An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph

Isomorphism identification is an essential step in the structure synthesis of Kinematic Chain (KC), and needs a large amount of analysis and calculation. To find an isomorphism identification method with simple rules, scientific feasibility and less analysis and calculation has always been a research hotspot of mechanism scholars. In this paper, the structure information of KC is described by dendrogram structure graph with multiple joints, and Branch-chain Matrix (BM) is separated from the dendrogram structure. The characteristics of BM are analyzed, and the concepts of intimacy between branch-chains and Repeatability Matrix (RM) corresponding to BM are proposed. Based on fact that both dendrogram graph and BM can uniquely determine the structural information of one KC, a new isomorphism identification method for KC, based on row optimal rearrangement and comparison of BM, is proposed. The operation steps are discussed in detail, and several cases are analyzed to show this method has advantages such as easy rules, small calculation of retrieval and comparison, and easy to be programmed.