Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

Abstract

In this paper, we study the synthesis of wire flexures to achieve orthogonal motion by using a recently developed screw theory based approach. For a given desired mobility pattern, our goal is to find a system of wire flexures that are simply connected in parallel between the functional stage and the ground. It has been shown that a wire flexure is essentially a pure force or a line screw. An n dof motion space (allowable motion) is realizable if its reciprocal constraint space can be spanned by 6 – n line screws or forces. We first enumerate all possible one to five degree of motion spaces that are formed by motions along the coordinate axes attached on the functional stage. For each of these 34 motion spaces, we apply the screw theory approach to find its reciprocal force space as well as its rank. We conclude that 18 of them are realizable, 4 are realizable only when their pitches have opposite signs and 12 are not realizable. For each of these 34 cases, we provide an example showing the maximum number of independent wire flexures.