Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

In this paper, we study the type synthesis of wire flexures to achieve orthogonal motions by using a recently developed screw theory based design 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 $n$ degree-of-freedom (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 34 possible 1–5DOF 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. At last, a typical design is provided for each of these motion spaces.