Abstract: Spherical actuators have been able to achieve spatial 3 degree of freedom(DOF) motion, which provides support for the realization of driveless spherical joints and intelligent compliance devices. But existing load self-respect than small spherical actuator driven manipulator, such as the limited direct driving problem, difficult to meet the demand of high precision, lightweight trajectory planning. To solve the above problems, a novel rigid-flexible coupling system(R-FCS) of spherical actuator is designed, and a hybrid polynomial trajectory planning method of "cubic polynomial + improved quartic polynomial" applied to the system is proposed, and compared with the single polynomial trajectory planning method. Firstly, the partial differential dynamics model of the manipulator in the following coordinate system is established based on Hamilton's principle, and the dynamics model of the R-FCS is constructed based on the dynamics model of the spherical actuator. Then, the improved hybrid polynomial trajectory planning method is used to realize the backstepping sliding mode tracking control of the R-FCS. Finally, the R-FCS test platform of spherical actuator for mechanical wrist joint is built. The simulation and test results show that this method can avoid the fluctuation and discontinuity caused by the unreasonable angular acceleration setting, make the mechanical wear of the system less, the movement is more stable, and the fluctuation of the angular velocity is improved, which verifies the effectiveness and accuracy of the scheme.