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RESEARCH PAPERS

Topological Representations and Characteristics of Variable Kinematic Joints

[+] Author and Article Information
Hong-Sen Yan

Department of Mechanical Engineering, National Cheng Kung University, No.1, Ta-Hsueh Road, Tainan 70101, Taiwan, R.O.Chsyan@mail.ncku.edu.tw

Chin-Hsing Kuo

Department of Mechanical Engineering, National Cheng Kung University, No.1, Ta-Hsueh Road, Tainan 70101, Taiwan, R.O.Cchkuo717@yahoo.com.tw

J. Mech. Des 128(2), 384-391 (Jun 17, 2005) (8 pages) doi:10.1115/1.2166854 History: Received September 09, 2004; Revised June 17, 2005

There exist some mechanisms with variable topologies that have interesting applications, for examples, legged walking machines, mechanical push-button stopper locks, and various toys. A variable kinematic joint is a kinematic joint that is capable of topological variation in a mechanism with variable topology. This work aims at the topological representations and characteristic analysis of variable kinematic joints. During the operation process of a mechanism, the topology states of a variable kinematic joint can be expressed symbolically as the joint sequences, graphically the digraphs, and mathematically the matrices. With the applications of graph theory, it proves that the topological characteristics of variable kinematic joints appeared with the abilities of reversibility, continuity, variability of degrees of freedom, joint homomorphism, contractibility, and expansibility. Two examples are provided for illustrating how the proposed concepts can be used to analyze and synthesize the variable joints. The results of this work provide a logical foundation for the systematic structural synthesis regarding the kinematic joints and mechanisms with variable topologies.

FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
Topics: Motion , Topology , Mechanisms
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Figures

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Figure 1

Operation concept of a mechanical push-button stopper lock mechanism

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Figure 2

A variable joints (pin-in-slot joint)

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Figure 3

A variable joint with a series of type variations of kinematic pairs

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Figure 4

A variable prismatic joint

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Figure 5

A variable revolute joint

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Figure 6

A variable joint with the combination of variable types and variable orientations of kinematic pairs

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Figure 7

Digraph of the variable joint shown in Fig. 3

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Figure 8

Two homomorphic joints and their digraph

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Figure 9

Contractibility of variable joints: an example of Fig. 8

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Figure 10

Expansibility of variable joints: an example of Fig. 9

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Figure 11

A two-member key chain

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Figure 12

A creation of the two-member key chain

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Figure 13

A four-bar Geneva mechanism

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Figure 14

Graph and matrix representations of the joint incident to the slider and the rectangular block of the Geneva mechanism

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