how do i pick a gear ratio for a lift

To optimize a linear lift, you should select a baseline motor gearbox and then adjust your spool size to fine-tune the speed and torque, rather than swapping out gearboxes . Game Manual 0 explains that linear extensions are highly efficient and do not require the complex, high-ratio gearboxes that arms typically need. Because the translational speed of the slide is proportional to the spool's radius, and torque is inversely proportional to speed, changing the physical size of the spool achieves the exact same mechanical effect as changing your gear ratio .

This approach is only altered if you cannot find or manufacture a spool of the required size, or if you must utilize a motor you already own. In these cases, Game Manual 0 suggests you can change the gear ratio by building an external reduction using gears, chain, or belts .

According to Game Manual 0, swapping to a smaller spool is often much more convenient than rebuilding a gearbox. For instance, if a system currently uses a 3.7:1 gear ratio with a 2-inch spool, but you decide a 5:1 ratio would offer a better balance of speed and torque, you can achieve this exact performance by swapping to a smaller spool with a diameter of (2 × 3.7)/(5) inches. When designing this system, you must also ensure the lift's cable wraps cleanly without overlapping, as overlapping increases the effective spool diameter and alters the tension .

For further details on lift assembly, the REV Robotics Docs provide a guide on a Three Stage Cascading Lift for the REV DUO Build System (https://docs.revrobotics.com/duo-build/linear-motion-kit/three-stage-cascading-lift) .

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Rigging > Picking the right spool size

Game Manual 0·CC BY-NC 4.0

Spools have a special property that isn't often discussed, but is extremely useful when creating linear slide systems. Just as the system's speed and torque can be changed by changing its gear ratio, speed and torque can also be changed by changing the spool size. The motor rotates the spool at a constant angular speed. Thus, the translational speed (the speed of the slide) is proportional to the radius of the spool, and since torque is inversely proportional to speed, changing the spool size changes torque as well.

This is important to recognize, as changing spool size is often more convenient than changing gear ratio to get the desired combination of speed and torque. To illustrate this, say you have a linear extension system with a 3.7:1 gear ratio. You then decide that a 5:1 gear ratio would provide a more desirable combination of speed and torque than your current 3.7:1 ratio.

In many cases, instead of swapping gearboxes, it makes more sense to swap out spools to a smaller one. If your spool is currently 2 inches, your new size should be frac{2*3.7}{5} inches to achieve the same result.

You also need to make sure that when fully wrapped on the spool, your cable or string doesn't overlap. Overlapping can result in a change in spool diameter, which will change the tension in your string.