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.
This model transmits rotation between shafts crossed at 45°.
List of printed parts:
|2||hyp_gear.stl||The main hyperboloidal gear.|
|1||hyp_gear_end.stl||The end portion of the lower gear.|
|1||hyp_gear_end_long.stl||The end portion of the upper gear.|
|1||hyp_base.stl||The circular base on which all bearings are mounted.|
|2||hyp_stand_upper.stl||The parabola-shaped bracket for the upper gear.|
|2||hyp_stand_lower.stl||The bracket for the lower gear.|
|1||hyp_handle.stl||The handle to be attached to the end portion of the upper gear.|
For more information, and for assembly instructions, see http://www.otvinta.com/download13.html.
This video explains the math behind hyperboloidal gears, and how to design them in Blender.