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RESEARCH PAPERS

The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification

[+] Author and Article Information
Huafeng Ding

Robotics Research Center, Yanshan University, P. R. Chinadhf@ysu.edu.cn

Zhen Huang

Robotics Research Center, Yanshan University, P. R. Chinahuangz@ysu.edu.cn

J. Mech. Des 129(9), 915-923 (Sep 09, 2006) (9 pages) doi:10.1115/1.2748451 History: Received April 13, 2006; Revised September 09, 2006

Some new concepts, such as the perimeter loop, the maximum perimeter degree-sequence, and the perimeter topological graph, are first presented in this paper, and the method for obtaining the perimeter loop is also involved. Then, based on the perimeter topological graph and some rules for relabeling its vertices canonically, a one-to-one descriptive method, the canonical adjacency matrix set of kinematic chains, is proposed. Another very important characteristic of the descriptive method is that in the canonical adjacency matrix set the element number is reduced dramatically, usually to only one. After that, an effective method to identify isomorphism of kinematic chains is given. Finally, some typical examples of isomorphism identification including two 28-vertex topological graphs are presented in this paper.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Chain
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Figures

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Figure 1

(a) A 10-bar kinematic chain, (b) its perimeter topological graph, and (c) its canonical perimeter topological graph

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Figure 2

(a) A 9-bar kinematic chain, (b) its PTG based on L(2) as the perimeter loop, (c) its PTG based on L(1⊕2) as the perimeter loop, (d) its PTG based on L(2⊕3) as the perimeter loop, (e) its PTG based on L(1⊕2⊕3) as the perimeter loop, and (f) its canonical perimeter topological graph

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Figure 3

(a), (b) Two 10-bar kinematic chains, (c) the canonical perimeter topological graph of (a), and (d) the canonical perimeter topological graph of (b)

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Figure 4

(a), (c), (e) Three 12-bar kinematic chains, (b) the canonical perimeter topological graph of (a), (d) the canonical perimeter topological graph of (c), and (f) the canonical perimeter topological graph of (e)

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Figure 5

(a), (b) Two 15-vertex topological graphs, (c) the canonical perimeter topological graph of (a), and (d) the canonical perimeter topological graph of (b)

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Figure 6

(a), (b) Two 28-vertex topological graphs, and (c) their common canonical perimeter topological graph

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