New Trends in Mechanism and Machine Science (eBook)

Preface 6
Contents 8
Part I Mechanics of Robots 1 15
1 Calculation of the Ball Raceway Interferences Due to Manufacturing Errors and Their Influence on the Friction Moment in Four-Contact-Point Slewing Bearings 16
Abstract 16
1 Introduction 16
2 Interferences Calculation Procedure 17
2.1 Measurement of the Raceways Geometry 17
2.2 Analytical Model for Interference Calculation 18
3 Finite Element Model for Friction Moment Calculation 20
4 Results and Discussion 22
5 Conclusions and Future Work 22
Acknowledgments 23
References 23
2 Meshing Analysis for TA Worm Drive 25
Abstract 25
1 Introduction 25
2 Meshing Geometry of TA Worm Drive 26
3 Numerical Example and Discussion 29
4 Conclusions 31
Acknowledgments 32
References 32
3 Trade-Off for Space Mechanisms Actuator Technology via a General Purpose Language and Domain Specific Simulations Framework 33
Abstract 33
1 Introduction 33
2 Background of the Experiment 34
3 Trade-Off Without the Framework 34
4 Experiment and Result with the Framework 36
4.1 Libraries of Domain Specific Tools 38
4.2 Libraries Within Generic Purpose Modeling Tools 38
5 Intermediate Results and Outlook 39
Acknowledgments 40
References 40
4 Tolerance Analysis of Planar Serial Manipulators with Decoupled and Non-decoupled Dynamics 41
Abstract 41
1 Introduction 42
2 The Planar Serial Manipulators with Decoupled and Non-decoupled Dynamics 42
2.1 Dynamic Model and Control of Original Structure 43
2.2 Dynamic Model and Control of Decoupled Structure 44
3 Tolerance Analysis of Planar Serial Manipulators with Decoupled and Non-decoupled Dynamics 46
4 Numerical Simulations 47
5 Conclusion 48
References 49
Part II Mechanism Analysis 1 50
5 Coupler-Link Mobility Analysis of Planar Four-Bar Linkages 51
1 Introduction 51
2 Coupler-Driven Four-Bar Linkage 52
2.1 Constraint Equations 52
3 A Triangle of Motion Constraint 54
4 Mobility Regions 55
5 Condition for a Full Rotation of the Coupler Link 56
6 Examples 57
7 Conclusions 59
References 59
On the Dynamic Equivalence of Planar Mechanisms, an Inertia Decomposition Method 60
1 Introduction 60
2 Method 61
2.1 Inertia Decomposition of a Body 62
2.2 Inertia Decomposition of a Mechanism 63
2.3 Inertia Recomposition of a Mechanism 64
3 Results 66
4 Conclusion 67
References 67
7 Determination of a Rigid Body Orientation by Means of Indirect Measurements 69
Abstract 69
1 Introduction 69
2 Geometry of the System 70
3 Target-Free Method with Redundant Measurements 71
3.1 Least Squares Problem 72
3.2 Determination of the Vectors qi 73
4 Three-Sensors Method Involving a Target 74
4.1 Simulations 75
5 Discussions of Results 76
6 Conclusions 77
Acknowledgments 77
References 77
Algebraic Analysis of a New Variable-DOF 7R Mechanism 78
1 Introduction 78
2 Construction of a New Variable-DOF 7R Mechanism 79
3 Analysis of the New 7R Mechanism 79
3.1 Two 1-DOF 7R Motion Modes 83
3.2 Two-DOF Double-Bennett Mode 84
3.3 Transition Configurations 84
4 Conclusions 85
References 86
Overconstrained Single Loop Four Link Mechanisms with Revolute and Prismatic Joints 87
1 Introduction 87
2 Analysis of Single Loop Four Link Mechanisms 88
2.1 4R Mechanism 89
2.2 3R1P Mechanism 91
2.3 2R2P Mechanism 91
2.4 1R3P Mechanism 93
2.5 4P Mechanism 93
3 Conclusion 94
References 94
Part III Parallel Manipulators 1 96
Planar Stewart Gough Platforms with Quadratic Singularity Surface 97
1 Introduction 97
1.1 Review and Outline 98
2 Existence Theorem 98
3 Geometric Interpretation of rk(N)=4 101
4 Rational Parametrization of the Singularity Locus 103
5 Direct Kinematics 104
5.1 Leg-Replacement 105
6 Conclusion 106
References 106
Forward Kinematic Analysis of the 3-underlineRPRS Parallel Manipulator 107
1 Introduction 108
2 Mathematical Formulation 109
2.1 Geometry 109
2.2 Loop-Closure Equations 110
2.3 Solution 111
3 Numerical Results 112
4 Conclusions 113
References 115
Computing the Safe Working Zone of a 3-underlineRRS Parallel Manipulator 116
1 Introduction 117
2 Kinematic Formulation 117
2.1 Geometry 117
3 Formulation and Computation of the SWZ 119
3.1 Loss-Type Singularity Condition, S1=0 119
3.2 Gain-Type Singularity Condition, S2=0 120
3.3 Link Interference Condition, S3 = 0 120
4 Numerical Results 122
5 Conclusion 123
References 123
Comparison of 3-RunderlinePS and 3-SunderlinePR Parallel Manipulators Based on Their Maximum Inscribed Singularity-Free Circle 124
1 Introduction 124
2 Manipulator Architectures 126
3 Constraint Equations of the 3-SPR Parallel Manipulator 127
4 Operation Modes 128
5 Singularity Analysis 128
5.1 Singularity Loci 129
6 Maximum Inscribed Circle Radius for 3-RunderlinePS and 3-SunderlinePR PMs 130
7 Conclusions 132
References 133
14 On the Workspace Representation and Determination of Spherical Parallel Robotic Manipulators 134
Abstract 134
1 Introduction 134
2 Kinematic Formulation 135
2.1 Parameterizing of the 3-RRR-Type SPRM 136
2.2 Geometric Modeling of a Limb 137
3 Workspace Determination of 3-RRR-Type SPRM 139
3.1 New Representation of the Orientation Operational Space 140
3.2 Application to Workspace Determination 140
4 Conclusions 141
References 142
Part IV Tensegrity Mechanisms 143
15 Compliant Gripper Based on a Multistable Tensegrity Structure 144
Abstract 144
1 Introduction 144
2 Theory 145
2.1 Influence of the Member Properties 146
2.2 Mechanical Compliance 147
2.3 Design of the Gripper Arms 148
2.4 Actuation of the Gripper 149
3 Experiments 150
4 Conclusions 151
Acknowledgments 151
References 151
16 Compliant Multistable Tensegrity Structures with Simple Topologies 153
Abstract 153
1 Introduction 153
2 Theory 154
2.1 Form-Finding Process 155
2.2 Algorithm for Searching Multiple States of Self- equilibrium 156
3 Examples 157
4 Conclusions 160
Acknowledgments 160
References 160
Towards the Control of Tensegrity Mechanisms for Variable Stiffness Applications: A Case Study 162
1 Introduction 162
2 System Description and Modeling 163
2.1 Description 163
2.2 Kinematic and Static Modeling 164
3 Control Method 165
3.1 Tension Distribution Algorithm 165
3.2 Stiffness Modulation Through Prestress 166
4 Simulations 167
4.1 Trajectory Tracking 167
4.2 Stiffness Modulation 168
5 Conclusions and Perspectives 169
References 169
Kinematic Analysis of a Continuum Parallel Robot 171
1 Introduction 171
2 Fundamentals of Flexible Bars Clamped at both Ends 172
3 Kinematic Analysis of the 2 DoF Parallel Continuum Robot 175
4 Numerical and Experimental Validation 177
5 Conclusions and Future Work 178
References 178
Part V Mechanics of Robots 2 179
19 3D Formulation for Revolute Clearance Joints 180
Abstract 180
1 Introduction 180
2 Formulation of Revolute Clearance Joints 181
3 Numerical Example 186
4 Concluding Remarks 187
Acknowledgments 188
References 188
20 Efficiency Assessment in Spur Gears with Shifting and Profile Modifications 189
Abstract 189
1 Introduction 189
2 Efficiency Calculation 190
3 Shifting and Profile Modification Modelling 191
4 Results 192
5 Conclusions 196
Acknowledgments 196
References 197
21 Motion Design Considering Moment of Inertia 198
Abstract 198
1 Introduction 198
2 Harmonic Synthesis 199
3 Motion Design Considering Moment of Inertia 201
4 Example: Slider Crank Mechanism 203
5 Conclusion 205
References 205
Recent Developments on Cylindrical Contact Force Models with Realistic Properties 206
1 Introduction 206
2 Finite Element Model for Spatial Revolute Joints 208
3 Results and Discussion 209
4 Concluding Remarks 212
References 213
23 On the Determination of the Meshing Stiffness and the Load Sharing of Spur Gears 215
Abstract 215
1 Introduction 215
2 Minimum Elastic Potential Energy Model 216
3 Non Conjugate Contact Conditions 219
3.1 Tooth Deflections 219
3.2 Frictional Effects 220
3.3 Profile Modifications 220
4 Conclusions 222
Acknowledgments 222
References 222
Part VI Industrial and Non-industrial Applications 1 224
24 WinMecC: Software for the Analysis and Synthesis of Planar Mechanisms 225
Abstract 225
1 Introduction 225
2 Complex Mechanisms 227
3 Kinematic and Dynamic Module 227
3.1 Numeric Results 228
3.2 Graphic Display 228
4 Synthesis of Mechanisms 231
5 Conclusions 233
References 234
25 Manipulator Motion Planning in Redundant Robotic System for Fiber Placement Process 235
Abstract 235
1 Introduction 235
2 Robotic Fiber Placement Problem 236
3 Robotic System Model 237
4 Optimization Problem 238
4.1 Motion Generation Problem 238
4.2 Search Space Discretization 239
5 Path Planning Algorithm 241
6 Application Example 242
7 Conclusions 243
Acknowledgments 243
References 244
Free and Open Source Software Applications for Education of TMM Discipline in Bauman University 245
1 Introduction 245
2 Operating Systems and Emulators 247
3 CAD Systems 247
4 Computer Mathematics and Algebra 249
5 IDEs and Special Software 250
6 Conclusions 251
References 251
27 A Novel One-DoF Gravity Balancer Based on Cardan Gear Mechanism 253
Abstract 253
1 Introduction 253
2 Conventional Gravity Balancer 254
3 The Inverted Cardan Gear Mechanism 255
4 Planetary Gear Train for Half-Angle Transformation 256
5 The New Gravity Balancer Mechanism 257
6 Simulation 259
7 Conclusions 259
References 259
28 Galvanometer Laser Scanning: Custom-Made Input Signals for Maximum Duty Cycles in High-End Imaging Applications 261
Abstract 261
1 Introduction 261
2 Galvoscanning with Common Input Signals 262
3 Custom-Made Inputs for Optimal Galvoscanning 265
4 Discussions and Conclusions 266
Acknowledgments 267
References 267
Part VII Control Issues 270
29 Optimal Motion of Flexible Objects with Oscillations Elimination at the Final Point 271
Abstract 271
1 Introduction 271
2 Theoretical Justification of an Optimal Translational Motion 273
3 Experimental Verification of the Optimal Translational Motion 277
4 Conclusions 279
Acknowledgments 280
References 280
30 Alternating Error Effects on Decomposition Method in Function Generation Synthesis 282
Abstract 282
1 Introduction 282
2 Derivation of the I/O Equations for the Double-Spherical 6R Linkage 284
3 A New Way of Error Calculation 285
4 Numerical Examples and Results 287
5 Conclusions 289
Acknowledgments 289
References 289
Control-Based Design of a Five-Bar Mechanism 291
1 Introduction 292
2 Recalls on Leg-Based Visual Servoing of Parallel Robots 293
3 Control-Based Design of the Five-Bar Mechanism 294
3.1 Controller-Based Robot Performance 294
3.2 Optimal Design Process 296
3.3 Results of the Optimization Process 297
4 Conclusion 298
References 299
Part VIII History of Mechanisms 300
F. Reuleaux, F. Wittenbauer: Their Influence on Evolution of Applied Mechanics in Russia at the Beginnings of XXth Century 301
1 Overview 301
2 Franz Reuleaux 302
3 Ferdinand Wittenbauer 304
4 Summary 306
References 307
33 Applying Modern CAD Systems to Reconstruction of Old Design 309
Abstract 309
1 Introduction 309
2 Evolution of a Flexible Gear 310
3 Responsyn’s Basic Principles 311
4 Forces in the Flexible Gear 312
5 The Responsyn and the History of Mechanism and Machine Science 314
6 3D Reconstructions 314
7 Producing Animation 316
8 Conclusions 316
References 316
Part IX Cable Mechanisms 318
Increase of Position Accuracy for Cable-Driven Parallel Robots Using a Model for Elongation of Plastic Fiber Ropes 319
1 Introduction 319
2 Robot Model 320
3 Description of Elongation Phenomenon 321
4 Real-Time Implementation 322
5 Accuracy Measurements 323
6 Conclusions 325
References 326
35 Pose-Independent Counterweighting of Cable-Suspended Payloads with Application to Rehabilitation 328
Abstract 328
1 Introduction 328
2 Modeling Approach 329
3 Counterweight Design 333
4 Discussion and Conclusions 335
Acknowledgments 335
References 335
Preliminaries of a New Approach for the Direct Kinematics of Suspended Cable-Driven Parallel Robot with Deformable Cables 337
1 Introduction 337
2 Cable Model 338
3 DK Kinematico-Static Equations 339
4 The Continuity Model 339
4.1 The Inverse Model 339
4.2 The Direct Model 340
4.3 The Singularity Cases 341
4.4 Maximum Number of DK Solutions 342
5 Example 342
6 Conclusion 343
References 344
Static Analysis of Planar 3-DOF Cable-Suspended Parallel Robots Carrying a Serial Manipulator 345
1 Introduction 345
2 Static Model 347
3 Wrench-Feasibility Analysis 349
4 Conclusions 352
References 352
Part X Mechanism Design and Synthesis 1 354
38 Structural Synthesis, Mobility Analysis and Creation of Complete Atlas of Multiloop Planar Multiple-Jointed Kinematic Chains on Base All Possible Sets of Color Multiple Joints for Industrial Applications 355
Abstract 355
1 Introduction 356
1.1 Symbols and Abbreviations 356
2 Unified Equations for Topological Structure and Mobility Analysis and for Number Synthesis of Multibody Mechanical Systems 357
3 Algorithm for Synthesis and Enumeration of All Possible Sets of Color Multiple Joints for K-Loop Mechanisms 358
4 Basic Theorem About Valid Sets of Multiple Joints for Closed K-Loop Kinematic Chains 360
5 Structural and Mobility Analysis of Industrial Applications of Synthesized Multiple-Jointed Systems 361
6 Conclusions 362
References 362
39 Design and Development of a Triggered Type Underactuated Grasping Mechanism and Its Application to an Experimental Test Bed 363
Abstract 363
1 Introduction 363
2 Switching Mechanism: Concept Generation and Selection 365
3 Design and Development of the Experimental Test Bed 368
4 Conclusion 369
References 370
40 Solving the Minimum Distance Problem for the Synthesis of Mechanisms 371
Abstract 371
1 Introduction 372
2 The Minimum Distance Problem. Formulation 373
3 Requirements 374
4 Optimization of the Error Function 376
5 Numerical Tests 376
6 Conclusions and Future Work 377
Acknowledgments 378
References 378
41 Mobile Robot with Multiple Modes Based on 4-URU Parallel Mechanism 379
Abstract 379
1 Introduction 379
2 Mechanism Design 380
3 Modes Analysis 382
3.1 Rolling Mode 382
3.2 Walking Mode 383
3.3 Jumping Mode 384
3.4 Hoisting Mode 385
3.5 Collapsing Mode 385
4 Conclusions 386
Acknowledgments 387
References 387
Part XI Mechanisms for Biomechanics and Surgery 388
42 An Experimental Characterization of Human Knee Joint Motion Capabilities 389
Abstract 389
1 Introduction 389
2 Anatomy of the Knee Joint 390
3 Experimental Layout and Testing Modes 391
4 Experimental Tests and Results 394
5 Conclusions 396
Acknowledgments 397
References 397
43 An Innovative Parallel Robotic System for Transperineal Prostate Biopsy 398
Abstract 398
1 Introduction 398
2 The Parallel Robot for Prostate Biopsy 399
2.1 The Geometric Model 401
3 Singularity Analysis 403
4 Conclusions 405
Acknowledgments 405
References 405
A 2PRP-2PPR Planar Parallel Manipulator for the Purpose of Lower Limb Rehabilitation 407
1 Introduction 408
2 Proposed Manipulator Design 409
2.1 Conceptual Design of the Proposed Manipulator 409
2.2 Kinematics of the Proposed Manipulator 411
3 Results and Discussions 412
4 Conclusion 414
References 414
Singularity Analysis of a Wall-Mounted Parallel Robot with SCARA MotionsLower Limb Exoskeleton with Hybrid Pneumaticaly Assisted Electric Drive for Neuroreabilitation 416
1 Introduction 417
2 Synthesis of the Walking Pattern 417
3 Drives Models 419
4 Control Law 420
5 Mathematical Model of Control Law for One Joint 420
6 Conclusions 423
References 424
Part XII Mechanism Design and Synthesis 2 425
An Adjustable Constant Force Mechanism Using Pin Joints and Springs 426
1 Introduction 426
2 Mechanism Architecture 427
2.1 Constant Force Mechanism 427
2.2 CFM with Revolute Joints 429
3 Effect of Friction on the CFM 430
3.1 Statics 431
3.2 Friction Model 431
3.3 Friction at Output 432
4 Conclusion 433
References 434
Synthesis and Optimisation of Large Stroke Flexure Hinges 435
1 Introduction 436
2 Method 437
2.1 Assessment of Performance 437
2.2 Synthesis of New Designs 437
2.3 Finding the Optimal Geometry 438
3 Modelling and Optimisation 438
4 Synthesis and Optimisation of Conceptual Designs 439
4.1 Three Flexure Cross Hinge (TFCH) 439
4.2 Butterfly Hinges (BFH1) 440
4.3 Infinity Flexure Hinges (IFH2) 441
5 Résumé and Conclusions 442
References 442
On the Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture 444
1 Introduction 444
2 Composition of the Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture 445
3 Basic Inherently Force Balanced Mechanism Solutions 448
4 Conclusions 450
References 451
Part XIII Mechanism Analysis 2 452
49 A Workspace Analysis of 4R Manipulators via Level-Set Formulation 453
Abstract 453
1 Introduction 453
2 Level-Set Workspace Analysis of 4R Manipulators 454
3 A Numerical Example 456
4 Conclusions 460
References 460
A Constructive Method for the Approximation of the Multiple Inverse Kinematics Solutions of Noncuspidal 6 DoF Manipulators 462
1 Introduction 462
2 The Determination of the Training Sets 464
3 Determining the ANNs Architecture by the Constructive Method 465
4 The Case Study 466
4.1 Discussion of Results 468
5 Conclusions 470
References 470
51 Single-Loop Foldable 8R Mechanisms with Multiple Modes 472
Abstract 472
1 Introduction 472
2 Mechanism Design from Mono-mode to Multi-mode 473
3 Mobility and Foldability of Multi-mode Foldable Mechanisms 474
3.1 Double-Centered 8R Mechanism 474
3.2 Perpendicular-Axis 8R Mechanism 476
4 Conclusions 478
Acknowledgments 478
References 479
52 Calibration of TCP-Fixed Bevel Units 480
Abstract 480
1 Motivation 480
2 A Serial Wrist for Plasma Cutting 481
3 Calibration Strategies 482
3.1 External Calibration Approach 483
3.2 Evaluation of Calibration Procedures 483
4 Calibration of Bevel Units 484
4.1 Method Classification 484
4.2 Numerical Implementation 485
4.3 Considerations Regarding the Measurement Device 485
4.4 Compensation 486
5 Comments on the Application 487
6 Conclusions 488
References 489
Part XIV Industrial and Non-industrial Applications 2 490
53 Mechanism Type Synthesis Approach for Automated Handling and Multiaxial Draping of Reinforcing Textiles 491
Abstract 491
1 Introduction 492
2 Task Definition 493
3 Type Synthesis 495
4 Conclusions 499
Acknowledgments 499
References 499
54 Design of a Reciprocal Hip Mechanism with Adjustable Flexion-Extension Coupling Ratios for Prosthetic Applications 501
Abstract 501
1 Introduction 501
2 Design of the Adjustable Hip FECRs Mechanism 502
3 Experiment 505
4 Results and Discussion 506
5 Discussion 508
6 Conclusions 509
Acknowledgments 509
References 509
55 Wind Turbine Based on Antiparallel Link Mechanism 510
Abstract 510
1 Introduction 510
2 Statement of the Problem 511
2.1 Description of a Model of the Mechanism 511
2.2 Model of Active Forces 512
2.3 Dynamical Equations and a Statement of the Problem 513
3 Sufficient Conditions of Existence and Orbital Stability of a Periodic Trajectory 513
4 Bifurcation Diagrams of Periodic Trajectories 514
5 An Estimation of a Trapped Power 515
6 Discussion 515
7 Conclusions 516
Acknowledgments 517
References 517
56 Model and Analysis of a Novel Piezo-Electric Rotational Motor Based on Deformation Wave Precession 518
Abstract 518
1 Introduction 518
2 Operating Principle 519
2.1 Steady State Sliding Condition 520
3 Motor Model 521
4 Performance Evaluation 524
5 Conclusions 526
References 526
57 Estimating Characteristics of a Contact Between Sensing Element of Medical Robot and Soft Tissue 527
Abstract 527
1 Introduction 527
2 Methods 528
2.1 Two-Layer Tissue Modeling 529
2.2 Numerical Calculation 531
3 Three-Layer Tissue Modeling 533
4 Conclusions 534
Acknowledgments 534
References 534
Part XV Parallel Manipulators 2 536
58 A Coordinate-Free Dynamical Model for Cable-Driven Parallel Robots 537
1 Introduction 537
2 Dynamical Model of CDPRs 539
2.1 Constitutive Laws 539
2.2 Geometry 540
2.3 Appell's Function 541
2.4 Dynamics 542
3 Conclusions 543
References 544
59 Path Generation Synthesis of Planar Double-Slider Linkages via the Elliptic Coupler Curve 545
Abstract 545
1 Introduction 545
2 The Double-Slider Linkage 547
3 Determining Linkage Dimensions from Coefficients 549
4 The General Case (? ? ?/2 and h ? 0) 550
5 Conclusions 552
Acknowledgments 552
References 552
60 A Controller for Avoiding Dynamic Model Degeneracy of Parallel Robots During Type 2 Singularity Crossing 553
1 Introduction 553
2 Dynamic Model at Singularity Locus 554
2.1 Dynamic Modelling of Parallel Mechanisms, Type 2 Singularity Degeneracy Condition and Criteria for Singularity Crossing 554
2.2 Solution to the Inverse Dynamic Model at Singularity Locus 556
3 Design of a Computed Torque Control Law in Cartesian Space 557
4 Case Study 559
5 Conclusions 560
References 561
61 Singularity Analysis of a Wall-Mounted Parallel Robot with SCARA Motions 562
1 Introduction 562
2 Manipulator Under Study 564
3 Kinematic Modeling of the Robot 564
4 Singularity Analysis of the Robot 565
5 Numerical Analysis and Singularity Loci 568
6 Conclusions 569
References 570
62 Design of a Cable-Driven Four-Bar Mechanism for Arm Rehabilitation 571
Abstract 571
1 Introduction 571
2 Mechanism Design and Description of the Model 572
2.1 Kinematic Synthesis 573
2.2 Kinematics and Parameters 573
3 Actuation Optimization 575
4 Conclusions 578
Acknowledgments 578
References 578