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介绍了一种新型的传动机构超环面行星蜗杆传动，运用啮合理论的包络法建立了这种传动中行星轮与蜗杆、行星轮与内齿轮啮合的基本方程，进而得到了蜗杆和内齿轮的齿面方程、螺旋升角方程、界限曲线方程及诱导法曲率方程等。并以球形行星轮轮齿为例，运用数值计算方法得出了蜗杆、内齿轮的轴截面形状、蜗杆及内齿轮在计算圆上不同截面的螺旋升角值和这种传动的一界及二界曲线的形状等，为这种新型传动的设计、加工、制造提供了理论依据。
A new type of toroidal transmission with toroidal worm gear is introduced. The envelope equation of meshing theory is used to establish the basic equations of meshing between planet gear, worm gear, planet gear and internal gear. The worm gear and internal gear Of the tooth surface equation, spiral angle equation, the limit curve equation and induction method curvature equation. Taking the spherical planetary gear teeth as an example, the axial cross-sectional shapes of the worm and the internal gear are obtained by numerical calculation. The values of the helix angle of different sections of the worm and internal gear in calculating the first and second The curve of the shape of the sector, etc., for this new type of transmission design, processing, manufacturing provides a theoretical basis.