This paper proposes an approach for calculating the transmission ratio of nutation drive based on the working principle of the nutation movements. Then, the analysis of the influences for the nutation angle on the transmission ratio is carried out. The controllable tooth profile modelling for external and internal spiral bevel gears with double circular-arc is proposed. Based on the proposed tooth profile modeling, the three dimensional modeling and virtual assembly of the nutation drive have been further completed. Finally, the kinematical simulation is preceded in the simulating system and the comparative results have been accomplished between the simulation results and the theoretical ones of the transmission ratio.