@rasputin I just used the general log spiral equation
where angle is in radians, e is the natural log base (aka Euler's number 2.71828) and tweaked the constants a + k until it looked right. I tried using a helix and radial bias but the gears were jumping. I guess it's the properties of logs that makes it work. Also, when I added the struts, with a helix I had to use a spline on the step effector to make things fit, but with the log curve the struts fitted without a spline.
I usually animate gears with XPresso, but with the varying radii that would be beyond my math skills. Dynamics to the rescue !
The video above is version 2 - I didn't like how dynamics had introduced a small collision gap, so after baking for TR I increased the teeth size. The dynamics is Compound Collision Shape, but with all the geometry it was too slow in the viewport. I added some switched off rigid body tags to parts that don't contribute to the dynamics calculation.
Here's the video I got the design from. The guy has some good stuff eg non-circular gears
I'm still trying to figure out square gears...