In this paper we present a technique for designing planar parallelmanipulators with platforms capable of reaching any number of desired poses. Themanipulator consists of a platform connected to ground by RPR chains. The set ofpositions and orientations available to the end-effector of a general RPR chainis mapped into the space of planar quaternions to obtain a quadratic manifold.The coefficients of this constraint manifold are functions of thelocations of the base and platform R joints and the distance betweenthem. Evaluating the constraint manifold at each desired pose and defining thelimits on the extension of the P joint yields a set of equations.Solutions of these equations determine chains that contain the desired poses aspart of their workspaces. Parallel manipulators that can reach the prescribedworkspace are assembled from these chains. An example shows the determination ofthree RPR chains that form a manipulator able to reach a prescribedworkspace.
