In quest of a reliable and efficient isomorphism index for simple jointed kinematic chains

A variety of computational techniques for the detection of isomorphism in kinematic chains have been published in the literature over the last several decades. Each one of them suffers from some shortcoming or the other amply demonstrated through counterexamples for each of the tests. Having detected several such counterexamples in the categories of 12-link simple jointed kinematic chains possessing one and three degrees of freedom, this paper attempts to propose an isomorphism test that will express the given closed chain into several rooted-tree structures, which are in turn expressed in the form of a set of strings. These set of strings have been found to represent a chain in a robust manner, and hence can be considered as the isomorphism index of the given chain. The entire procedure of converting the given kinematic chain through to its representation has been programmed in python.