Parallel Robotic Machine Tools

Parallel Robotic Machine Tools
Dan Zhang
Contents
1 Introduction . 1
1.1 The History of Parallel Robots 1
1.2 Introduction of Conventional Machine Tools . 5
1.3 Parallel Robot-based Machine Tools 9
1.4 Scope and Organization of this Book . 16
2 Kinematics of Mechanisms 19
2.1 Preamble 19
2.2 Position and Orientation of Rigid Body . 19
2.2.1 Rotation Matrix . 19
2.2.2 Euler Angles 22
2.3 Homogeneous Transformation . 24
2.4 Denavit–Hartenberg Representation . 27
2.5 Jacobian Matrix 28
2.6 Conclusions . 31
3 Architectures of Parallel Robotic Machine 33
3.1 Preamble 33
3.2 Fundamentals of Mechanisms . 33
3.2.1 Basic Kinematic Elements of Mechanisms 33
3.2.2 Classification of Mechanisms 36
3.3 Graph Representation of Kinematic Structures . 38
3.4 Design Criteria . 38
3.5 Case Study: Five Degrees of Freedom Parallel Robotic Machine . 40
3.5.1 Serial Mechanisms 41
3.5.2 Parallel Mechanisms 41
3.5.3 Hybrid Mechanisms 47
3.6 Redundancy . 48
3.7 Conclusions . 48
4 Planar Parallel Robotic Machine Design 51
4.1 Preamble 51
4.2 Planar Two Degrees of Freedom Parallel Robotic Machine 57
ixx Contents
4.3 Planar Three Degrees of Freedom Parallel Robotic Machine 61
4.4 Conclusions . 68
5 Spatial Parallel Robotic Machines with Prismatic Actuators . 69
5.1 Preamble 69
5.2 Six Degrees of Freedom Parallel Robotic Machine
with Prismatic Actuators . 70
5.2.1 Geometric Modeling and Inverse Kinematics . 70
5.2.2 Global Velocity Equation . 72
5.2.3 Stiffness Model . 73
5.3 General Kinematic Model of n Degrees of Freedom
Parallel Mechanisms with a Passive Constraining Leg
and Prismatic Actuators 76
5.3.1 Geometric Modeling and Lumped Compliance Model . 76
5.3.2 Inverse Kinematics . 81
5.3.3 Jacobian Matrices . 82
5.3.4 Kinetostatic Model for the Mechanism with
Rigid Links . 84
5.3.5 Kinetostatic Model for the Mechanism
with Flexible Links . 86
5.3.6 Examples 87
5.4 Conclusions . 91
6 Spatial Parallel Robotic Machines with Revolute Actuators 93
6.1 Preamble 93
6.2 Six Degrees of Freedom Parallel Robotic Machine
with Revolute Actuators . 93
6.2.1 Geometric Modeling 93
6.2.2 Global Velocity Equation . 95
6.2.3 Stiffness Model . 96
6.3 General Kinematic Model of n Degrees of Freedom
Parallel Mechanisms with a Passive Constraining Leg
and Revolute Actuators 101
6.3.1 Geometric Modeling and Lumped Compliance Model .101
6.3.2 Inverse Kinematics .102
6.3.3 Jacobian Matrices .106
6.3.4 Kinetostatic Model for the Mechanism with Rigid Links 109
6.3.5 Kinetostatic Model for the Mechanism
with Flexible Links .109
6.3.6 Examples 111
6.4 Conclusions .115
7 Reconfigurable Parallel Kinematic Machine Tools .117
7.1 Preamble 117
7.2 Theoretical Design .118Contents xi
7.3 Kinematics Model 120
7.4 Case Study 122
7.5 Conclusions .125
8 Performance Evaluation of Parallel Robotic Machines 127
8.1 Preamble 127
8.2 Global Stiffness Evaluation 127
8.2.1 Case Study: A Novel Three Degrees
of Freedom Parallel Manipulator 127
8.2.2 Kinematic Modeling 129
8.2.3 The Global Stiffness Evaluation .131
8.3 Optimal Calibration Method .133
8.4 Conclusions .138
9 Design Optimization of Parallel Robotic Machines .139
9.1 Preamble 139
9.2 Optimization Objective and Criteria .140
9.3 Basic Theory of Evolutionary Algorithms 141
9.4 Single-Objective Optimization 146
9.4.1 Objective of Global Stiffness 146
9.4.2 Spatial Six-Degree-of-Freedom Mechanism
with Prismatic Actuators .147
9.4.3 Spatial Six-Degree-of-Freedom Mechanism
with Revolute Actuators 149
9.4.4 Spatial Five-Degree-of-Freedom Mechanism
with Prismatic Actuators .151
9.4.5 Spatial Five-Degree-of-Freedom Mechanism
with Revolute Actuators 153
9.4.6 Spatial Four-Degree-of-Freedom Mechanism
with Prismatic Actuators .156
9.4.7 Spatial Four-Degree-of-Freedom Mechanism
with Revolute Actuators 158
9.4.8 Spatial Three-Degree-of-Freedom Mechanism
with Prismatic Actuators .160
9.4.9 Spatial Three-Degree-of-Freedom Mechanism
with Revolute Actuators 161
9.4.10 The Tricept Machine Tool Family .163
9.5 Multiobjective Optimization .166
9.5.1 Case Study 1: Three Degrees of Freedom
Parallel Manipulator – Two Translations
and One Rotation .166
9.5.2 Case Study 2: Tripod Compliant Parallel
Micromanipulator .179
9.6 Conclusions .185xii Contents
10 Integrated Environment for Design and Analysis
of Parallel Robotic Machine .187
10.1 Preamble 187
10.2 Case Study 188
10.3 Conclusions .203
References .205
Index
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