Earlier quoted context omitted.
Yeah, I think one of the nice things about making it a "clean" number (either an integer or a rational with a small integer denominator) is that you can easily validate it without needing high-precision measurement equipment: put a mark on both gears (maybe even embedded in the 3D print), line up the marks, rotate the large gear 1 full rotation, and count the number of rotations the smaller gear makes. Check to see i…
His capstan reduction can't go all the way around even once.
He could also go with narrower rope, and spread the load over more windings, which would give him more throw.