## Mechanism Design: Enumeration of Kinematic Structures According to FunctionTraditionally, 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 |

307 | |

### Other editions - View all

Mechanism Design: Enumeration of Kinematic Structures According to Function Lung-Wen Tsai No preview available - 2000 |

### Common terms and phrases

adjacency matrix Appendix ASME Journal atlas automatic transmission Automation in Design axis binary link chain chain of length characteristic polynomial connected contracted graph conventional graph degrees of freedom Drive 2 X X dual graph EGMs EGTs enumeration Epicyclic Gear Trains feasible fixed link Freudenstein functional requirements Functional schematic fundamental circuit gear pair gear set geared edges geared mechanisms graph shown graph theory incidence matrix independent loops input links joint axes Journal of Mechanisms kinematic chain kinematic pairs kinematic structure labeled graphs limb link assortments motion moving platform number of degrees number of independent number of joints number of links number of loops number of vertices output link parallel manipulators permutation planar graph planetary gear prismatic joint revolute joints Robotics rotation shown in Figure Solving Equation structural characteristics synthesis ternary links three-dof total number transmission mechanism Tsai turning pairs turning-pair edges vertex degree wrist mechanisms X X Drive