[Kevin Sevcik]

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.