The tooth profile synthesis of swing movable teeth drives was performed. The tooth profile equation of the internal teeth ring was established. The analysis result shows the deformation distribution of the movable tooth in the normal direction at the contact point of the wave generator is a sine function. Furthermore, the forces of the wave generator, the movable tooth pin and the internal teeth ring acting on the movable tooth were analyzed. Based on the Hertz theory and material mechanics, the contact strength calculation methods for the meshing pairs of the movable tooth and the wave generator as well as the movable tooth and the internal teeth ring were discussed. The calculation method for the bending strength of the pin was also derived. The research result provides a theoretical basis for designing and applying swing movable teeth drives.