Enumeration of Basic Kinematic Chains Using the Theory of Finite Groups

Abstract

A procedure for systematically and completely enumerating all nonfractionated planar kinematic chains having N links and F degrees of freedom has been developed. This procedure employs the theory of finite symmetry groups to eliminate isomorphic chains. The analysis of 8-, 9-, and 10-link chains having 1, 2, and 3 degrees of freedom, respectively, is presented as an example.