On the design of parallel manipulators for a prescribed workspace: A planar quaternion approach

In this paper we present a technique for designing parallel planar manipulators capable of reaching any set of points in a prescribed workspace. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a single RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. The structure of these equations is used to define a solution technique that yields the desired chains. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that construct a manipulator that reaches the prescribed workspace.