In order to meet the current demand for lumbar joint rehabilitation, in view of the specificity and complexity of the lumbar joint, based on the physiological characteristics and rehabilitation movement characteristics of the human lumbar joint, firstly, the configuration synthesis of the branch chain and mechanism of the lumbar joint rehabilitation robot was carried out, and the 2-UPU & 2-UPS lumbar joint rehabilitation robots were selected as the research objects. Secondly, an in-depth analysis of its kinematic performance was conducted, and the degrees of freedom were analyzed through the helical theory. The correctness of the proposed comprehensive mechanism scheme was verified, and the characteristics of the rehabilitation motion were demonstrated. Again, a kinematic inverse solution model was established, and its correctness was verified by using MATLAB and RECURDYN simulation software. Finally, based on the inverse kinematic solution model, the kinematic performance of the mechanism was further analyzed. The search method was adopted to determine whether its workspace met the requirements of rehabilitation exercise. The Jacobian matrix of the mechanism was constructed through the spinor theory, and then its singular configuration in the workspace was analyzed. The research results show that during the rehabilitation exercise process, the mechanism does not have performance problems caused by strange configurations, and its kinematic performance is good.