Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory

3T1R four-degrees-of-freedom (DOF) parallel manipulators (3T1R-PMs) are the parallel counterparts of the 4-DOF SCARA serial robots. In a 3T1R-PM, the moving platform can generate 3T1R motion (also called Schonflies motion), which refers to a rotation about any axis with a given direction in conjunction with 3-DOF translations. A method is proposed for the type synthesis of 3T1R-PMs based on screw theory. The wrench systems of a 3T1R parallel kinematic chain (3T1R-PKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of 3T1R-PMs. The type synthesis of legs for 3T1R-PKCs, the type synthesis of 3T1R-PKCs, as well as the selection of actuated joints of 3T1R-PMs, are dealt with in sequence. 3T1R-PKCs with and without inactive joints are synthesized. The phenomenon of dependent joint groups in a 3T1R-PKC is revealed for the first time. Several 3T1R-PMs with identical type of legs are obtained.