The solid modeling of bevel gears has been recognized as a major design challenge. Various approaches have been proposed to approximate the theoretical involute-generated contact surface of bevel gears. As a means to accurately represent contact surfaces of these gears, the exact spherical involute is introduced here. The solid models of straight and spiral bevel gears are obtained by applying simple sweeping techniques to their tooth profiles which are described by the exact spherical involute. Furthermore, the volumetric properties of the modeled bevel gears are readily computed from their piecewise-linear approximation.

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