Hyperboloidal

This gear model is full to the brim with mathematics, and it works well, too. The reference surface of each of these two gears is the one-sheet hyperboloid, which is formally defined as a "surface of revolution obtained by rotating a hyperbola about the perpendicular bisector to the line between the foci." The profiles of the gear teeth are involute curves. Even the bearings for the top gear are shaped as parabolas.