A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances

Abstract

This paper presents a novel method based on screw theory for the analysis of position accuracy in spatial parallel manipulators with revolute joint clearances. The method is general, and can tackle with an arbitrary pose error function, expressed as a quadratic function of the end-effector displacement. The method performs a maximization of the pose error function, based on a 2-step computational procedure. The first computational step is analytical and leads to a sub-optimal estimate of the maximum pose error. This analytical solution represents the exact maximum pose error for the calculus of the angular accuracy in the special case of fully translational parallel mechanisms. The second computational step is numerical, and starting from the previous solution, can converge to the exact maximum pose error in a limited number of iterations. The relevance of the method is demonstrated through some application examples, where the worst-case angular and linear position accuracy in translating fully parallel manipulators is determined. As a further contribution, this paper shows how the position accuracy due to joint clearances in parallel manipulators is strictly dependent of the mechanism pose and its association to kinematic isotropy.