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This paper presents a method for designing a novel type of movable tooth drive characterized by logarithmic spiral conjugated tooth profiles, which are in almost full surface contact owing to such innovative tooth geometry, in comparison with the conventional involute or cycloidal tooth profiles creating a linear contact. Firstly, the existence conditions of the conjugated curve of the logarithmic spiral are researched by establishing the meshing equation, and its geometric and kinematic properties are identified to design the conjugated tooth profiles of the movable tooth and ring gear. Then, wave generator profile, according to the requirement that it should be completely convex and smooth, is designed and modified to ensure the consistency with load capacity of the conjugated tooth profiles. On this basis, dimensional synthesis of the mechanism is performed following the influence analysis of main factors on the force/motion transmission characteristic of the whole machine. Finally, the virtual prototype is developed and the proposed design method is validated by relevant force performance simulation. The outcomes lay a significant foundation for the design of such logarithmic spiral tooth profile transmission.

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