As my team and I were building today, we released that our team along with the other 5 teams working in the shop (2602B-F), we as a collective had used up the entire supply of 84 tooth gears! This leaves my team in a, less than ideal state. Our design states we need two stages, both with gear ratios of 7:1, to lift each other up about a foot. Our design uses two motors to lift about 8 pounds on a .375 meter C-Channel, yet a gear ratio of 5:1 falls short by half a pound. Is there any way my team can make gear system greater than 5:1 as a temporary solution while we wait for our parts to ship? If not, any recommendations on how to increase the lifting power without cutting weight?

Hm… That seems fairly difficult to solve if you don’t add another set of gearing. If you are able to, try 4-6 motor lift. 2 Motor lift is a really big risk that is hard to take, especially as 1:5.
Hopefully this helps

It would require moving the motors, but you could do 12 to 36, that 36 attached directly to a 12, and that 12 to another 36. It gives you 1:9 with more friction, so it would be strong enough despite the extra friction. That’s a lot of moving things around if you’ve got something on the way, though.

Do watch out comparing the same type of lift with gear ratios without knowing the lengths of the arms involved. The torque required to swing a bar goes as the length cubed, and to lift the load on it as the length squared. So, roughly speaking (depends on relative weights), 10% longer bars will require 25% more torque.

Yes, you could throw on a lot more rubber bands. Just watch out because you might hit a point where you can’t lower it far enough.

I realized I should clarify a point I made above. Normally we think of torque as T = r x F. From that you might think that a longer arm to the load would only increase the torque linearly, and quadratically for the arm itself (linear for mass and so for force in addition to the linear r). However, we’re generally not just holding things statically using the motors. Far more often what we’re really concerned about is being able to accelerate things. So more typically we’re looking at T = I a, where I = r^2 m. It’s the extra r that shows up here that is responsible for quadratic and cubic instead of linear and quadratic, respectively. It’s actually more complex than that due to combinations of rotational and linear motion, but as a quick estimate when caring about what your motor can perform well handling, I think the quadratic and cubic estimate is the way to go.