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A novel class of spatial four degree-of-freedom Schönflies-motion parallel manipulators with four identical subchains is presented. Their features are that each serial subchain undergoes the pure Schönflies motion without redundant joints. The parallel mechanisms possess the simplest topology and are suitable for pick-and-place operations. Kinematic analysis of the 4-PRPaR parallel manipulator, including its inverse and forward kinematics, singularity, and workspace, is discussed in detail. The analysis shows that the moving platform and the base must be in dissimilar dimension for good manipulability performance. The optimal design of the parallel manipulator is formulated as a multiobjective optimization problem. A novel performance index characterizing the approximation of the generated workspace to the prescribed regular workspace, the regular workspace share, is proposed to serve as one of the design objectives. The other objective is the global condition index, which measures the manipulability. The multiobjective optimization problem provides multiple optimal solutions for choice. Simulation verifies that the designed parallel manipulator can approximate the prescribed regular workspace with good condition index.