Using Rows and Columns of Distance Matrix to Identify Isomorphisms in Kinematic Chains

Abstract

—There has always been a need to develop simple, reliable, and efficient methods for identifying isomorphic kinematic chains (KCs). Discriminating against a large number of KCs in a short period of time is a complex and difficult task at the moment. Most isomorphism identification techniques involve complex concepts and intermediate parameter comparisons, especially as the number of bars increases. The proposed method identifies isomorphism in KCs by generating an invariant from the rows and columns of the distance matrix. All of the results obtained using this method on 8-bar, 10-bar, and 12-bar, three complex 13-bar, 15-bar, and 28-bar simple joint planar kinematic chains, as well as 10-bar and 12-bar simple joint non-planar kinematic chains, agree with the published results. The method's reliability and efficiency are confirmed when the results are compared to previously published works.