3D Tutorial 13: Hyperboloidal Gears: Math and How to Model Them in Blender

Hyperboloidal gears are essentially regular spur gears with their top and bottom twisted in the opposite directions. A hyperboloidal gear's reference surface is a hyperboloid, which is a surface obtained from a regular cylinder by twisting its top and bottom.

Two identical hyperboloidal gears are capable of transmitting rotation at any angle between 0° and 90° with the gear ratio of 1. This tutorial explains the math behind turning two touching cylinders into mating hyperboloids given the cylinders' dimensions and desired shaft angle, and how to model and test a pair of meshing hyperboloidal gears in Blender.

The end result of this tutorial, a .blend file containing a smoothly running hyperboloidal gear pair, can be downloaded via the link below.

3D-Printable Hyperboloidal Gear Model