[FotoPlasma]

Potentiometers which recycle at 360degrees do exist. It took a couple hours of searching through local surplus stores, but I found 10, over the course of the build period in 2003.

We used these on our swerve system.
If you have any questions specific to our implementation of the system, I'd be more than happy to answer them.

At the transition point from lowest to highest resistance on the pot, you'll most definitely have a couple degrees of deadspace, which can be fixed by using two potentiometers for each enclosed system, one facing one direction, and the other in the opposing direction. When you're oriented in one of the two deadzones of the system, you can decide to take input from whichever potentiometer isn't in its own deadzone. However, for our robot, we did no such thing, and it worked fine, just a thought for future seasons.

This will give you a resolution of 256 ticks per revolution, which is better than some of the lower-end rotary optical encoders carried by DigiKey, which are not too cheap, if I recall correctly.

As for FIRST's regulations, you can use any pots (as long as they're 100k, if I recall correctly).