I am trying to figure out a formula for the gears ratio that I would need.
I think a formula should involve torque in someway. Can anyone help me?
Gear ratio should be output torque/input torque.
You want to be operating at the max power point of your motor to lift the fastest for any particular load. This is because Power = Force x Speed. Your force is constant (ish) so maximizing power maximizes speed.*
So, max power on our DC motors is at 1/2 the stall torque. So you know the input torque you want to gear for is 1/2 your stall torque.
Your output torque… depends on the weight you’re lifting and the radius/pitch/other of your mechanical system. If you’re using a pulley, the output torque is weight * pulley radius.
So, your ideal gear ratio is 2 * weight * radius / stall torque. If you get, say, a 3 from this equation, then you gear for 3 turns of your input for every 1 turn of the output.
*NB: This is not to say that if you gear for maximum power lifting of 3 robots, you’ll lift slower when you lift 1 robot. It just means you’ll lift 1 robot slower than if you’d geared for lifting 1 robots.
Well it really depends on how you lift them. Let’s say you are lifting two robots at maximum weight straight in the air with one winch-type mechanism. I think with batteries and bumpers, that would end up to be about 300 pounds. So you take the radius of the output shaft of the winch which the cable is wrapped around and multiply it by the weight. This will give you the torque necessary to raise the two robots. (do a quick unit check and make sure you get either in-lbs, ft-lbs, newton-meters, or some other force unit multiplied by a distance unit).
That was for a very specific way of lifting the robots. Like I said, it depends how you want to lift them. You’re on the right track though thinking torque. Try a wikipedia search about gear ratios. That should help also. Good luck!