A highly efficient integrated transmission unit -external generating wave movable teeth transmission − was proposed and two kinds of typical transmission types were researched. Fixed and moving coordinate systems were established based on movable teeth transmission theory. On the basis of the profile of a wave generator, the teeth profile equations of ring gear were deduced by using the transform matrix and profile enveloping principle. The effects of the teeth number of the ring gear,

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... g wave coefficient, and tooth profile coefficient on the profile of the ring gear were investigated. The formula for calculating curvature radius of the ring gear was given. The pressure angle formulas were deduced, and the change rule of the pressure angle extremum was researched to obtain a continuous transmission condition. The relationship between design parameters and performance effect was analysed based on the analysis of the curvature and pressure angle. The results show that the transmission precision reached 97.67%, and the proper design parameters could guarantee transmission performance. Those researches lay a theoretical foundation for the design and application of an external generating wave movable teeth title.