Loading...Mechanism Design – Enumeration of Kinematic Structures According to Function
Lung-Wen Tsai
Presidential Chair Professor Department of Mechanical Engineering
Bourns College of Engineering University of California, Riverside
Contents
1 Introduction
1.1 Introduction
1.2 A Systematic Design Methodology
1.3 Links and Joints
1.4 Kinematic Chains, Mechanisms, and Machines
1.5 Kinematics of Mechanisms
1.6 Planar, Spherical, and Spatial Mechanisms
1.7 Kinematic Inversions
1.8 Summary
References
2 Basic Concepts of Graph Theory
2.1 Definitions
2.1.1 Degree of a Vertex
2.1.2 Walks and Circuits
2.1.3 Connected Graphs, Subgraphs, and Components
2.1.4 Articulation Points, Bridges, and Blocks
2.1.5 Parallel Edges, Slings, and Multigraphs
2.1.6 Directed Graph and Rooted Graph
2.1.7 Complete Graph and Bipartite
2.1.8 Graph Isomorphisms
2.2 Tree
2.3 Planar Graph
2.4 Spanning Trees and Fundamental Circuits
2.5 Euler’s Equation
2.6 Topological Characteristics of Planar Graphs
2.7 Matrix Representations of Graph
2.7.1 Adjacency Matrix
2.7.2 Incidence Matrix
2.7.3 Circuit Matrix
2.7.4 Path Matrix
2.8 Contracted Graphs2.9 Dual Graphs
2.10 Summary
References
Exercises
3 Structural Representations of Mechanisms
3.1 Introduction
3.2 Functional Schematic Representation
3.3 Structural Representation
3.4 Graph Representation
3.4.1 Advantages of Using Graph Representation
3.5 Matrix Representation
3.5.1 Adjacency Matrix
3.5.2 Incidence Matrix
3.6 Summary
References
Exercises
4 Structural Analysis of Mechanisms
4.1 Introduction
4.2 Correspondence Between Mechanisms and Graphs
4.3 Degrees of Freedom
4.4 Loop Mobility Criterion
4.5 Lower and Upper Bounds on the Number of Joints on a Link
4.6 Link Assortments
4.7 Partition of Binary Link Chains
4.8 Structural Isomorphism
4.9 Permutation Group and Group of Automorphisms
4.9.1 Group
4.9.2 Group of Automorphisms
4.10 Identification of Structural Isomorphism
4.10.1 Identification by Classification
4.10.2 Identification by Characteristic Polynomial
4.10.3 Optimum Code
4.10.4 Degree Code
4.11 Partially Locked Kinematic Chains
4.12 Summary
References
Exercises
5 Enumeration of Graphs of Kinematic Chains
5.1 Introduction
5.2 Enumeration of Contracted Graphs
5.3 Enumeration of Conventional Graphs
5.4 Atlas of Graphs of Kinematic Chains5.5 Summary
References
Exercises
6 Classification of Mechanisms
6.1 Introduction
6.2 Planar Mechanisms
6.2.1 Planar Linkages
6.2.2 Planar Geared Mechanisms
6.2.3 Planar Cam Mechanisms
6.3 Spherical Mechanisms
6.4 Spatial Mechanisms
6.4.1 Spatial One-dof Mechanisms
6.4.2 Spatial Multi-dof, Multiple-Loop Mechanisms
6.5 Summary
References
Exercises
7 Epicyclic Gear Trains
7.1 Introduction
7.2 Structural Characteristics
7.3 Buchsbaum–Freudenstein Method
7.4 Genetic Graph Approach
7.5 Parent Bar Linkage Method
7.6 Mechanism Pseudoisomorphisms
7.7 Atlas of Epicyclic Gear Trains
7.7.1 One-dof Epicyclic Gear Trains
7.7.2 Two-dof Epicyclic Gear Trains
7.7.3 Three-dof Epicyclic Gear Trains
7.8 Kinematics of Epicyclic Gear Trains
7.8.1 Fundamental Circuit Equations
7.8.2 Examples
7.9 Summary
References
Exercises
8 Automotive Mechanisms
8.1 Introduction
8.2 Variable-Stroke Engine Mechanisms
8.2.1 Functional Requirements
8.2.2 Structural Characteristics
8.2.3 Enumeration of VS-Engine Mechanisms
8.3 Constant-Velocity Shaft Couplings
8.3.1 Functional Requirement
8.3.2 Structural Characteristics8.3.3 Enumeration of C-V Shaft Couplings
8.4 Automatic Transmission Mechanisms
8.4.1 Functional Requirements
8.4.2 Structural Characteristics
8.4.3 Enumeration of Epicyclic Gear Mechanisms
8.5 Canonical Graph Representation of EGMs
8.5.1 Structural Characteristics of Canonical Graphs
8.5.2 Enumeration of Canonical Graphs
8.5.3 Identification of Fundamental Circuits
8.5.4 Detection of Transfer Vertices
8.6 Atlas of Epicyclic Gear Transmission Mechanisms
8.7 Summary
References
Exercises
9 Robotic Mechanisms
9.1 Introduction
9.2 Parallel Manipulators
9.2.1 Functional Requirements
9.2.2 Structural Characteristics
9.2.3 Enumeration of Planar Parallel Manipulators
9.2.4 Enumeration of Spherical Parallel Manipulators
9.2.5 Enumeration of Spatial Parallel Manipulators
9.3 Robotic Wrist Mechanisms
9.3.1 Functional Requirements
9.3.2 Structural Characteristics
9.3.3 Enumeration of Three-dof Wrist Mechanisms
9.4 Summary
References
Exercises
A Solving m Linear Equations in n Unknowns
A.1 Solving One Equation in n Unknowns
A.2 Solving m Equations in n Unknowns
References
B Atlas of Contracted Graphs
C Atlas of Graphs of Kinematic Chains
D Atlas of Planar Bar Linkages
E Atlas of Spatial One-dof Kinematic Chains
F Atlas of Epicyclic Gear Trains
G Atlas of Epicyclic Gear Transmission Mechanisms
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