The curve(s) formed by the rollers are called "curtate cycloids" (Another backward paper calls them Prolate. )
There are equations here: http://mathworld.wolfram.com/CurtateCycloid.html

They are used on violins and archtop guitars, so a script might have some utility:-)

http://liutaiomottola.com/formulae/curtate.htm

A modified sine wave script would be ?easy?
Maybe the curve could be booleaned to make the gear "rack," or a portion of it anyway?


- Brian