Mechanism Design: Enumeration of Kinematic Structures According to Function

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CRC Press, Sep 19, 2000 - Technology & Engineering - 328 pages
Traditionally, mechanisms are created by designer's intuition, ingenuity, and experience. However, such an ad hoc approach cannot ensure the identification of all possible design alternatives, nor does it necessarily lead to optimum design. Mechanism Design: Enumeration of Kinematic Structures According to Function introduces a methodology for systematic creation and classification of mechanisms.

With a partly analytical and partly algorithmic approach, the author uses graph theory, combinatorial analysis, and computer algorithms to create kinematic structures of the same nature in a systematic and unbiased manner. He sketches mechanism structures, evaluating them with respect to the remaining functional requirements, and provides numerous atlases of mechanisms that can be used as a source of ideas for mechanism and machine design.

He bases the book on the idea that some of the functional requirements of a desired mechanism can be transformed into structural characteristics that can be used for the enumeration of mechanisms. The most difficult problem most mechanical designers face at the conceptual design phase is the creation of design alternatives. Mechanism Design: Enumeration of Kinematic Structures According to Function presents you with a methodology that is not available in any other resource.
 

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Contents

Introduction
1
12 A Systematic Design Methodology
2
13 Links and Joints
3
14 Kinematic Chains Mechanisms and Machines
9
15 Kinematics of Mechanisms
11
16 Planar Spherical and Spatial Mechanisms
12
17 Kinematic Inversions
15
18 Summary
16
623 Planar Cam Mechanisms
133
63 Spherical Mechanisms
135
64 Spatial Mechanisms
136
641 Spatial Onedof Mechanisms
138
642 Spatial Multidof MultipleLoop Mechanisms
140
65 Summary
141
Exercises
143
Epicyclic Gear Trains
145

References
17
Basic Concepts of Graph Theory
21
212 Walks and Circuits
22
214 Articulation Points Bridges and Blocks
23
217 Complete Graph and Bipartite
24
218 Graph Isomorphisms
25
22 Tree
26
24 Spanning Trees and Fundamental Circuits
28
25 Eulers Equation
30
27 Matrix Representations of Graph
31
271 Adjacency Matrix
32
272 Incidence Matrix
33
273 Circuit Matrix
35
274 Path Matrix
36
28 Contracted Graphs
38
29 Dual Graphs
40
210 Summary
43
References
44
Structural Representations of Mechanisms
47
32 Functional Schematic Representation
48
33 Structural Representation
51
34 Graph Representation
52
341 Advantages of Using Graph Representation
53
35 Matrix Representation
57
352 Incidence Matrix
58
36 Summary
59
References
60
Exercises
61
Structural Analysis of Mechanisms
65
43 Degrees of Freedom
66
44 Loop Mobility Criterion
71
45 Lower and Upper Bounds on the Number of Joints on a Link
72
46 Link Assortments
74
47 Partition of Binary Link Chains
76
48 Structural Isomorphism
79
49 Permutation Group and Group of Automorphisms
81
491 Group
82
492 Group of Automorphisms
83
410 Identification of Structural Isomorphism
85
4102 Identification by Characteristic Polynomial
86
4103 Optimum Code
89
4104 Degree Code
90
411 Partially Locked Kinematic Chains
92
412 Summary
93
References
94
Exercises
95
Enumeration of Graphs of Kinematic Chains
101
52 Enumeration of Contracted Graphs
102
53 Enumeration of Conventional Graphs
107
54 Atlas of Graphs of Kinematic Chains
111
55 Summary
112
Exercises
113
Classification of Mechanisms
115
62 Planar Mechanisms
116
622 Planar Geared Mechanisms
129
72 Structural Characteristics
146
73 BuchsbaumFreudenstein Method
151
74 Genetic Graph Approach
158
75 Parent Bar Linkage Method
159
76 Mechanism Pseudoisomorphisms
161
77 Atlas of Epicyclic Gear Trains
162
771 Onedof Epicyclic Gear Trains
163
773 Threedof Epicyclic Gear Trains
164
78 Kinematics of Epicyclic Gear Trains
165
781 Fundamental Circuit Equations
167
782 Examples
168
79 Summary
172
Exercises
174
Automotive Mechanisms
179
821 Functional Requirements
180
823 Enumeration of VSEngine Mechanisms
181
83 ConstantVelocity Shaft Couplings
184
832 Structural Characteristics
185
833 Enumeration of CV Shaft Couplings
186
84 Automatic Transmission Mechanisms
189
841 Functional Requirements
194
842 Structural Characteristics
197
843 Enumeration of Epicyclic Gear Mechanisms
198
85 Canonical Graph Representation of EGMs
199
851 Structural Characteristics of Canonical Graphs
201
852 Enumeration of Canonical Graphs
204
853 Identification of Fundamental Circuits
209
854 Detection of Transfer Vertices
214
86 Atlas of Epicyclic Gear Transmission Mechanisms
215
87 Summary
217
Exercises
219
Robotic Mechanisms
221
921 Functional Requirements
222
923 Enumeration of Planar Parallel Manipulators
225
924 Enumeration of Spherical Parallel Manipulators
227
925 Enumeration of Spatial Parallel Manipulators
228
93 Robotic Wrist Mechanisms
231
931 Functional Requirements
234
932 Structural Characteristics
238
933 Enumeration of Threedof Wrist Mechanisms
240
94 Summary
243
References
245
Exercises
247
Solving m Linear Equations in n Unknowns
249
A2 Solving m Equations in n Unknowns
250
References
252
Atlas of Contracted Graphs
253
Atlas of Graphs of Kinematic Chains
255
Atlas of Planar Bar Linkages
261
Atlas of Spatial Onedof Kinematic Chains
275
Atlas of Epicyclic Gear Trains
279
Atlas of Epicyclic Gear Transmission Mechanisms
291
Index
307
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