Geometric and meshing characteristics of sine tooth profile planetary transmissions with small tooth difference

To address the inherent problems of traditional cycloidal-pin gear transmissions—such as localized wear, large pressure angle fluctuations leading to low reliability of eccentric bearings, and high-precision requirements for uniform pin-tooth distribution—this paper proposes a novel small-tooth-difference planetary transmission scheme utilizing a sinusoidal tooth profile. Based on the kinematic inversion method and differential geometry theory, the parameterized tooth profiles and general meshing equations for the fixed internal ring gear and the conjugate planetary gear are established, and the influence of key geometric parameters on the evolution of tooth profile morphology and interference limits is analyzed. Through analytical and high-precision numerical methods, the characteristic absence of meshing limit points in this gear pair is demonstrated, and the variation laws of meshing characteristics, such as pressure angle, sliding ratio, and induced normal curvature, are systematically revealed. The systematic study indicates that the evolution of the pressure angle exhibits nonlinear periodicity and frequency multiplication characteristics. The multi-tooth simultaneous meshing mechanism (with a theoretical contact ratio reaching 4.56 and 4–5 teeth alternately bearing the load) completely overcomes transmission dead points, even when the local pressure angle of a single tooth reaches 90°. Furthermore, the contact interface is dominated by near-pure rolling, the micro-sliding ratio is suppressed to the order of 10 ⁻³ , and it possesses excellent second-order curvature continuity. This study provides a solid theoretical foundation for the development of novel precision speed reducers.