Proceeded from the topological characteristics of Geared Linkage Mechanisms (GLM) structure, a fully new graph, combinatorial graph, which can be used to describe the topological relationship in a Geared Linkage Kinematic Chain (GLKC), is firstly proposed. Then the corresponding matrix, combinatorial matrix, and the structural invariants of GLKC are presented. Based on the structural invariants, this paper establishes a systematic procedure for detecting isomorphism among GLKCs using the powers of combinatorial matrix. A computer program based on the procedure has been applied successfully for detecting isomorphism among both the planar kinematic chains as well as GLKCs.

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