Numerous robots have been widely used to deliver rehabilitative training for hemiplegic patients to improve their functional ability. Because of the complexity and diversity of upper limb motion, customization of training patterns is one key factor during upper limb rehabilitation training. Most of the current rehabilitation robots cannot intelligently provide adaptive training parameters, and they have not been widely used in clinical rehabilitation. This article proposes a new end-effector upper limb rehabilitation robot, which is a two-link robotic arm with two active degrees of freedom. This work investigated the kinematics and dynamics of the robot system, the control system, and the realization of different rehabilitation therapies. We also explored the influence of constraint in rehabilitation therapies on interaction force and muscle activation. The deviation of the trajectory of the end effector and the required trajectory was less than 1 mm during the tasks, which demonstrated the movement accuracy of the robot. Besides, results also demonstrated the constraint exerted by the robot provided benefits for hemiplegic patients by changing muscle activation in the way similar to the movement pattern of the healthy subjects, which indicated that the robot can improve the patient's functional ability by training the normal movement pattern.