Synthesis of Spatial RPRP Closed Linkages for a Given Screw System

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negativemobility. These problems can be avoided for some overconstrained but movable linkages if the finite screw system associated to the motion of the linkage is known. The finite screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite tasks positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.