The first try was the one featured in the middle school science class. It was very simple and worked by simply turning the roll of toilet paper and letting gravity do all the work. This was bad because sometimes, the toilet paper would not fall out. This design also meant that different amounts of toilet paper would get extruded out each time. This is because the diameter of the toilet paper roll changes as it is used. This meant that the extrusion never really worked.  

In order to solve the issue of the toilet paper not coming out, I decided to actively pull it from the roll, instead of letting it fall. Having a system that pulls it also means that the leverage and amount extruded are consistent, no matter the diameter of the roll. In order to pinch the toilet paper, this version uses one free-spinning rubber idler and a driven wheel that presses the paper into this rubber idler. This did not work, as they did not have enough traction, and also tended to bunch the toilet paper up into a ball. 

After some experimenting, I realized that while my system for moving the toilet paper did not work, the toilet paper did get stuck in all my gears. This led me to my next idea - really long gears. I designed really long and high backlash gears, as you can see in the photo. They are able to hold the toilet paper tight. Because they are rigid, there is no space for the toilet paper to ball up, so it does not. I also added a cap at the end, to hold the rollers parallel, which helped performance.