The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

Camus’s theorem provides a universal approach to the synthesis of conjugate profiles when the relative motion program is assigned through the relative centrodes (pitch curves). The main point is to choose the most convenient auxiliary curve, in order to trace the pair of conjugate tooth profiles as trajectories of a point or envelope of a second curve attached to this auxiliary curve. Thus, Camus’ concept of auxiliary surface (AS) is extended to the case of involute gears with skew axes with the aim to provide a unified theory to synthesize any type of gears.