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IJMERR 2023 Vol.12(5): 297-305
DOI: 10.18178/ijmerr.12.5.297-305

Identification of Kinematic Chains Isomorphism Based on the Distance between Non-binary Vertices

Mohamed Aly Abdel Kader* and Abdeslam Aannaque
Mohammadia School of Engineering, Mohamed V University, Rabat, Morocco
Email: abdeslam.aannaque@emi.um5.ac.ma (A.A.)
*Correspondence: mohamedaly_abdelkader@um5.ac.ma (M.A.A.K.)

Manuscript received February 21, 2023; revised March 22, 2023; accepted May 29, 2023.

Abstract—This paper proposes a method for identifying isomorphisms between different kinematic chains that is highly efficient, reliable, and simple, with a short CPU running time (KC). In contrast to many methods proposed by researchers in this field, which require significant computing time, particularly in kinematic chains with a large number of bars. Isomorphism identification is critical for designers in order to avoid duplicate solutions and focus all of their energy and creativity on novel, independent kinematic chain solutions. The shortest path between non-binary bars is primarily used in this article to solve the problem of isomorphism identification. The computational complexity and efficiency of the method are evaluated and compared to existing published methods for a variety of cases, including 8-bar, 10-bar, 12-bar, three-complex 13-bar, 15-bar, 28-bar, and 42-bar single-joint kinematic chains. These comparisons demonstrate the superiority of the proposed method.

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

Cite: Mohamed Aly Abdel Kader and Abdeslam Aannaque, "Identification of Kinematic Chains Isomorphism Based on the Distance between Non-binary Vertices," International Journal of Mechanical Engineering and Robotics Research, Vol. 12, No. 5, pp. 297-305, September 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.