A novel 2SPU+U+RRR 5-DOF hybrid mechanism with one 2-DOF parallel mechanism and one 3-DOF serial mechanism was presented. This 5-DOF hybrid mechanism had advantages of large workspace and high stiffness compared with traditional hybrid mechanism. A prototype of this hybrid mechanism was constructed and it was equivalent to a U+RRR parallel mechanism, the analytic formulas for solving its inverse/forward displacement kinematics were derived and the forward displacement was derived based on D-H method. The unique solution of the inverse kinematics was determined based on the shortest distance rule, and the correctness of the analytical expression of the inverse/forward displacement kinematics was verified. The length of the two SPU active legs were derived based on the rotation angle of the Hooke hinge, thus the analytic formulas for solving the inverse displacement kinematics of the 2-DOF parallel mechanism was derived. Theoretical kinematics formulas and results provided foundation for the control of the hybrid mechanism, structure optimization design, dynamics performance analysis, manufacturing and applications and the study also enriches the application area of lower-mobility parallel mechanisms. A novel interpolation algorithm for an arc based on equal radian data sampling was derived, the calculation of interpolation algorithm was greatly simplified. In order to verify the correctness of the interpolation algorithm for an arc, the experimental prototype and its control system were built. The simulation result by Matlab and the experimental prototype result showed that the interpolation algorithm for an arc was correctness and this algorithm had great application prospect.