Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar single degree-of-freedom chains

Abstract

An algorithm to exhaustively enumerate and structurally classify planar simple-jointed kinematic chains using the hierarchical representation of Fang and Freudenstein is proposed in which all isomorphic chains are automatically eliminated in the enumeration procedure such that isomorphism testing on the final set of chains is eliminated. An efficient rule-based technique for eliminating degenerate kinematic chains is also proposed. This efficient scheme allows for the exhaustive enumeration of complicated cases that have received little or no attention in the past due to the difficult and time-consuming aspect of testing the kinematic chains for isomorphisms. For verification, the algorithm is first applied to enumerate the single degree-of-freedom 6-, 8-, and 10-bar cases, then to the 12-bar case (for which the results verify or contradict those reported in three previous papers), and finally to the previously intractable 14-bar case.