OpenSCAD Roller Pinion Rack Profile

Apparently there's this great thing out there for linear motion called a roller pinion. It has all of the advantages of a rack and pinion for simplicity, but it'also precise, has low backlash,is efficient, and quiet.

I spent some time trying to figure out how to derive the profile. I believe I'm really close to the right profile. I'm hoping others can help me make it a real thing.

It would be nice to use these for anything that needs precise linear movement.

I'm thinking that for the r