KINEMATIC CHAINS FOR ROBOT HANDS .1. ORDERLY NUMBER-SYNTHESIS

Number synthesis of kinematic chains usually involves the generation o f a complete list of kinematic chains followed by a time-consuming, co mputer-intensive procedure for the elimination of isomorphs. A signifi cant unsolved problem in number synthesis is the guaranteed precise el imination of all isomorphs. Since there is no efficient algorithm for always determining whether two kinematic chains are isomorphic, any '' efficient'' algorithm has a finite probability of rejecting a unique, potentially useful, chain. This paper reviews the history of number sy nthesis and presents a new orderly method for synthesising kinematic c hains. This new Melbourne method guarantees to produce a complete list of chains, which, only when some doubt to the uniqueness of a chain e xists, may include an isomorphic chain. As a consequence, this techniq ue produces significantly fewer isomorphs in the output list than do p revious techniques; often no isomorphs are produced by the method what soever. It is proposed that in many situations where the synthesis of kinematic chains is required, the processing of duplicate chains in th e early stage of design is preferable to the omission of a potentially useful chain.