Advances in Robot Kinematics: Motion in Man and Machine (eBook)

Jadran Lenarcic has been Professor at the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, since 1988. He is Director of the J. Stefan Institute of Automatics, Biocybernetics and Robotics since 2005. He is a member of the executive committee of the International Federation for the Theory of Machines and Mechanisms, member of the Board of the European Robotics network, and memebr of the Executive Board of the European Association of Research and Technology Organisations. He is regular member of the Slovenian Academy of Engineering Science.

Table of Contents 6
Preface 12
PART 1 14
Calibration and Validation of a Rigid Body Kinematic Model of Flexure Hinges 15
1 Introduction 15
2 Rigid Body Kinematic Models of Flexure Hinges 17
2.1 Leaf Spring Model 17
2.2 Kimball–Tsai Method 18
2.3 Modified Kimball–Tsai Method 18
3 Flexure Hinge Test Bench 19
4 Parameter Calibration of a Flexure Hinge 19
5 Validation and Model Comparison 20
6 Conclusion and Outlook 21
Acknowledgements 22
References 22
Dynamic Jacobian Inverses of Mobile Manipulator Kinematics 23
1 Introduction 23
2 Basic Concepts 24
2.1 Kinematics 24
2.2 Jacobian 25
2.3 Adjoint Jacobian 25
2.4 Regular and Singular Configurations 25
2.5 Continuation Method 26
3 Dynamic Inverses 27
4 Example Jacobian Inverses 29
4.1 Right Inverses 28
4.2 Non-Right Inverses 29
4.2.1 Adjoint Jacobian 29
4.2.2 Adjugate DexterityMatrix Inverse 29
4.2.3 Singularity Robust Inverse 30
5 Computer Simulations 30
6 Conclusions 32
Acknowledgements 32
References 32
A Robust Forward Kinematics Analysis of 3-RPR Planar Platforms 34
1 Introduction 34
2 Cayley–Menger Determinants and Bilateration 36
3 Distance-Based Coordinate-Free Formulation 37
4 Numerical Example 39
5 Conclusions 41
Appendix 42
References 43
Hierarchical Decomposition and Kinematic Abstraction with Virtual Articulations 44
1 Introduction 44
2 Hierarchical Linkages 45
3 Structure Abstraction 47
4 Decomposition Algorithms 48
5 Scaling Results 51
6 Conclusions 53
Acknowledgements 53
Researching into Non-Singular Transitions in the Joint Space 55
1 Introduction 55
2 Kinematic Problems 56
2.1 Case Study 57
3 Locus of Cusp Points 58
4 Non-Singular Transitions in the Joint Space 59
5 Conclusions 61
Acknowledgements 62
References 62
MARIONET, A Family of Modular Wire-DrivenParallel Robots 63
1 Introduction 63
2 Actuation Scheme 64
3 The MARIONET family 65
3.1 MARIONET-REHAB 66
3.2 MARIONET-CRANE 67
3.3 MARIONET-ASSIST and MARIONET-VR 68
4 Lessons Learned 68
4.1 Improving the DRM 68
4.2 Kinematics 69
4.3 Singularity 69
5 Conclusion 70
References 70
Using Cosserat Point Theory for EstimatingKinematics and Soft-Tissue Deformation DuringGait Analysis 72
1 Introduction 72
2 Motion and Deformation of a Tetrahedron 73
3 Experimental Setup 75
4 Results 75
4.1 Group 1 Results (Rigid Tetrahedra) 77
4.2 Group 2 Results (Deformable Tetrahedra) 77
5 Conclusions 78
Acknowledgements 78
References 78
PART 2 80
Mechanical Generators of 2-DoF Translation along a Ruled Surface 81
1 Introduction 81
2 2-DoF Translation along a Ruled Helicoid 82
3 Mechanical Generators of 2-DoF Translation along a Ruled Helicoid 85
4 Mechanical Generators of 2-DoF Translation along a RevoluteHyperboloid 87
5 Conclusions 88
Acknowledgements 88
References 88
Worm-Like Robotic Locomotion in Flexible Environment 89
1 Introduction 89
2 Contact Compliance Analysis 90
3 Structural Compliance Analysis 91
3.1 Model of Intestines 92
3.2 Superposition Principle 94
4 Two-Cell Robot Example 94
4.1 Analysis 95
4.2 Approximate Closed-Form Solution 95
4.3 Comparison to Exact Solution 95
5 Conclusions 96
References 96
Actuation Strategy Based on the Acceleration Model for the 3-PRPR Redundant Planar Parallel Manipulator 98
1 Introduction 98
2 Acceleration Model Formulation 99
3 Motion Planning 101
4 Numerical Examples 102
5 Conclusions 105
References 105
Kinematics and Design of a 5-DOF Parallel Robot Used in Minimally Invasive Surgery 106
1 Introduction 106
2 The Surgical Parallel Robot 107
3 The Geometric Model 108
4 Kinematics 110
5 Singularity Analysis 110
6 Design of PARASURG 5M 111
7 Conclusions 113
References 113
Main Theorem on Sch¨onflies-Singular Planar Stewart Gough Platforms 114
1 Introduction 114
1.1 Notation 115
1.2 Related Work 115
2 Main Theorem for the General Case 116
3 Main Theorem for the Special Case 118
4 Conclusion 121
References 122
A Novel Actuation Module for Wearable Robots 124
1 Introduction 124
2 Design of the Actuation Scheme 126
3 Embodiments of the Reversing Mechanism 128
4 Features of the Actuation Module 130
5 Conclusions 132
References 132
Parallel Robot with Antagonistic Dielectric Elastomer Actuation for Human-Machine Interaction 133
1 Introduction 133
2 The Manipulator Concept 135
3 Static Analysis of the Manipulator Concept 136
4 Dielectric Elastomer vs. Traditional Actuation 141
5 Conclusions 141
References 142
Using Redundancy in Serial Planar Mechanisms to Improve Output-Space Tracking Accuracy 143
1 Introduction 143
2 Speed-Ratio Control for Non-Redundant Manipulators 144
3 Speed-Ratio Control for Three-DOF, Planar Manipulators 146
4 Examples 147
5 Conclusions 150
References 150
PART 3 151
Combining Structural and Kinematic Analysis Using Interval Analysis for a Wire-Driven Manipulator 152
1 Introduction 152
2 Related Work 153
3 Structural Analysis Overview 154
4 The Proposed Algorithm 154
4.1 Criteria for Workspace Delineation 154
4.2 Structural Analysis Using Interval Analysis 155
4.3 Algorithm 155
4.4 Remarks 156
5 Examples 157
5.1 A 2-DOF Planar Robot with a 3-Bar Truss 157
5.2 A 2-DOF Planar Robot with a 9-Bar Truss 158
6 Conclusions 160
References 161
Multiple-Point Kinematic Control of a Humanoid Robot 162
1 Introduction 162
2 Kinematic Modelling 163
2.1 Hierarchical Model of Humanoid Robot 164
2.2 Virtual Joints 165
2.3 Augmented Jacobian 166
2.4 Center-of-Mass Jacobian 167
2.5 Conflicting Tasks 169
3 Simulations in VR 169
3.1 Standing up from a Sitting Position 170
3.2 Collision Avoidance 170
3.3 More Complex Tasks 171
4 Conclusions and Future Work 172
References 173
Optimum Design of a Pan-Tilt Drive for Parallel Robots 174
1 Introduction 174
2 Kinematics of the Pan-Tilt Mechanism 176
3 Optimization of the Pan-Tilt Mechanism 177
3.1 Minimization of the Transmission Defect 178
4 Conclusions 180
Appendix 181
References 181
LQP-Based Controller Design for Humanoid Whole-Body Motion 182
1 Introduction 182
2 Modelling 183
2.1 Whole-Body Dynamics 183
2.2 Contact Model 184
2.3 Task Description and Control 184
3 LQP-Based Controller Design 185
3.1 Designing LQP 185
3.2 Performing Tasks 186
4 Application to the Virtual iCub 186
4.1 Managing Multi-Tasks 186
4.2 Sit-to-Stand on One Foot 187
4.3 Walking 188
5 Conclusion 188
References 189
Persistent Screw Systems 190
1 Introduction 190
2 Definition 191
3 Forms of Persistent Screw Systems 194
4 Persistent Screw Systems of Dimension 3, 4 and 5 196
5 Conclusions 198
Acknowledgements 199
References 199
Localisation of the Instantaneous Axis of Rotation in Human Joints 200
1 Introduction 200
2 Determination of the Instantaneous Axis of Rotation Location 201
2.1 The SCoRE Method 201
2.2 Our Method 202
3 Simulation 203
3.1 Experimental Protocol 203
3.2 Simulations Results 204
4 Experimental Study on Human Subjects 205
4.1 Protocol and Apparatus 205
4.2 Data Processing and Modelling 205
4.3 Results 206
4.4 Discussion 207
5 Conclusions and Future Work 207
References 207
A Kinematic Observation and Conjecture for Creating Stable Constructs of a Peptide Nanoparticle 208
1 Introduction 208
2 Computational Model 210
2.1 Hydrogen Bond 210
2.1.1 Geometry of Hydrogen Bonds 210
2.1.2 Energy of Hydrogen Bonds 211
2.2 Mobility Analysis 212
3 Design and Manipulation of a Peptide Nanoparticle 212
3.1 Computational Model of the Nanoparticle 212
3.2 Experimental Method to Build the Nanoparticle 214
4 Conclusions 214
Acknowledgements 215
References 215
Forward Kinematic Problem of 5-PRUR Parallel Mechanisms Using Study Parameters 216
1 Introduction 216
2 Architecture 217
3 FKP Formulation Using Study’s Kinematic Mapping 218
3.1 Kinematic Modeling of the Principal Limb 218
3.2 FKP Formulation of the 5-PRUR, Extension from the Principal Limb 221
4 Cartesian Representation of Study Parameters 224
5 Study Parameters Representation of the Cartesian Coordinates 224
6 Conclusion 225
References 225
PART 4 227
The Development of a Reconfigurable Parallel Robot with Binary Actuators 228
1 Introduction 228
2 The Fivebar Structure 229
3 Four Point Synthesis Approach 230
4 (Re-)Configuration of Binary Robots 233
4.1 Robot Components for (Re-)Configuration 233
4.2 Mechanical Calibration of Binary Robots 233
5 Operational Status 234
6 Conclusions 234
On the Design of 5R Serial Manipulators with Isotropic Positioning 236
1 Introduction 236
2 Kinematic Model 237
3 Isotropic Design 238
3.1 Manipulator A with Near Isotropic Positioning 238
3.2 Manipulator B with Isotropic Positioning 240
3.3 Arbitrary 5R Manipulator with Isotropic Positioning 241
4 Positioning and Orienting Tasks 242
References 243
A Virtual Mechanism Enhanced Approach for Object Tracking with Humanoid Robot Head 244
1 Introduction 244
2 Methods 246
2.1 The Perceptual Problem – Acquiring 3-D Position of Object 246
2.2 The Control Problem – Virtual Mechanism Approach 247
2.3 Controller Design 249
3 Results 250
3.1 Object Tracking with Narrow-Angle Cameras 250
4 Conclusions 252
References 253
Tangent Space RRT with Lazy Projection:An Efficient Planning Algorithm for Constrained Motions 254
1 Introduction 254
2 Tangent Space RRT Algorithm 257
3 Case Study 260
3.1 Two-Arm Manipulation 260
4 Conclusions and Future Work 262
References 262
PART 5 264
Equilibrium Analysis of Tensegrity Structures with Elastic Ties 265
1 Introduction 265
2 Problem Formulation 267
2.1 Geometric Constraint 268
2.2 Potential Energy 268
2.3 Problem Statement 269
3 Solution Approach 269
4 Numerical Example 271
5 Conclusions 273
References 273
Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle 275
1 Introduction 275
2 Grassmann–Cayley Algebra in the Projective Space P3 276
3 Theory of Reciprocal Screws 276
4 The H4 Constraint Analysis 277
4.1 Twist System and Wrench System of the 4S Parallel Linkage 278
4.2 Constraint Wrenches of the H4 Robot 279
4.3 Actuation Wrenches and Global Wrench System of the H4 Robot 280
5 Singularity Analysis of the H4 Robot 280
5.1 Wrench Diagram of the H4 Robot in P3 280
5.2 Superbracket of the H4 Robot 281
5.3 Geometric Conditions for the H4 Robot Singularities 282
6 Conclusions 283
References 284
Human Motion Reconstruction and Synthesis of Human Skills 285
1 Introduction 285
2 Musculoskeletal Motion Reconstruction 286
2.1 Experimental Procedure and Musculoskeletal Model 287
2.2 Control Framework 288
2.2.1 Marker Space Control Formulation 288
2.2.2 Human Motion Control Hierarchy 290
3 Results and Real-Time Simulation 291
4 Conclusions 291
Acknowledgements 293
References 293
Overconstrained Mechanisms with Radially Reciprocating Motion 295
1 Introduction 295
2 Characteristics of the PRRP Chain 296
3 Construction of the Radially Reciprocating MotionMechanism 297
4 The New Radially Reciprocating Motion Mechanisms 299
5 Conclusions 301
References 302
Control of Bipedal TurningWhile Running 303
1 Introduction 303
2 Heuristics 304
3 Model 306
4 Control Laws 307
5 Results 308
6 Conclusion 310
References 310
Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots 311
1 Introduction 311
2 Geometrico-Static Model 312
3 The Stability of Equilibrium 315
4 Application Example: The 33-CDPR 318
5 Conclusions 320
References 321
The Inverse Kinematics of 3-D Towing 322
1 Introduction 322
2 The Static Equilibrium Condition 323
3 The Inverse Kinematics Problem 324
4 An Analytic Algorithm Based on Dialytic Elimination 325
5 An Example 326
6 Conclusions 329
Acknowledgements 329
References 329
A Complete Method for Workspace Boundary Determination 330
1 Introduction 330
2 Necessary Conditions 331
3 Singularity Classification 333
4 Numerical Solution 334
5 A Comparative Example 336
6 Conclusions 338
Acknowledgements 339
Referenc 339
PART 6 340
Inverse Kinematics of Humanoid-RobotReaching through Human Visuo-Motor Learning 341
1 Introduction 341
2 Closed Loop Motion Transfer and Data Acquisition 343
3 Statically Stable Inverse Kinematics Determination 344
4 Statically Stable Motion Generation of the Humanoid Robot 346
5 Conclusions 347
Acknowledgements 348
References 348
Automated Fitting of an ElastokinematicSurrogate Mechanism for Forearm Motion from MRI Measurements 349
1 Introduction 349
2 Forearm Elastokinematic Surrogate Mechanism 350
3 Model Parameter Fitting from MRI Measurements 353
4 Simulation Results 356
5 Conclusions 357
References 358
Self-Motions of 6–3 Stewart–Gough Type Parallel Manipulators 359
1 Introduction 359
2 Equations of Self-Motions 360
3 The Butterfly Motion 361
4 The General Case 362
5 The Four-Bar Self-Motion 363
6 Conclusions 366
Acknowledgements 366
References 366
Constraint Compliant Control for a Redundant Manipulator in a Cluttered Environment 367
1 Introduction 367
2 Constraint Compliant Control 369
2.1 Passive Avoidance 369
2.2 Active Avoidance in Additional Objective 370
2.3 Particular Case of the Joint Velocity Limit – Scaling 370
3 Implementation and Comparative Results 371
3.1 Implementation 372
3.2 Results and Analysis 373
4 Conclusion and Perspectives 375
Acknowledgements 376
References 376
Geometric Interpolation by Quartic Rational Spline Motions 377
1 Introduction 377
2 Geometrically Continuous Rational Spline Motions 378
3 Interpolation Problem 379
4 Construction of Quartic Rational Spline Motions 380
5 Conclusion 383
References 384
Position Level Kinematics of the Atlas Motion Platform 385
1 Introduction 385
2 Atlas Velocity Level Kinematic Model 387
3 Atlas Position Level Kinematic Model 388
4 Experimental Validation 389
5 Orientation Estimate for Nonconstant Velocity Inputs 391
6 Conclusions 391
References 392
An Optimum Path Planning for LARMClutched Arm 393
1 Introduction 393
2 The LARM Clutched Arm 394
3 Formulation for Path Planning 395
4 Numerical Examples 397
5 Conclusions 400
References 400
A Simple Kinematic Model of a Human Body for Virtual Environments 401
1 Introduction 401
2 Human Body Kinematics 402
2.1 Kinematic Model 403
2.2 Motion Assessment 403
2.3 Singularity Handling 404
2.4 Virtual Mirror 407
3 Conclusions 408
References 408
PART 7 409
On the Development of Low Mass Shaking Force Balanced Manipulators 410
1 Introduction 410
2 Force Balanced Manipulator with Three Degrees of Freedom 411
3 Force Balanced Manipulator with Four Degrees of Freedom 415
4 Evaluation and Experiments 418
5 Conclusion 419
References 419
Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms 420
1 Introduction 420
2 Condition for Singularity Invariance 421
3 Point-Line Component 422
4 Point-Plane Component 423
5 Line-Line Component 423
6 Line-Plane Component 425
7 Conclusions and Future Work 426
References 427
Geometric Kinematics of Rigid Bodies with Point Contact 428
1 Introduction 428
2 Darboux Frame and Darboux Vector 429
3 Sliding Motion 430
4 Spin-Rolling Motion 430
5 Sliding-Spin-Rolling Motion 431
5.1 Derivation of Geometric Invariants of Rolling Motion 432
5.2 Derivation of Geometric Invariants of Sliding Motion 434
5.3 Geometric Velocity of Sliding-Spin-Rolling Motion 434
6 Conclusions 435
References 435
Singularity Locus of 6–4 Fully-Parallel Manipulators 436
1 Introduction 436
2 Notations and Preliminary Computations 438
3 New Expression of the Singularity-Locus Equation 439
4 Discussion 440
5 Conclusions 442
Appendix A 442
Appendix B 443
References 443
The Pre-Stereographic Model of the General Three-System of Screws 445
1 Introduction 445
2 Screws and Projective Spaces 446
2.1 Physical and Geometrical Screws 446
2.2 Models of Projective Space 446
3 A Model of the General Three-System 447
3.1 The Pre-Stereographic Sphere 447
3.2 The Pitch Axis 449
3.3 The Screw Axis Location 449
4 Possible Applications of the Pre-Stereographic Model 450
5 Conclusions 452
References 452
Difficulty of Kinematic Synthesis of Usable Constrained Planar 6R Robots 453
1 Introduction 453
2 Literature Review 454
3 Kinematics Equations of a Planar nR Chain 455
4 Synthesis of RR Constraints 456
5 Identification of Usable Four-bar Linkages 457
6 Probability of a Usable Four-bar Linkage 458
7 Probability of Usable Constrained 2R Robots 459
8 Probability of Usable Constrained 6R Robots 460
9 Conclusions 460
References 461
Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints 462
1 Introduction 462
2 Manipulator Model 463
3 Static Equilibrium 465
4 Stiffness Matrix 466
5 Kinetostatic Control 467
6 Application Example 468
7 Conclusions 470
References 471
Characterization of Parallel Manipulator AvailableWrench Set Facets 472
1 Introduction 472
2 AvailableWrench Set Definition 473
3 Faces and Representation of a Convex Polytope 474
4 The AvailableWrench Set as a System of Linear Inequalities 475
4.1 Proofs of the First and Second Assertions 476
4.2 A Finite System of Linear Inequalities 477
5 Hyperplane Shifting Method 478
6 Conclusion 479
References 479
PART 8 480
Constraint-Screw System Based Synthesis of Limb Arrangement of the 3-PUP Parallel Mechanism 481
1 Introduction 481
2 The PUP Limb and Its Geometry Constraints 482
3 Constraint Screw Systems for the 3-PUP Parallel Mechanism 483
3.1 Screw Systems Based on Torque Constraints 484
3.2 Screw Systems Including Force Constraints 484
4 Various Limb Arrangements of the 3-PUP Parallel Mechanism and Their Instantaneous Mobility Corresponding to the Screw Systems 485
4.1 Limb Arrangement Corresponding to Type I 485
4.2 Limb Arrangement Corresponding to Type II 486
4.3 Limb Arrangement Corresponding to Type III 486
5 Conclusions 487
References 488
On Structural Properties of Sets of Finite Displacement Screws 489
1 Introduction 489
2 Notation and Basic Geometry 490
3 Specification of a Finite Displacement Screw 490
4 Sets of Relocation Screws 491
5 Presence of a Nodal Line 492
6 Interpretation 493
7 Mechanism with Explicit Line Symmetry 494
8 Conformation with a 2-System 495
9 Conclusion 496
References 496
An Autonomous and Safe Homing Strategy for Parallel Kinematic Five-Bar Manipulators 497
1 Introduction 497
1.1 The Five-Bar Mechanism 498
2 A Strategy for Autonomous Homing 498
3 Analysis of the Homing Strategy Proposed 499
3.1 Segmentation into Two Phases 500
3.1.1 Analysis of the Second Phase 500
3.1.2 Analysis of the First Phase 500
3.2 Choice of Workspace Partitioning and its Restrictions 501
4 Generalization for the Non-Symmetric Five-Bar 503
5 Conclusions 503
References 504
Singularities of Regional Manipulators Revisited 505
1 Introduction 505
2 The Kinematic Mapping 507
3 Jacobian Matrices 508
4 The Singular Locus 510
5 Cusps 511
6 Example: Ortho-Parallel Manipulator 512
7 Conclusions 513
References 514
Robot-Based HiL Test of Joint Endoprostheses 516
1 Introduction 516
2 HiL Simulator for Testing of Endoprostheses 517
3 Simplified Mathematical Model of the HiL Simulator 519
4 Biomechanical Multibody Model 522
5 Conclusion 522
References 523
An Algorithm for Real-Time Forward Kinematics of Cable-Driven Parallel Robots 524
1 Introduction 524
2 Forward Kinematics of Cable-Driven Parallel Robots 525
3 Real-Time Algorithm 526
4 Implementation and Experimental Results 529
5 Conclusions 532
References 532
Numerical Synthesis of Overconstrained Mechanisms Based on Screw Theory 534
1 Introduction 534
2 Open Kinematical Chains with Helical Joints 535
2.1 Screw System of the Helical Joints 535
2.2 Differential Displacement of the Screw Axes 536
3 Single Loop Spatial Mechanisms with Helical Joints 536
3.1 Closure Condition at the Velocity Level 537
3.2 Differential Displacement of the Screw Axes 537
4 Synthesis of Overconstrained Spatial Mechanisms 538
5 Numerical Synthesis Algorithm 540
6 Results and Outlook 541
References 541
Author Index 542
Subject Index 544