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3D Model 02: 3D-Printable Hyperboloidal Gear Model

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 gears have an involute tooth profile. Also, the bearings for the top gear are shaped as parabolas, and the base is a plain circle.

This model transmits rotation between shafts crossed at 45°.

Click to download these .STL files

Download Link
Size:941 KB
Last Updated:2018-05-01

List of 3D-Printed Parts:

2hyp_gear.stlThe main hyperboloidal gear.
1hyp_gear_end.stlThe end portion of the lower gear.
1hyp_gear_end_long.stlThe end portion of the upper gear.
1hyp_base.stlThe circular base on which all bearings are mounted.
2hyp_stand_upper.stlThe parabola-shaped bracket for the upper gear.
2hyp_stand_lower.stlThe bracket for the lower gear.
1hyp_handle.stlThe handle to be attached to the end portion of the upper gear.


  • 14 metric M3 Phillips-head countersunk screws;
  • 12 metric M3 nuts.

Installation Instructions:

  1. While holding the gear upright, slide an M3 nut to its socket using a groove on the inside of the gear's bottom, as shown here by the red arrow.
  2. Attach the gear_end using an M3 screw.
  3. Insert the other 3 nuts into their sockets, and install 3 other screws one by one.
  4. Repeat steps 1 to 3 with the 2nd gear and gear_end_long.
  5. Mount the 1st gear between two lower brackets (stand_lower), insert the brackets into their slots on the base, secure with screws and nuts.
  6. Mount the 2nd gear between two upper brackets (stand_upper). insert the brackets into their slots on the base, secure with screws and nuts.
  7. Install the handle, align holes, secure with two screws.

Video of the Model in Action:

Enjoy your hyperboloidal gear model!