Abstract: In order to enrich the types of movable tooth transmission and design a reduction device with higher transmission efficiency and better performance, this paper proposes an external shock wave swing movable tooth transmission system and conducts an in-depth study on the tooth profile of its center wheel. Using the equivalent mechanism of the external shock wave and the swing movable tooth and the tooth profile envelope mechanism, the theoretical tooth profile equation and the actual tooth profile equation of the center wheel are derived, and the changes in the center wheel tooth profile and the actual tooth profile equation are analyzed. The relationship between the parameters. The curvature equation of the theoretical tooth profile of the center wheel is deduced, and the regularity of the curvature is verified through an example.