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I am posting here because the "official" Vex forums don't seem to support EDR anymore :-( but anyhow...

I am teaching a class and we are using VEX parts to build a simple winch, the whole point is to experiment with gear ratios.

Well and good. We are using standard 393 motors hooked up to a VEX cortex with the standard 7.2 V battery.

In our experiment we will be loading up the VEX motor (using a simple spool) to lift a weight with a string. I was looking up the stall torque of the motors, and I wanted to get an idea of whether I should, for safety's sake (safety to the motor that is) use the clutches. I know at least one kid will try to lift a brick or something, and the first part of the experiment is using the Vex motor with no gearing, and we will be increasing the gear ratios as we go to demonstrate the increase in torque. The word I get is that the stall torque on a VEX 393 is somewhere around 1.67 N•m assuming full speed (set at 127 in RobotC, if I am reading this correctly) and that means that for the winches (which have a radius ~1 cm, 0.01 m) that means a 17 kg mass on the end will load it with 17•9.8•0.01 = 1.66 N•m, which is a lot! But while that gives me some confidence that even with a really heavy mass on the end the motor will work, I wanted to be sure we wouldn't damage it, hence the question about using the little green clutches VEX supplies. Should I use those just in case? Many VEX posts say they aren't necessary anymore...

Anyhow any insight is appreciated.

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The clutch isn't necessary. While you don't want to leave it stalled for a super long time, stalling your electric motor won't cause it any harm. It'll just act as a static electromagnet and generate some heat. Unless you leave it for a while you're not going to generate enough heat do damage anything.

The one thing I would look out for is only use the motor to lift off the ground. If you suspend a large weight and try to get the motor to pull or hold it, the weight defeating the motor will generate back EMF and enough current produced in that way could do damage to the motor or the controller.

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