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The concept of a medical parallel robot applicable to chest compression in the process of cardiopulmonary resuscitation (CPR) is proposed in this paper. According to the requirement of CPR action, a three-prismatic-universal-universal (3-PUU) translational parallel manipulator (TPM) is designed and developed for such applications, and a detailed analysis has been performed for the 3-PUU TPM involving the issues of kinematics, dynamics, and control. In view of the physical constraints imposed by mechanical joints, both the robot-reachable workspace and the maximum inscribed cylinder-usable workspace are determined. Moreover, the singularity analysis is carried out via the screw theory, and the robot architecture is optimized to obtain a large well-conditioning usable workspace. Based on the principle of virtual work with a simplifying hypothesis adopted, the dynamic model is established, and dynamic control utilizing computed torque method is implemented. At last, the experimental results made for the prototype illustrate the performance of the control algorithm well. This research will lay a good foundation for the development of a medical robot to assist in CPR operation.