8.9 Characteristics of First-Order Transfer Functions 290

8.10 Characteristics of Second-Order Transfer Functions 292

8.11 Characteristic Equation: Pole/Zero Mapping 294

8.12 Steady-State Error 296

8.13 Root Locus Method 298

8.14 Proportional Controllers 303

8.15 Proportional-Plus-Integral Controllers 306

8.16 Proportional-Plus-Derivative Controllers 308

8.17 Proportional-Integral-Derivative Controller (PID) 311

8.18 Lead and Lag Compensators 313

8.19 Bode Diagram and Frequency-Domain Analysis 313

8.20 Open-Loop vs. Closed-Loop Applications 314

8.21 Multiple-Input and Multiple-Output Systems 314

8.22 State-Space Control Methodology 316

8.23 Digital Control 320

8.24 Nonlinear Control Systems 322

8.25 Electromechanical Systems Dynamics: Robot Actuation and Control 323

8.26 Design Projects 326

8.27 Summary 327

References 327

Problems 327

9 Actuators and Drive Systems 331

9.1 Introduction 331

9.2 Characteristics of Actuating Systems 331

9.2.1 Nominal Characteristics – Weight, Power-to-Weight Ratio, Operating Pressure, Voltage, and Others 331

9.2.2 Stiffness vs. Compliance 332

9.2.3 Use of Reduction Gears 332

9.3 Comparison of Actuating Systems 335

9.4 Hydraulic Actuators 335

9.5 Pneumatic Devices 337

9.6 Electric Motors 338

9.6.1 Fundamental Differences Between AC- and DC-Type Motors 339

9.6.2 DC Motors 341

9.6.3 AC Motors 344

9.6.4 Brushless DC Motors 345

9.6.5 Direct-Drive Electric Motors 346

9.6.6 Servomotors 346

9.6.7 Stepper Motors 347

9.7 Microprocessor Control of Electric Motors 360

9.7.1 Pulse Width Modulation 361

9.7.2 Direction Control of DC Motors with an H-Bridge 363

9.8 Magnetostrictive Actuators 364

9.9 Shape-Memory Type Metals 364

9.10 Electroactive Polymer Actuators (EAPs) 364

9.11 Speed Reduction 365

9.12 Other Systems 367

9.13 Design Projects 367

9.14 Summary 370

References 371

Problems 372

10 Sensors 375

10.1 Introduction 375

10.2 Sensor Characteristics 375

10.3 Sensor Utilization 377

10.4 Position Sensors 378

10.4.1 Potentiometers 378

10.4.2 Encoders 379

10.4.3 Linear Variable Differential Transformer (LVDT) 382

10.4.4 Resolvers 383

10.4.5 (Linear) Magnetostrictive Displacement Transducer (LMDT or MDT) 383

10.4.6 Hall-effect Sensors 384

10.4.7 Global Positioning System (GPS) 384

10.4.8 Other Devices 385

10.5 Velocity Sensors 385

10.5.1 Encoders 385

10.5.2 Tachometers 385

10.5.3 Differentiation of Position Signal 386

10.6 Acceleration Sensors 386

10.7 Force and Pressure Sensors 386

10.7.1 Piezoelectric 386

10.7.2 Force-Sensing Resistor 386

10.7.3 Strain Gauge 387

10.7.4 Antistatic Foam 388

10.8 Torque Sensors 388

10.9 Microswitches 389

10.10 Visible Light and Infrared Sensors 389

10.11 Touch and Tactile Sensors 390

10.12 Proximity Sensors 391

10.12.1 Magnetic Proximity Sensors 391

10.12.2 Optical Proximity Sensors 391

10.12.3 Ultrasonic Proximity Sensors 392

10.12.4 Inductive Proximity Sensors 392

10.12.5 Capacitive Proximity Sensors 393

10.12.6 Eddy Current Proximity Sensors 393

10.13 Range Finders 393

10.13.1 Ultrasonic Range Finders 394

10.13.2 Light-Based Range Finders 395

10.14 Sniff Sensors 396

10.15 Vision Systems 396

10.16 Voice-Recognition Devices 396

10.17 Voice Synthesizers 397

10.18 Remote Center Compliance (RCC) Device 397

10.19 Design Project 400

10.20 Summary 400

References 401

11 Image Processing and Analysis with Vision Systems 403

11.1 Introduction 403

11.2 Basic Concepts 403

11.2.1 Image Processing vs. Image Analysis 403

11.2.2 Two- and Three-Dimensional Image Types 403

11.2.3 The Nature of an Image 404

11.2.4 Acquisition of Images 405

11.2.5 Digital Images 405

11.2.6 Frequency Domain vs. Spatial Domain 406

11.3 Fourier Transform and Frequency Content of a Signal 406

11.4 Frequency Content of an Image: Noise and Edges 409

11.5 Resolution and Quantization 410

11.6 Sampling Theorem 412

11.7 Image-Processing Techniques 415

11.8 Histograms of Images 415

11.9 Thresholding 418

11.10 Spatial Domain Operations Convolution Mask 419

11.11 Connectivity 424

11.12 Noise Reduction 426

11.12.1 Neighborhood Averaging with Convolution Masks 427

11.12.2 Image Averaging 428

11.12.3 Frequency Domain 429

11.12.4 Median Filters 429

11.13 Edge Detection 430

11.14 Sharpening an Image 436

11.15 Hough Transform 437

11.16 Segmentation 440

11.17 Segmentation by Region Growing and Region Splitting 441

11.18 Binary Morphology Operations 444

11.18.1 Thickening Operation 446

11.18.2 Dilation 446

11.18.3 Erosion 447

11.18.4 Skeletonization 447

11.18.5 Open Operation 448

11.18.6 Close Operation 448

11.18.7 Fill Operation 448

11.19 Gray Morphology Operations 449

11.19.1 Erosion 449

11.19.2 Dilation 449

11.20 Image Analysis 449

11.21 Object Recognition by Features 450

11.21.1 Basic Features Used for Object Identification 450

11.21.2 Moments 451

11.21.3 Template Matching 456

11.21.4 Discrete Fourier Descriptors 456

11.21.5 Computed Tomography (CT) 457

11.22 Depth Measurement with Vision Systems 457

11.22.1 Scene Analysis vs. Mapping 457

11.22.2 Range Detection and Depth Analysis 458

11.22.3 Stereo Imaging 458

11.22.4 Scene Analysis with Shading and Sizes 459

11.23 Specialized Lighting 459

11.24 Image Data Compression 460

11.24.1 Intraframe Spatial Domain Techniques 460

11.24.2 Interframe Coding 461

11.24.3 Compression Techniques 461

11.25 Color Images 462

11.26 Heuristics 462

11.27 Applications of Vision Systems 462

11.28 Design Project 463

11.29 Summary 464

References 464

Problems 465

12 Fuzzy Logic Control 475

12.1 Introduction 475

12.2 Fuzzy Control: What is Needed 476

12.3 Crisp Values vs. Fuzzy Values 476

12.4 Fuzzy Sets: Degrees of Truth and Membership 477

12.5 Fuzzification 477

12.6 Fuzzy Inference Rules 480

12.7 Defuzzification 481

12.7.1 Center of Gravity Method 481

12.7.2 Mamdani Inference Method 481

12.8 Simulation of a Fuzzy Logic Controller 485

12.9 Applications of Fuzzy Logic in Robotics 487

12.10 Design Project 488

12.11 Summary 489

References 489

Problems 490

Appendix A 491

Appendix B 499

Index 501

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