The authors proposed a method that allows the relations between the pitch cone angles and spiral angles to be determined directly. These relations are represented by a system of three nonlinear equations that are derived from: (i) conditions of tangency of the pitch cones and (ii) the specific location of the head—cutter that generates hypoid gears with face—hobbed teeth of uniform depth. A computer program for the determination of pitch cone parameters has been developed.
Equations have also been derived that allow to determine the location of apices of pitch cones with respect to the line of shortest distance, the coordinates of point of tangency of the pitch cones and the orientation of the plane that is tangent to the pitch cones. The proposed method is illustrated with a numerical example.