Title: A new structural code for detecting isomorphism of kinematic chains with simple, multiple and gear pairs

Authors: Rajneesh Kumar Rai; Sunil Punjabi

Addresses: Department of Mechanical Engineering, Shri Dadaji Institute of Technology and Science, Khandwa-450001, MP, India ' Department of Mechanical Engineering, Ujjain Engineering College, Ujjain-456010, MP, India

Abstract: The paper presents a new structural code for the isomorphism detection of kinematic chains (KCs) of mechanisms. Here, a KC is first converted into its corresponding graph and a weight is assigned to each edge of the graph depending upon the type of pair (joint) the edge is representing. Then, the shortest distances of a vertex (under consideration) from the other remaining vertices are decided. These distances are calculated based on the weights of the different edges. Finally, the eccentricities of all the vertices are decided and a structural code is obtained by arranging all the eccentricities in an ascending or a descending order. Similarity between these codes decides the isomorphism. Since the eccentricity considers the structural distances, it is considered as a structural invariant. The method is very simple and has been successfully tested for different types of KCs with different pairs.

Keywords: eccentricity of graph; gear joint; isomorphism; multiple joint; structural code; simple joint.

DOI: 10.1504/IJDE.2024.138946

International Journal of Design Engineering, 2024 Vol.13 No.1, pp.92 - 114

Received: 05 Jun 2023
Accepted: 11 Mar 2024
Published online: 04 Jun 2024 *

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