Theory of Parallel Mechanisms

Name: Theory of Parallel Mechanisms
Brand: Springer
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Zhen Huang Qinchuan Li Huafeng Ding(Author)

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1st Edition

Published on 26. July 2012

XIV, 422 pages

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978-94-007-4201-7 (ISBN)

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Content

Intro
Theory of Parallel Mechanisms
Preface
Contents
Chapter 1: Basics of Screw Theory
1.1 Introduction
1.2 Equation of a Line
1.3 Mutual Moment of Two Lines
1.4 Line Vectors and Screws
1.4.1 The Line Vector
1.4.2 The Screw
1.5 Screw Algebra
1.5.1 Screw Sum
1.5.2 Product of a Scalar and a Screw
1.5.3 Reciprocal Product
1.6 Instantaneous Kinematics of a Rigid Body
1.6.1 Instantaneous Rotation
1.6.2 Instantaneous Translation
1.6.3 Instantaneous Screw Motion
1.7 Statics of a Rigid Body
1.7.1 A Force Acting on a Body
1.7.2 A Couple Acting on a Body
1.7.3 A Twist Acting on a Body
References
Chapter 2: Dependency and Reciprocity of Screws
2.1 Concept of Screw Systems
2.2 Second-Order Screw System
2.2.1 Linear Combination of Two Screws
2.2.2 Special Two-Screw System
2.3 Third-Order Screw System
2.3.1 Principal Screws
2.3.2 Special Three-Screw Systems
2.4 Grassmann Line Geometry
2.5 Screw Dependency in Different Geometrical Spaces
2.5.1 Basic Concepts
2.5.2 Different Geometrical Spaces
2.6 Reciprocal Screws
2.6.1 Concept of a Reciprocal Screw
2.6.2 Dualism in the Physical Meaning of Reciprocal Screws
2.7 Reciprocal Screw System
2.8 Reciprocal Screw and Constrained Motion
2.8.1 Three Skew Lines in Space
2.8.2 Three Lines Parallel to a Plane Without a Common Normal
2.8.3 Three Non-concurrent Coplanar Lines
2.8.4 Three Coplanar and Concurrent Line Vectors
2.8.5 Three Line Vectors Concurrent in Space
2.8.6 Three Line Vectors Parallel in Space
References
Chapter 3: Mobility Analysis Part-1
3.1 The Concept and Definition of Mobility
3.2 Mobility Open Issue
3.2.1 Grübler-Kutzbach Criterion
3.2.2 Mobility Open Issue
3.3 Mobility Principle Based on Reciprocal Screw
3.3.1 Mechanism Can Be Expressed as a Screw System
3.3.2 Development of Our Unified Mobility Principle
3.3.3 The Modified G-K Formulas
3.4 Constraint Analysis Based on Reciprocal Screw
3.4.1 The Common Constraint
3.4.2 Parallel Constraint
3.4.3 Over-Constraint
3.4.4 The Generalized Kinematic Pair
3.5 Mobility Property Analyses
3.5.1 Translation and Rotation
3.5.2 Rotational Axis
3.5.3 Instantaneous Mobility and Full-Cycle Mobility
3.5.4 Full-Field Mobility
3.5.5 Parasitic Motion
3.5.6 Self-motion
References
Chapter 4: Mobility Analysis Part-2
4.1 Mobility Analysis of Simple Mechanisms
4.1.1 Open Chain Linkage
4.1.2 Roberval Mechanism
4.1.3 RUPUR Mechanism
4.1.4 Hervé Six-Bar Mechanism
4.1.5 Spatial 4P Mechanism
4.1.6 Delassus H-H-H-H Mechanism
4.1.7 Hervé's CCC Mechanism
4.2 Mobility Analysis of Classical Mechanisms
4.2.1 Bennett Mechanism
4.2.2 Five-Bar Goldberg Linkage
4.2.3 Six-Bar Goldberg Linkage
4.2.4 Myard Linkage with Symmetrical Plane
4.2.5 Bricard with Symmetrical Plane
4.2.6 Altmann Abb.34 Mechanism
4.2.7 Altmann Six-Bar Linkage
4.2.8 Waldron Six-Bar Linkage
4.3 Mobility Analysis of Modern Parallel Mechanisms
4.3.1 4-DOF 4-URU Mechanism
4.3.2 3-CRR Mechanism
4.3.3 Zlatanov and Gosselin's Mechanism
4.3.4 Carricato's Mechanism
4.3.5 Delta Mechanism
4.3.6 H4 Manipulator
4.3.7 Yang's Mechanism
4.4 Mobility Analysis of Hoberman Switch-Pitch Ball
4.4.1 Structure Analysis
4.4.2 Three-Link Chain
4.4.3 Eight-Link Loop
4.4.4 Double Loop
4.4.5 Three-Loop Chain
4.4.6 The Whole Mechanism
4.5 Six-Hole Cubiform Mechanism
4.5.1 Double-Hole Linkage
4.5.2 Four-Hole Linkage
4.5.3 Five-Hole Linkage
4.5.4 The Whole Six-Hole Mechanism
References
Chapter 5: Kinematic Influence Coefficient and Kinematics Analysis
5.1 Concept of KIC
5.2 KIC and Kinematic Analysis of Serial Chains
5.2.1 Position Analysis
5.2.2 First-Order KIC
5.2.3 Second-Order KIC
5.3 Kinematic Analysis of Parallel Mechanism
5.3.1 First-Order KIC and Mechanism Velocity Analysis
5.3.1.1 Velocity of Point P in the Platform
5.3.1.2 Velocity of Point Q in Link k of Limb r
5.3.2 Second-Order KIC and Mechanism Accelerations
5.3.2.1 Acceleration of Platform
5.3.2.2 Acceleration of Link k in Limb r
5.4 Virtual Mechanism Principle of Lower-Mobility Parallel Mechanisms
5.4.1 Virtual Mechanism Principle
5.4.2 Kinematic Analysis Based on Virtual Mechanism Principle
References
Chapter 6: Full-Scale Feasible Instantaneous Screw Motion
6.1 Introduction
6.2 Determination of Principal Screws
6.2.1 The Representation of Pitch and Axes
6.2.2 Principal Screws of a Third-Order Screw System
6.2.2.1 Quadratic Curve Degenerating Theory
6.2.2.2 Quadric Degenerating Theory
6.3 Full-Scale Feasible Instantaneous Screws of the 3-RPS Mechanism
6.3.1 Virtual Mechanism and Jacobian Matrix
6.3.2 Upper Platform Is Parallel to the Base
6.3.3 The Upper Platform Rotates by an Angle a About Line a2a3
6.3.4 General Configuration of the 3-RPS Mechanism
6.4 Full-Scale Feasible Instantaneous Screw of a 3-UPU Mechanism
6.4.1 Mobility Analysis
6.4.1.1 Analysis of Limb
6.4.1.2 Whole Mechanism
6.4.2 First-Order Influence Matrices and Kinematic Analysis
6.4.3 Initial Configuration
6.4.4 The Second Configuration
6.5 Full-Scale Feasible Instantaneous Screw of a 3-RPS Pyramid Mechanism
6.5.1 First-Order Influence Coefficient Matrix
6.5.2 Principal Screws and Full-Scale Feasible Motions
6.5.2.1 Original Configuration
6.5.2.2 Three Input Links Have the Same Length
6.5.2.3 Common Configuration
6.6 A 3-DOF Rotational Parallel Manipulator Without Intersecting Axes
6.6.1 An Open Problem of the PMs with Intersecting Axes
6.6.2 A 3-D Revolute Mechanism Without Intersecting Axes
6.6.2.1 Mobility Analysis of the 3-RPS Cubic PM
6.6.2.2 The Property of Mobility and Full-Scale Feasible Moving Screws
6.6.3 The Orientation Workspace
6.6.3.1 Position Analysis of the 3-RPS Cubic PM
6.6.3.2 The Orientation Workspace
6.6.4 Examples
6.6.5 Discussions About the Differences Between the SPMs and the 3-RPS Cubic PM
References
Chapter 7: Special Configuration of Mechanisms
7.1 Introduction
7.2 Classification of the Special Configuration
7.2.1 Singular Kinematics Classification
7.2.2 Classification of the Singularity via a Linear Complex
7.3 Singular Kinematic Principle
7.4 Singularity Loci of 3/6-Stewart for Special Orientations
7.4.1 Typical Singularity Structures of 3/6-SP
7.4.2 Hyperbolic Singularity Equation Derived in an Oblique Plane
7.4.3 Singularity Equation Derived in 3D Space
7.4.3.1 Singularity Equation for the Orientation (90° ? 0)
7.4.3.2 Singularity Equation for the Orientation (±90° ? 0)
Derivation of the Equation
Analysis of the Singularity Property
Analysis of Other Singularities
7.4.4 Singularity Distribution in 3D Space
7.5 Structure and Property of the Singularity Loci of 3/6-Stewart for General Orientations(f ? ±30°, ±90°, ±150°)
7.5.1 Singularity Equation Based on Theorem 7.2 for General Orientations
7.5.2 Singularity Analysis Using Singularity-Equivalent-Mechanism
7.5.2.1 Parallel Case
Singularity-Equivalent-Mechanism
Forward Position Analysis of the Singularity Equivalent-Mechanism
Singularity Equation in the theta Plane
7.5.3 General Case
7.5.3.1 Singularity-Equivalent-Mechanism
7.5.3.2 Forward Position Analysis of the Singularity-Equivalent-Mechanism
7.5.3.3 Singularity Equation in the theta Plane
7.5.4 Five Special Cases of the Singularity Equation
7.6 Structure and Property of the Singularity Loci of the 6/6-Stewart
7.6.1 Jacobian Matrix
7.6.2 Singularity Analysis in 3D Space
7.6.3 Singularity Analysis in Parallel Principal-Sections
7.6.3.1 Singularity Locus Equation in the theta Plane
7.6.3.2 Property Identification of the Singularity Loci in Parallel Principal Sections
7.6.3.3 Singularity Analysis When ? = 0
7.7 Singularity of a 3-RPS Manipulator
7.7.1 3-RPS Mechanism
7.7.1.1 Constraint Equation of the 3-RPS Parallel Manipulator
7.7.1.2 Position and Orientation Analysis
7.7.2 Singularity and Its Spatial Distribution
7.7.2.1 Singularity Equation
7.7.2.2 Two Special Cases
7.7.2.3 Singularity Distribution in 3D Space
Singular Surface
Singular Points in a Vertical Line
7.7.3 Geometry and Constraint Analysis
Appendix A
References
Chapter 8: Dynamic Problems of Parallel Mechanisms
8.1 Over-Determine Inputs
8.1.1 Influence Coefficient Matrices and Inertia Forces
8.1.2 The Accordant Equation for Over-Determinate Inputs
8.1.3 Optimization of Over-Determinate Input
8.1.4 The Weight Distribution of the Input Torques
8.2 Kinetostatic Analysis of 4-UPU Parallel Mechanisms
8.2.1 Main-Pair Reaction Forces1
8.2.1.1 Main-Pair Reactions Produced by Force Fh$Fh
8.2.1.2 Main-Pair Reactions Produced by Limb Applied Force F1t$F1t
8.2.1.3 All the Constraint Reactions of Other Pairs
8.2.2 Numerical Example
8.3 Kinetostatic Analysis of 4-R(CRR) Parallel Manipulator
8.3.1 4-R(CRR) Parallel Manipulator
8.3.2 Main-Pair Reaction
8.3.2.1 Main-Pair Reactions Produced by Platform Force
8.3.2.2 Main-Pair Reactions Produced by Limb Force
8.3.3 Active Moments and Reactions of Other Pairs in Limbs3
8.3.3.1 Reactions of Revolute Pair at bi
8.3.3.2 Reactions of Cylindrical Pair at ci
8.3.3.3 Active Moments and Reactions of Revolute Pair at Ai
8.3.4 Numerical Example
8.3.5 Discussion
References
Chapter 9: Constraint Screw-Based Method for Type Synthesis
9.1 Description of Constraints Acting on a Rigid Body
9.2 Limb Twist and Limb Constraint Systems
9.2.1 Limb Twist System
9.2.2 Limb Constraint System
9.3 Platform Twist and Platform Constraint Systems
9.3.1 Platform Twist System
9.3.2 Platform Constraint System and Classification of Lower-Mobility PMs
9.4 Constraint-Screw Based Synthesis Method
9.4.1 Procedure of the Constraint-Screw Based Synthesis Method
9.4.2 Generation of Different Architectures of PM
9.4.3 Discrimination for Instantaneous PMs
9.5 Examples
9.5.1 Type Synthesis of a 3R2T 5-DOF PM
9.5.1.1 Constraint Synthesis
9.5.1.2 Generation of Limb Chains
9.5.1.3 Generation of PMs
9.5.2 Type Synthesis of 2R3T 5-DOF PMs
9.5.2.1 Constraint Synthesis
9.5.2.2 Generation of Limb Chains
9.5.2.3 Generation of PMs
9.5.3 Type Synthesis of 1R3T 4-DOF PMs
9.5.3.1 Constraint Synthesis
9.5.3.2 Generation of Limb Chains
9.5.3.3 Generation of PMs
9.5.4 Type Synthesis of 3R1T 4-DOF PMs
9.5.4.1 Constraint Synthesis
9.5.4.2 Generation of Limb Chains
9.5.4.3 Generation of PMs
9.5.5 Type Synthesis of 2R2T 4-DOF PMs
9.5.5.1 Constraint Synthesis
9.5.5.2 Generation of Limb Chains
9.5.5.3 Generation of PMs
9.5.6 Type Synthesis of a 2R1T 3-DOF PM
9.5.6.1 Constraint Synthesis
9.5.6.2 Generation of Limb Chains
9.5.6.3 Generation of PMs
9.5.7 Type Synthesis of a 3T 3-DOF PM
9.5.7.1 Constraint Synthesis
9.5.7.2 Generation of Translational PMs with 3-DOF Limb Chains
9.5.7.3 Generation of Translational PMs with 4-DOF Limb Chains
9.5.7.4 Generation of Translational PMs with 5-DOF Limb Chains
9.5.8 Type Synthesis of a 3R 3-DOF PM
9.5.8.1 Constraint Synthesis
9.5.8.2 Generation of Rotational PMs with 3-DOF Limb Chains
9.5.8.3 Generation of Rotational PMs with 4-DOF Limb Chains
9.5.8.4 Generation of Rotational PMs with 5-DOF Limb Chains
9.5.9 Type Synthesis of a 1R2T 3-DOF PM
9.6 Type Synthesis of Non-symmetrical PMs
References
Chapter 10: Digital Topology Theory of Kinematic Chains and Atlas Database
10.1 Topology Modeling of Mechanisms
10.1.1 Modeling of Simple Joint Kinematic Chains
10.1.2 Modeling of Multiple Joint Kinematic Chains
10.1.2.1 Conventional Topological Graph
10.1.2.2 New Topological Graph
10.1.3 Modeling of Geared (cam) Kinematic Chains
10.1.3.1 Conventional Topological Graph
10.1.3.2 New Topological Graph
10.2 Loop Operation Algebra of Kinematic Chains
10.2.1 Loop and Its Representation
10.2.2 "Ø" Operation of Loops
10.2.3 "?" Operation of Loops
10.2.4 "?" Operation of Loops
10.2.5 Loop Analysis
10.2.5.1 Independent Loop Set
10.2.5.2 Loop Relationship
10.2.6 Edge-Based Operations of Loops
10.2.6.1 The "Ø" Operation of Loops
10.2.6.2 The "?" Operation of Loops
10.2.6.3 The "?" Operation of Loops
10.3 Isomorphism Identification
10.3.1 Perimeter Topological Graph
10.3.2 Canonical Perimeter Topological Graph
10.3.3 Characteristic Perimeter Topological Graph
10.3.4 Examples of Isomorphism Identification
10.3.5 Analysis of Computational Complexity
10.4 Detection of Rigid Sub-chains
10.5 Digital Atlas Database and Synthesis
References
Index

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Theory of Parallel Mechanisms

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