On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains

Abstract

Abstract This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains. Salient features of this method, which is based on graph theory, include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for symmetry analysis in kinematic chains; and the utilization of symmetry in the coding process resulting in an unique well arranged numbering of links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with those chains.