A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three-legged, three-degree-of-freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The inverse kinematic solutions, though trivial, are implicit in the formulation of the constraint surface equations. Herein the forward kinematic solutions of planar parallel robots with arbitral, mixed leg architecture are exposed completely, and in a unified way, for the first time. Copyright

Journal of Mechanical Design, Transactions of the ASME
Department of Mechanical and Aerospace Engineering

Hayes, M.J.D, Zsombor-Murray, P.J. (P. J.), & Chen, C. (C.). (2004). Unified kinematic analysis of general planar parallel manipulators. Journal of Mechanical Design, Transactions of the ASME, 126(5), 866–874. doi:10.1115/1.1767186