Geometric optimization of manipulator structures for working volume and dexterity

Broadly speaking, the regional structure of a manipulator, which consists of the inboard three joints and the members associated with them, determines the workspace shape and volume. The orientation structure, which, for a six degree of freedom manipulator, consists of the three furthest outboard joints and members, determines the geometric dexterity or orientation potential of the manipulator. It is possible, using straightforward geometric arguments, to determine the optimal dimensions of the regional structure for a given total length. By the use of the spherical counterpart of Grashof´s theorem formulated by Freudenstein, it is possible also to show that there is an optimum geometry of the orientation structure.