I want to make a wheel that behaves pretty much like a mouse wheel does — when you rotate it with your finger and release, it rotates back or forward by itself to match a nearest discrete position.
What are the common ways to do so?
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One way to do this would be using permanent magnets arranged in a circle spaced out on a base plate with a central pivot point for a top plate (your said wheel) that has a ferrous disc mounted in it. Use the magnets with either pole facing up. As you rotate the wheel, the ferrous disc will be attracted to whichever magnet it is closest to, you can space the magnets to give you any detent pattern you like.
Genova or Geneva mechanism is stepper mechanism, there are plenty of websites explaining Geneva mechanism or drive, like this wikipedia article Geneva drive