People with hemiplegia require ongoing rehabilitation exercises to regain function in their upper limbs. However, due to the increasing number of elderly and disabled people, the number of rehabilitation professionals is insufficient. As a solution to this problem, researchers have been exploring various upper limb rehabilitation exercise robots. Unfortunately, these robots are often large and heavy, making them cumbersome to wear and use. The proposed exoskeleton rehabilitation robot consists of two robotic modules: an elbow module (1 DOF) and a wrist module (1 DOF). In order to analyze the robot"s workspace, the kinematics were calculated using the D-H parameters. To generate the trajectories, five able-bodied individuals wore the robot and performed the hand-wash motion, resulting in a total of 10 trajectory data sets. The reference trajectories were then generated by polynomial regression based on the collected data. Lastly, a passive mode control was experimented with in the rehabilitation process, and the results demonstrated the promising effectiveness of the proposed robot.