Synthesis of spatial RPRP loops for a given screw system

Abstract

The dimensional synthesis of spatial chains for a prescribed set of positions can be used for the design of parallel robots by joining the solutions of each serial chain at the end effector. In some cases, this may yield a system with negative mobility. The synthesis of some overconstrained but movable linkages can be done if the finite screw system associated to the motion of the linkage is known. For these cases, the screw system could be related to the finite tasks positions traditionally defined in the synthesis theory. This paper presents the simplest case, that of the spatial RPRP closed chain, for which one solution exists. © Springer Science+Business Media B.V. 2010.