Generation of tooth surfaces by two-parameter enveloping

Abstract The equations obtained permit us to determine and investigate surfaces and conditions for tooth undercutting in the case when the generation of these surfaces can be mathematically described by means of a pattern with two independent parameters of enveloping. This method is illustrated by two examples of surface generation: 1. (a) Hobbing of involute conical gears with a cylindrical worm-shaped cutter; 2. (b) Meshing with a variable angle between the axes of geas. Both of these examples have certain independent value.