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Technical Briefs

Unified Topological Representation Models of Planar Kinematic Chains

[+] Author and Article Information
Huafeng Ding

Robotics Research Center, Yanshan University, Qinhuangdao 066004, China; Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Qinhuangdao 066004, Chinadhf@ysu.edu.cn

Jing Zhao

 Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Qinhuangdao 066004, Chinahappyzj03@163.com

Zhen Huang

Robotics Research Center, Yanshan University, Qinhuangdao 066004, Chinahuangz@ysu.edu.cn

J. Mech. Des 131(11), 114503 (Oct 13, 2009) (6 pages) doi:10.1115/1.4000215 History: Received January 11, 2009; Revised September 02, 2009; Published October 13, 2009

This paper attempts to establish unified topological models and corresponding mathematical representations for planar simple joint, multiple joint, and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then, new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological model of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to undertake unified structure synthesis and further to establish conceptual design platform for various planar mechanisms. Synthesis examples of both multiple joint and geared chains are given, which show the effectiveness of the unified topological models.

FIGURES IN THIS ARTICLE
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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Chain
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Figures

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Figure 1

(a) A nine-link simple joint kinematic chain and (b) its topological graph

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Figure 2

(a) A multiple joint kinematic chain, (b) its conventional bicolor topological graph, (c) its new bicolor topological graph, and (d) its basic topological graph

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Figure 3

(a) A multiple joint kinematic chain, (b) its new bicolor topological graph, and (c) its basic topological graph

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Figure 4

(a) A bicolor topological graph and (b) its corresponding multiple joint chain, and (c) another bicolor topological graph and (d) its corresponding multiple joint chain

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Figure 5

(a) A geared kinematic chain, (b) its conventional tricolor topological graph, (c) its new topological graph, and (d) its basic topological graph

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Figure 6

(a) A geared kinematic chain and (b) its new topological graph

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Figure 7

The new bicolor topological graph for a multiple joint chain

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Figure 8

New topological graphs and their corresponding geared chains derived from Fig. 7

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