Geometric Modeling and Meshing Characteristics of the Toroidal Drive

This paper investigates the geometric properties of the toroidal drive, reveals the meshing characteristics, and develops analytical models of both axial section and normal section of the toroidal tooth profile. Based on coordinate transformation, the meshing function is obtained and leads to the necessary condition of existence of the enveloping surface. The helix and helix lead angle are then proposed for meshing between the sun-worm and planet worm-gears and both undercutting curve and meshing limit curve are introduced. This further leads to the induced normal curvature for evaluating gearing properties and the selection of the best suitable meshing parameters. The geometric analysis and analytical modeling present a tool for design, leading to three tables of numerical results and design parameters. This is then demonstrated in a three-dimensional modeling of both helical sun-worm and stationary internal gear of the toroidal drive.