A method of transformation from spatial RSSR mechanism to spherical 4R mechanism for spatial driving mechanism design is presented. The necessary conditions of transformation from spatial RSSR mechanism to spherical 4R mechanism are also analyzed. Furthermore,it is proved theoretically that,spatial RSSR mechanism,by defined parameters,can be transformed into spherical 4R mechanism with axes intersection at one point. The prerequisite for each design parameter in transformation from spatial RSSR mechanism to spherical 4R mechanism,when spatial RSSR acts as a driving crank,is thus deduced,which lays a theoretical basis for the application of practical engineering. Based on the method of transformation from spatial RSSR mechanism to spherical 4R mechanism,theoretical calculation and test simulation,a spatial rapier-driving mechanism applicable for high-speed rapier looms is developed. Through this example,this method that spatial RSSR mechanism is replaced by spherical 4R mechanism is verified. The finding indicates that all the requirements of spatial RSSR mechanism can be met and the spherical 4R shows better performance,manufacturability and assemblability. Priority of spherical 4R mechanism is also validated in terms of structure,manufacturability,maintenance and kinematics and dynamics performance.