This paper presents a robot system developed for medical purpose. A 6-degree-of-freedom robot was introduced for physical exercise and rehabilitation. This system was proposed for stroke patients or patients who cannot use one of their arms or legs. The robot system exercises the hemiplegic part based on the motion of normal part of a patient. Kinematic studies on the human body and robot were applied to develop the robotic rehabilitation exercise system. A clamp which acts as an end effector of the robot to hold a patient was designed and applied to the robot to guarantee the safety of patients. The proposed robotic rehabilitation system was verified by simulations and experiments on arm (elbow and shoulder) motion. Patients are expected to be able to exercise various motions by themselves with the proposed robotic rehabilitation system.