Differential geometrical conditions of hypoid gears with conjugate tooth surfaces

Hypoid gears are one of the most general form of gearing, and a theoretical solution for them has been studied by many researchers. Many hypotheses and theorems about these gears have been proposed-some of them correct and many of them wrong. The tooth surfaces are parts of general curved surfaces and they must have principal directions and principal curvatures on every contact point. However, there has been no detailed re search on the fundamental elements of the surface. This study develops necessary conditions for determining these curvatures and principal directions for conjugate gearing with a contact line by introducing the concept of geodesic torsions. [S1050-0472(00)00503-1].