Type synthesis of 4-DOF SP-equivalent parallel manipulators: A virtual chain approach

SP-equivalent parallel mechanisms are the parallel counterparts of the 4-DOF SP serial manipulators, which are composed of one S (spherical) and one P (prismatic) joint. Using the virtual chain approach that we proposed elsewhere for the type synthesis of parallel mechanisms, this paper deals with the type synthesis of this class of 4-DOF parallel mechanisms. First, the application of the principle of virtual chain to the type synthesis of parallel mechanisms is recalled. Then, the type synthesis of 4-DOF SP-equivalent parallel mechanisms is performed in four steps, namely, the decomposition of the wrench system of an SP-equivalent parallel kinematic chain, the type synthesis of legs of SP-equivalent parallel kinematic chains, the generation of SP-equivalent parallel kinematic chains and the selection of actuated joints. SP-equivalent parallel kinematic chains with and without inactive joints are synthesized. The main characteristic of the proposed approach is that the type synthesis of legs for SP-equivalent parallel kinematic chains is reduced to the type synthesis of 4-DOF single-loop kinematic chains and thus easy to perform. The validity condition of actuated joints of SP-equivalent parallel mechanisms is reduced to the computation of a 4 × 4 determinant. In addition to all the 4-DOF SP-equivalent parallel kinematic chains and 4-DOF SP-equivalent parallel mechanisms proposed in the literature, a number of new 4-DOF SP-equivalent parallel kinematic chains and 4-DOF SP-equivalent parallel mechanisms are identified.