I was trying to show the students the power of math for robotics and I came up with a situation where the empirical value is different than our calculated value. I was wonder if you can figure out my mistake:

We have a Falcon with a 48:1 gearbox. The shaft is attached to 36T 20DP gear (1.9" outside diamer). It is driving a 20DP rack. We want to figure out how many “ticks” per inch of travel of the rack. Seems straight forward. I even used “critical dimension analysis” which they learn in chemistry.

My calculation is this:

2048 ticks per motor rotation * 48 motor rotation per output shaft rotation / 1.9 * PI inches per rotation = 16469 ticks per inch. When we do the measurement it is closer to 13000 ticks per inch.

Just a quick note, did you actually use the “outside diameter,” or were you using the pitch diameter? You should be using pitch diameter, which should be 36 teeth/20DP= 1.8", not 1.9". This is the circle that is actually acting on the rack gear.

That still does not give you the right output, in fact it makes you further away (17384). Double check the gear ratios and the gears you think you have are correct.

If you are not sure about the gearbox ratio just do the math to determine what it might be.

When I did the math in reverse assuming that you are, in fact, using a 36T spur gear, I get almost exactly a 36:1 ratio instead of the presumed 48:1.