This tutorial briefly explains the math behind non-circular gears, and demonstrates how to quickly design and test a pair of meshing non-circular gears in Blender 2.81 (earlier versions of Blender can be used too.)
The math is not exactly trivial, but we have developed an online calculator which completely shields you from all the intricacies of non-circular formulas. You do need to come up with an equation in polar coordinates for the first gear's pitch curve, and the calculator will generate the toothed outlines for both gears automatically. With the help of this calculator, you can design your own pair of unique, amazing and fully functional non-circular gears in minutes!
The end result of this tutorial, a Blender 2.81 .blend file, can be downloaded via the link below.