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In view of the extensive research and application status of the two-rotation-one-translation three-DOF (degrees of freedom) parallel mechanism in five-axis hybrid machining equipment, and inspired by the excellent performance design of the commercial Exechon parallel manipulator, a 2-PRU-PRRPa parallel manipulator with a parallelogram sub-loop structure in its branches was proposed. Firstly, using screw theory for the analysis of the DOF, it was determined that the mechanism possessed two rotational and one translational degrees of freedom. Secondly, based on the closed-loop vector method, the inverse kinematics analysis of the mechanism was carried out, establishing the mapping relationship between the input of the driving joint and the output of the moving platform’s end. Thirdly, considering the drive range and singular configurations, the workspace of the 2-PRU-PRRPa parallel mechanism was computed by using a search method. Subsequently, by differentiating the kinematic equations of the parallel mechanism, the velocity equations were derived. Additionally, based on the velocity Jacobian matrix, the input, output, and mixture singular configurations of the manipulator were analyzed. Furthermore, the mechanism’s performance was evaluated based on motion/force transmission indices, resulting in a transmission performance distribution map. Aiming for an optimal transmission space, the 2-PRU-PRRPa parallel manipulator was optimized by using spatial modeling methods. The kinematic analysis and performance optimization of the 2-PRU-PRRPa parallel manipulator offered critical insights for the advancement of five-axis hybrid machining systems.