On the basis of the theory of synthesis of spatial meshings the mathematical model of worm pair a general view on axial section of a coil of the worm which profile is set by any smooth curveis developed. For improvement of working conditions and qualitative parameters of the worm gear, the interfaced surfaces organizeis convex-concave contact of nearest curvature. The operating program
developed on the basis of created mathematical model, boots in NC-system the universal treating centre for generation of a worm and gear working surfaces
