Theory of conjugate surfaces formation by generating lines

Set forth herein is the theoretical basis of the most general case of conjugate surfaces formation for gearings (toroids etc.) by conjugate lines with two independent motion parameters, both in working and machine meshing. Each conjugate surface of the gear teeth constitutes an envelope of the corresponding family of cutting surfaces, performed by two-parametric lines motion (cutting edges) in the machine meshing. Formation of conjugate surfaces by uni-parametric lines motion is considered as a private case of the two-parametric one. A diagram and an analytic dependence is obtained for all theoretically possible methods of conjugate surfaces formation by generating lines.