It has become increasingly popular that robot is applied to assist patients with central nervous system injury in rehabilitation exercise. This paper introduces a novel 5-DOF upper limb exoskeleton rehabilitation robot. In MATLAB, the forward kinematics expression of the robot is established by using the D-H method and the workspace of the robot is analyzed by Monte Carlo method. Considering the physiological characteristics of the human body and the practical requirement of rehabilitation movement, this paper uses the "Swivel Angle" to solve the redundancy solution problem of inverse kinematics of the robot on line. In order to verify the correctness of the kinematics model of the robot, a simulation experiment based on the minimum jerk trajectory planning is designed. This work lays the foundation for the future studies on dynamics, control and human-computer interaction strategy of the robot.