Document Type : Research Paper


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



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.