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Isomorphic identification for kinematic chains using variable high-order adjacency link values

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Abstract

Isomorphism identification is a crucial issue in the type synthesis of kinematic chains (KCs). To date, various topological characteristics have been used to detect isomorphism, but the manner of the correspondence between two isomorphic KCs has seldom been investigated. In this paper, a method using variable high-order adjacency link values to identify isomorphisms in KCs is proposed. First, the definition of improved high-order adjacency link values, which are used to describe the characteristics of KCs, is introduced in detail. The variable high-order adjacency link values are then calculated repeatedly through reassignment procedure according to the repetitions of their elements for one KC. Finally, isomorphisms are identified and all manner of the correspondence are detected by comparing two high-order adjacency link strings from two KCs. The proposed method is tested on 8-link, 15-link, and 28-link KCs, and all results demonstrate its feasibility and efficiency.

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Abbreviations

KC-a, KC-b :

Kinematic chains noted a and b, respectively

D :

Adjacency matrix

n :

Number of links in KC

m :

Number of joints in KC

r :

Order of the adjacency link value

\(s_i^r\) :

r-order adjacency value of the link-i

S r :

r-order adjacency link string

\({{}_{\mathrm{a}}^{\mathrm{b}}\boldsymbol{M}}\) :

Correspondence manners between KC-a and KC-b

\({\boldsymbol{S}}_{{\rm{a}},k}^r\) :

r-order adjacency link string of KC-a after the k-th reassignment procedure

\({\boldsymbol{S}}_{{\rm{b}},k,l}^r\) :

One of r-order adjacency link string of KC-b with index l after the k-th reassignment procedure

p :

Number of reassignments for KC-a

q :

Number of reassignments for KC-b

c k :

Number of new r-order adjacency link string of KC-b after k-th reassignment procedure

T :

Replaced sequence

G :

Substituting sequence

X :

Set for assignment of initial link value

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Acknowledgments

This work is supported by Research Program supported by the National Natural Science Foundation of China (Grant No. 51675488, 51675487), China.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Leiying He, Faxin Liu, Liang Sun & Chuanyu Wu

  2. Key Laboratory of Transplanting Equipment and Technology of Zhejiang Province, Hangzhou, 310018, China

    Leiying He, Liang Sun & Chuanyu Wu

Authors
  1. Leiying He
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  2. Faxin Liu
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  3. Liang Sun
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  4. Chuanyu Wu
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Correspondence to Chuanyu Wu.

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Recommended by Associate Editor Ki-Hoon Shin

Chuanyu Wu (cywu@zstu.edu.cn), is a Professor in Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou, China. He received his doctoral degree in Mechanical Engineering from Zhejiang University in 2002. His researches focus on mechanical design and optimization.

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He, L., Liu, F., Sun, L. et al. Isomorphic identification for kinematic chains using variable high-order adjacency link values. J Mech Sci Technol 33, 4899–4907 (2019). https://doi.org/10.1007/s12206-019-0930-9

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  • DOI: https://doi.org/10.1007/s12206-019-0930-9

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