Loss of upper limb function often appears after stroke. In this paper the 3D mechanism design for an electromagnetically powered end-effector based robotic manipulator was developed for post-stroke physical therapy. The proposed system delivers a dexterous performance and has a novelty among end-effector based rehabilitation robots. Its design incorporates curved links, which expand the manipulators performance abilities, and, as a result, increase the range of types of rehabilitation therapies. The proposed robotic manipulator can provide a patient with three and two degrees of freedom in shoulder and elbow joints, respectively. It has seven degrees of freedom, and is capable of 7 kg payload. The design of manipulators linkages was optimized to decrease the weight of the system.