In order to derive a general and proper transformed coordinate system according to the characteristics of ball screw mechanism, a doublenut pretighten ball screw was selected as an example of study. The homogeneous transformation matrix between the each coordinate system of the doublenut ball screw was first established. Then, based on it, the unified and intuitive relationship was derived of small displacement and rotation and force between the coordinate systems of the ball screw, by using differential transformation method. The differential relationship of the ball bearing was derived by the present method, and compared with the authority of differential relationship of ball bearing in the literature, to verify the derivation method. And the differential relationship of the doublenut ball screw was established by the other method, and compared with that of come from used method to ensure the reliability of the expression of relationship derived. Finally, according to the derived differential relationship of ball screws, compared and analyzed modeling of contact rigidity in different axial, the calculated value of theoretic model established is more closed to the measured value in experiment than that of a traditional model.