I found a motorized slide potentiometer from Sparkfun that offers both a factory built belt system for horizontal movement, and an analog feedback potentiometer for positioning. Although it’s a hair smaller than I would have liked, this looks like a great solution to the difficulties of building the movement myself. The small toy motor attached to the potentiometer requires an h-bridge to change direction, which I can do with my Arduino YUN.
After setting this test up, I’ve been having trouble with them – they seem to be either loosing strength or the belt is getting stuck and restricting their movement. I’ll move onto code this week but keep this challenge in mind.