Number synthesis of kinematic chains based on permutation groups

Abstract

A systematic and precise approach is developed for enumerating non-isomorphic kinematic chains based on the theory of permutation groups. First, we define contracted link adjacency matrices of kinematic chains, and elements in the matrices are separated into four sets. We then propose an algorithm for assigning values to elements of these sets to generate non-isomorphic configurations according to their permutation groups. As a result, the numbers of simple kinematic chains with up to twelve links and seven degrees of freedom are listed.