On the duality of twist/wrench distributions in serial and parallel chain robot manipulators

Duality and reciprocity between twist and wrench systems is the essence of screw theory. The power of these concepts lies in the idea that once a result is obtained for one type of system it can immediately be applied to the dual system provided the appropriate physical interpretation is also translated. The interrelation between serial and parallel mechanisms is a consequence of this twist/wrench duality. The purpose of this investigation is to focus on some fundamental configurations of serial and parallel robot manipulators in an attempt to further elucidate the various correspondences that exist between their geometries and their kinematic equations. The focus is on zero-pitch screw systems, namely revolute joints for serial manipulators and force producing sub-chains in parallel manipulators. Solutions for twist/wrench distributions will be discussed for both proper and redundant systems.