The amount of cubes is somewhat arbitrary because geometry is a “gear ratio” in an of itself. All a gear ratio is doing is giving the motor output a mechanical advantage for the amount of work being done by the motor. When you increase the mechanical advantage through geometry, the drawback is that the tilter has to move a greater distance. Work is force*distance so in order to attain the same work done by a high gear ratio, you increase the distance. By increasing distance, I mean to get the same range of motion on the tray, you would need to have the tilter arm start lower for the tray to have the same starting angle.
This should make intuitive sense from a torque perspective as well. Less torque is required to rotate the tray when you increase the radius since torque is radius*force. The radius being the connection point on the tray from the tilter. I hope this makes more sense.
I hope this makes sense, but feel free to ask questions
What @mvas is explaining is that the linkage completely changes the ratio, so the actual gears don’t mean much. For instance, if for every degree your tilter gear moves, your tray tilts half a degree, the tilter linkage itself is providing a 2:1 ratio, effectively doubling the torque of your gear. If it takes 5 degrees of gear motion to move your tray 10 degrees, your linkage provides a 1:2 ratio effectively halving the torque of your gears. Therefore a 5:1 200rpm ratio with excellent geometry can provide the same amount of torque as a 21:1 100rpm ratio with absolutely terrible geometry. I’d recommend using a 7:1 ratio because they’re the simplest to build (no compound gearing, you might not have room for geometry good enough to supplement a 5:1) and figuring out your geometry so that you’ve got enough torque to push whichever amount of cubes your shooting for.
I have used 1:7 100 rpm, 1:21 100rpm, and 1:15 200 rpm. 1:15 200 rpm works great and can get us 12 cubes, but it takes a lot of finesse to get it to fit and everything. Same with 1:21. I am currently building our worlds bot, and we are switching back to 1:7 as it is a lot easier and more compact to make, and it allows a greater range of motion.