Abstract
In investigating the problems of engagement of different gear tooth profiles, the authors have found a generality for these problems. Meanwhile, according to the theory of computational geometry and numerical experiments, a parametric cubic spline function is found as a proper curve-fit technique to represent the tooth profiles of these gears. A general method and its numerical algorithm, based on the generality observed and the spline function chosen, is developed for the calculation of gear cutting tools and mating gears with arbitrary profiles. The cutting tools applied include: gear cutters, grinding wheels, and form milling cutters. The method can also be applied to the inspection of the manufacturing accuracy of the gear or helical screw profiles. A computational procedure is illustrated.
