Extension of the Euler-Savary Equation to Hypoid Gears

抄録

The Euler-Savary equation is the most fundamental relationship used to determine the relative curvature of a two-dimensional tooth profile which corresponds to relative motion.In this paper, the necessary conditions for gearing were analyzed, when a pair of tooth surfaces mesh continuously with a contact line and the basic relationships between tooth surfaces and their relative motion were derived mathematically.In addition, the relative normal curvature and the geodesic torsion of the tooth surfaces and relative motion were shown to be related to hypoid gears, and the Euler-Savary law was extended to the equation of three-dimensional tooth surfaces for the most general form of gearign.