Variable stiffness design of redundantly actuated planar rotational parallel mechanisms

Redundantly actuated planar rotational parallel mechanisms (RAPRPMs) adapt to the requirements of robots under different working conditions by changing the antagonistic internal force to tune their stiffness. The geometrical parameters of the mechanism impact the performances of modulating stiffness. Analytical expressions relating stiffness and geometrical parameters of the mechanism were formulated to obtain the necessary conditions of variable stiffness. A novel method of variable stiffness design was presented to optimize the geometrical parameters of the mechanism. The stiffness variation with the internal force was maximized. The dynamic change of stiffness with the dynamic location of the mechanism was minimized, and the robustness of stiffness during the motion of the mechanism was ensured. This new approach to variable stiffness design can enable off-line planning of the internal force to avoid the difficulties of on-line control of the internal force.