1992 Volume 58 Issue 556 Pages 3734-3741
Hypoid gears are the most general form of gearing, and their theoretical solution has been long in coming. Many guesses or theorems about gearing 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. But there have been no discus-sions on such fundamental elements of the surface. This paper develops necessary conditions for determining these curvatures and principal directions for gearing with a contact line, introducing the concept of geodesic torsions.