Optimal synthesis of parallel robots' actuators stiffness for given combinations of twist and wrench sets

Abstract Robot stiffness synthesis, with the goal of obtaining given instantaneous displacements for known loads, may result in a non-feasible stiffness matrix. This paper presents a stiffness synthesis scheme that generates a feasible stiffness matrix, which, for a known set of wrenches, results in optimized end-effector twists as close as possible to the given ones. This was achieved by minimizing the variance between the given and the actual motion screw parameters formulated as a non-linear optimization problem. This approach is demonstrated in an artificial spinal disc joint that consists of a passive parallel robot structure, designed to resemble the natural motion of adjacent spine vertebrae under a known set of loads.