Kinematic chains for robot hands—I. Orderly number-synthesis

Number synthesis of kinematic chains usually involves the generation of a complete list of kinematic chains followed by a time-consuming, computer-intensive procedure for the elimination of isomorphs. A significant unsolved problem in number synthesis is the guaranteed precise elimination 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 synthesis and presents a new orderly method for synthesising kinematic chains. This new Melbourne method guarantees to produce a complete list of chains, which, only when some doubt to the uniqueness of a chain exists, may include an isomorphic chain. As a consequence, this technique produces significantly fewer isomorphs in the output list than do previous techniques; often no isomorphs are produced by the method whatsoever. It is proposed that in many situations where the synthesis of kinematic chains is required, the processing of duplicate chains in the early stage of design is preferable to the omission of a potentially useful chain.