Isomorphic identification for kinematic chains using variable high-order adjacency link values

Isomorphism identification is a crucial issue in the type synthesis of kinematic chains (KCs). To date, various topological characteristics have been used to detect isomorphism, but the manner of the correspondence between two isomorphic KCs has seldom been investigated. In this paper, a method using variable high-order adjacency link values to identify isomorphisms in KCs is proposed. First, the definition of improved high-order adjacency link values, which are used to describe the characteristics of KCs, is introduced in detail. The variable high-order adjacency link values are then calculated repeatedly through reassignment procedure according to the repetitions of their elements for one KC. Finally, isomorphisms are identified and all manner of the correspondence are detected by comparing two high-order adjacency link strings from two KCs. The proposed method is tested on 8-link, 15-link, and 28-link KCs, and all results demonstrate its feasibility and efficiency.