A Novel Algorithm for Solving Design Equations for Synthesizing Platform Linkages

This paper revisits the problem of geometric design of platform linkages such that one or more of its points of the platform stays on a sphere or a plane. We develop a novel algorithm taking advantage of linear structure in the design constraint equations. The new algorithm reduces the problem of synthesizing platform linkages with spherical and plane constraints to a two-stepped process: null space analysis followed by a generalized eigenvalue problem. An example is provided to show the effectiveness of the algorithm.