Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs which use less number of actuators and can be reconfigured without disassembly. This paper deals with the type synthesis of 2-DOF PMs with both spatial parallelogram translational mode and equal-diameter spherical rotation mode. At first, a 2-DOF 3-4R overconstrained PM is proposed based on a 5-DOF US equivalent PM proposed in the literature. From this 2-DOF PM, we further obtain a 3-4R PM for equal-diameter spherical rotation and a 3-4R PM for spatial parallelogram translation. By finding the common conditions for the 2-DOF 3-4R PM for spatial parallelogram translation and 2-DOF 3-4R PM for equal-diameter spherical rotation, the types of 2-DOF 3-4R PMs with both spatial parallelogram translational mode and equal-diameter spherical rotation mode are then obtained. This work enriches the types of PMs with multiple operation modes and overconstrained mechanisms.

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