Resistance distance method for determination of isomorphism, stiffness and best input link among planar Kinematic chains

Abstract

The detection of isomorphism among kinematic chains and their derived mechanisms has been a hot area of research for the last several years. In this paper, a quantitative method (Resistance distance method) is proposed in order to compare all the distinct chains with specified number of links and degree of freedom, for rigidity of the chain and to select the best input link to introduce motion and to test isomorphism thoroughly and uniquely. In this method, the kinematic chains are represented in the form of resistance graph and from that graph a Laplacian matrix is generated which is further transformed into a resistance distance matrix.