The model for screw pair in the actuator of power screw, which is used in the active optics system, is established, and the mathematical expression of the motion is also derived based on the kind of friction. Specifically, the stick-slip motion as well as its criterion function is analyzed in detail, and then the influence of parameters of the screw pair on the stick-slip motion is obtained. With the above expression, the actual screw-driven system is adopted for modeling and optimization. In addition, the same screw pair is modeled and analyzed using software Simulink, and it can be demonstrated that both the mathematical expression and simulation provide very similar results.