Objective Aiming at the problem of shoulder joint subluxation and motor dysfunction caused by stroke in patients a spherical four-bar mechanism is applied to shoulder joint rehabilitation training and a single degree of freedom shoulder joint rehabilitation training mechanism is designed to achieve the expected motion rules during shoulder joint rehabilitation training. Methods A kinematic model of the spherical four-bar mechanism was established and the correctness of the kinematic model was verified through the MATLAB kinematic analysis program. By integrating the approximate rigid body guidance synthesis method and the least squares method an objective function model for the main branch chain and loop of the mechanism was established. The penalty function method was used to classify and process the constraints of the mechanism and a differential evolution DE algorithm for optimizing and synthesizing spherical fourbar mechanisms was established. Results The comprehensive numerical example of approximate rigid body guidance using the spherical four-bar mechanism was used for verification and the convergence of the iterative curve was strong. The results showed that the above objective function model was correct and feasible and the algorithm was efficient and reliable. On this basis the optimal size parameters that meet the functional requirements of shoulder rehabilitation training were solved. Conclusion SolidWorks and ADAMS software are applied to generate the linkage point motion trajectory and kinematic simulation curve of the mechanism. The simulation results show that the designed mechanism meets the expected motion trajectory requirements and has good kinematic performance. This provides a theoretical basis for the development of shoulder joint rehabilitation training devices with simple structures and reliable functions.