[defanor]

I think the most straightforward way is to have a separate usual mechanism for each ring, stacked vertically, passing the rotation from each ring through the inner ones without rotating them. But likely something nicer (more optimal) can be designed: either purely mechanical (to end up with just a single combined rotation on the output) or relying on more modern technologies (plenty of options on reading dial positions then).

[defanor]

Or the holes can just be staggered (so that each hole is at an unique angle): then the rings won't have to rotate separately, though the reading would have to be more precise/higher-frequency then, and it may be tricky to rotate the dial with a finger as precisely (with 6 rings and 15 mm per hole, that would be a 15 / 6 = 2.5 mm margin, roughly).