Stiffness of Parallel Manipulators With Serially Connected Legs

Abstract

A simple yet general method determines the stiffness matrix for parallel manipulators with serially connected legs. Link and actuator flexibilities for each leg are modeled by flexibility matrices that are additive. The effect of passive joints is implicitly included using reciprocal screws to yield a leg stiffness matrix that is generally singular. Since the legs act in parallel the leg stiffnesses are additive and yield the manipulator stiffness. The method is applicable to overconstrained, exactly constrained, and underconstrained robots in generic or singular configurations. It is illustrated using the Tricept robot containing a passive constraint leg and an overconstrained translating manipulator. Numerical results are confirmed using commercial structural analysis software.