This paper puts forward a new method for identification of kinematic chains isomorphism, which is called the topological structure code permutation group method of polyhedral solid. It can be put into practice by means of computer, and it is exact, dependable, quick and efficient. When isomorphism of two kinematic chains is identified by the method, it only need determine whether one permutation can be found out or not between topological structure codes of the two kinematic chains, or determine whether adjoint codes of the two topological structure codes are equal or not, it need not find out a symmetry group at all. It applies to all kinds of non-separable closed kinematic chains that don’t contain compound hinges.

In this paper, a new concept called polyhedral solid is put forward, the polyhedral solid model is given, and a theorem that describes the relation of faces, vertices, edges and geometric solids of a connected graph is given and proved. This paper expounds the definitions and general forms of the topological structure code and its adjoint code, the methods and rules of coding, the procedure of generating them. It also expounds and proves the beingness, accuracy and the uniqueness of the topological structure code and its adjoint code and the necessary and sufficient condition and criteria of kinematic chains isomorphism as well. The algorithm and some typical examples for identification of kinematic chains isomorphism are given.

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