This paper presents a novel Schönflies-motion Parallel Manipulator with RotationalPitch motion (SPM-RP) based on a single-platform fully parallel mechanism. An analysis of the position, workspace, velocity, and singularity of the SPM-RP is carried out in detail, and a dimensionless Jacobian is proposed to evaluate the manipulability of the SPM-RP. The analysis shows that the SPM-RP is with position-decoupled kinematics, a large singularity-free workspace, and excellent manipulability. The SPM-RP is actuated by four parallel prismatic actuators, enabling the manipulator to provide the identical kinematic performance at all generic cross sections perpendicular to the prismatic joint axes within its workspace. This paper thus proposes a reduced design optimization formulation, where the traditional optimization over the entire workspace is reduced to the optimization on a representative workspace cross section of the SPM-RP. According to this approach, the design optimization of the SPM-RP is carried out by maximizing its manipulability over the total orientation workspace, which is crucial for precision assembly. Based on the achieved optimal design, an SPM-RP prototype is developed. The mobility, orientation capability, total orientation workspace, and repeatability of the optimal design are tested and verified by the developed SPM-RP prototype. Experiments show that the SPM-RP can achieve a large total orientation workspace with excellent precision performance.