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IJMERR 2023 Vol.12(3): 159-168
DOI: 10.18178/ijmerr.12.3.159-168

Using Rows and Columns of Distance Matrix to Identify Isomorphisms in Kinematic Chains

Mohamed Aly Abdel Kader* and Abdeslam Aannaque
Mechanical Department, Mohammadia School of Engineering, Rabat, Morocco
*Correspondence: mohamedaly_abdelkader@um5.ac.ma (M.A.A.K.)

Manuscript received September 1, 2022; revised October 20, 2022; accepted January 31, 2023.

Abstract—There has always been a need to develop simple, reliable, and efficient methods for identifying isomorphic kinematic chains (KCs). Discriminating against a large number of KCs in a short period of time is a complex and difficult task at the moment. Most isomorphism identification techniques involve complex concepts and intermediate parameter comparisons, especially as the number of bars increases. The proposed method identifies isomorphism in KCs by generating an invariant from the rows and columns of the distance matrix. All of the results obtained using this method on 8-bar, 10-bar, and 12-bar, three complex 13-bar, 15-bar, and 28-bar simple joint planar kinematic chains, as well as 10-bar and 12-bar simple joint non-planar kinematic chains, agree with the published results. The method's reliability and efficiency are confirmed when the results are compared to previously published works.

Keywords—adjacency matrix, isomorphism, distance matrix, invariant identification

Cite: Mohamed Aly Abdel Kader and Abdeslam Aannaque, "Using Rows and Columns of Distance Matrix to Identify Isomorphisms in Kinematic Chains," International Journal of Mechanical Engineering and Robotics Research, Vol. 12, No. 3, pp. 159-168, May 2023. 

Copyright © 2023 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.