Al-Qadisiyah Journal for Engineering Sciences

A graph-based method for detecting isomorphism of geared kinematic chains using a circuit matrix and vertex degree array

Articles in Press

Document Type : Research Paper

Authors

Sajad Hussein Abdali
Farah Mohammed Saoud
Essam Esmail

Department of Mechanical Engineering., College of Engineering, University of Al-Qadisiyah, Iraq

https://doi.org/10.30772/qjes.2023.142060.1010
Abstract
Several approaches for detecting isomorphism in kinematic chains have been developed in recent literature. If two kinematic chains have a 1-1 correspondence and their incidences are maintained, they are isomorphic. In this work, a matrix-based method for identifying isomorphism is presented. The new method is based on fundamental circuits, vertex degrees, and spanning trees. A unique identifier for isomorphic graphs is proposed. Two graphs are isomorphic if their isomorphic identification numbers have the same value. This reduces the structural isomorphism test to a comparison of the isomorphic identification numbers of the two graphs under consideration. Regardless of vertex labeling of the graphs, which is problematic in other ways, similar isomorphic identification numbers are generated for isomorphic graphs. The new method is a comprehensive, systematic way for detecting isomorphism during the synthesis of kinematic chains. Isomorphic graphs are identified regardless of graph representation. The new approach is verified by the atlas of 6-link 2- degree of freedom planetary gear mechanisms (PGMs), the atlas of 5-link 2-degree of freedom planetary geared cam mechanisms (PGCMs) as well as some PGMs and PGCMs.

Keywords

Circuit Matrix
Isomorphism
kinematic chains
Spanning tree
Planetary gear mechanism (PGM)
Al-Qadisiyah Journal for Engineering Sciences

Articles in Press, Accepted Manuscript
Available Online from 12 January 2024

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