Identification of Cospectral Simple Jointed Kinematic Chains using Characteristic Polynomial of Degree Matrix and Structural Matrix

Abstract

Abstract Different methods to address the isomorphism in kinematic chains existed earlier and is well reported. In all the methods, link-adjacency matrix (LAM) represents the structural information of a given kinematic chain. Having gathered a large collection of co-spectral chains belonging to a large number of chain categories possessing (containing up to 20 links and up to 13 degrees of freedom), the present work aims at addressing the isomorphism by developing and implementing a methodology for isomorphism based on characteristic coefficients of the degree matrix and structural matrix representations of a specified Simple Jointed Kinematic Chain (SJKC) being computed and comparing. While the above two tests proved to be successful in most cases, two instances of cospectral cases were discovered wherein the above polynomial-based tests failed to detect dissimilarity in the chain structures. These cases are reported in the paper.