Selecting multi-freedom multi-loop kinematic chains to suit a given task

Developments of number synthesis and the means of enumerating kinematic chains have not lead to a significant flow of novel kinematic structures to successful mechanical designs. This paper addresses one of the difficulties, namely how to select a pertinent kinematic chain from the many that can be enumerated. To this end, a new and important concept called the variety of a kinematic chain is explained and discussed with particular attention to its relationship to the motion capabilities of mechanisms such as robot manipulators and gear trains. Many motion tasks have an inherent hierarchy of freedoms that closely relates to the variety of a kinematic chain, and hence variety can be used to select those candidate mechanisms best suited to an intended function. An epicyclic transmission is used to demonstrate this technique.