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Isomorphism identification of kinematic chains is one of the most important and challenging mathematical problems in the field of mechanism structure synthesis. In this paper, a new algorithm to identify the isomorphism of planar multiple joint and gear train kinematic chains has been presented. Firstly, the topological model (TM) and the corresponding weighted adjacency matrix (WAM) are introduced to describe the two types of kinematic chains, respectively. Then, the equivalent circuit model (ECM) of TM is established and solved by using circuit analysis method. The solved node voltage sequence (NVS) is used to determine the correspondence of vertices in two isomorphism identification kinematic chains, so an algorithm to identify two specific types of isomorphic kinematic chains has been obtained. Lastly, some typical examples are carried out to prove that it is an accurate, efficient, and easy mathematical algorithm to be realized by computer.

An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains