Geometric Modelling of Elliptical Gears Generated by Shaper Cutters

The geometric modeling of elliptical gears is formulated using envelope theory, by means of a suitable shaper-cutter with involute tooth profile. A general algorithm producing the pitch curves of elliptical gears and their rack with any number of lobes is proposed. Evolutes of pitch curves can be also obtained in order to choose a suitable shaper-cutter, even for pitch curves with concave-convex profiles. The complete modeling of both meshing elliptical gears and their rack is reported, several graphical results being shown for design and analysis purposes. Computer animations are also supported.