Goal-oriented resolution of the actuator redundancy in parallel manipulators

This paper addresses the inverse dynamics of redundantly actuated parallel manipulators. Such manipulators feature advantageous properties, such as a large singularity-free workspace, a high possible acceleration of the moving platform, and higher dexterity and manipulability. Redundant actuation allows for prestress, i.e. internal forces without generating end-effector wrenches. This prestress can be employed for various goals. It can be used to avoid backlash in the driving units or to generate a desired tangential end-effector stiffness. In this paper the inverse dynamics solution and thereupon the generation of prestress is addressed. The general formulation for the dynamics of redundantly actuated parallel manipulators is given. A closed-form solution is derived in terms of a single prestress parameter, for the special case of simple redundancy. This admits an explicit parametrization of prestress. With this formulation an open-loop prestress control is proposed and applied to the elimination of backlash. The approach is demonstrated for a planar 4RRR manipulator and a spatial heptapod.