Synthesis of Constrained nR Planar Robots to Reach Five Task Positions

In this paper, we design planar nR serial chains that provide one degree-of-freedom movement for an end-effector through five arbitrarily specified task positions. These chains are useful for deployment linkages or the fingers of a mechanical hand. The trajectory of the end-effector pivot is controlled by n-1 sets of cables that are joined through a planetary gear system to two input variables. These two input variables are coupled by a four-bar linkage, and the movement of the end-effector around its end joint is driven by a second four-bar linkage. The result is one degree-of-freedom system. The design of the cabling system allows control of the shape of the chain as it moves through the task positions. This combines techniques of deployable linkage design with mechanism synthesis to obtain specialized movement with a minimum number of actuators. Two example designs for a 6R planar chain are presented, one with a square initial configuration and a second with a hexagonal initial configuration.