Aiming at the error caused by the forcing analysis on the cycloid ball planetary transmission through the ball system and solving sum term inaccuracy to the elastic rotation angle,an exact solution of elastic rotation angle is presented by using the meshing stiffness coefficient and the numerical analysis software,and the changing law of dynamic rotation angle is explained. The model of force analysis and mathematical model are established,the expression of elastic rotation angle parameter is obtained. The concept of torsional stiffness is presented,and through the change of torsional stiffness,the changing nature of the dynamic rotation angle is reflected. The Fourier series expansion of the torsional stiffness in a period is carried out,the influence of different parameters on torsion stiffness is analyzed,and the simulation experiments are carried out. The results show that with the increasing of the short amplitude coefficient,rolling circle radius,number of steel balls and the ball radius values,the torsional stiffness coefficient and amplitude becomes larger,the influence of the number of steel balls on the rotational stiffness coefficient is the greatest.