Imagine a trough a little wider than the thickness of the thickest ring. Arrange a pair of low pressure air jets entering the trough opposite each other, fed by a fixed pressure supply through an orifice.
Now, if a thick ring passes by, the backpressure on the air gage, measured between the jet and the limiting orifice, rises.
If a thinner ring passes by, there's more clearance between the ring and the jet, hence less backpressure.
I'm actually a little fuzzy on the internal details, but I think that's the essence of how they work. We used them at Ford in the sixties to measure bearing diameters on axle shafts. They can easily resolve 'tenths' of difference from the master they're set with. I don't think they have a large measuring range, and they may not be linear, but in an application like this, you don't care. All you're sorting for is 'is it 3 mm thick, or a little less'.
There was actually no stated requirement to measure the absolute value of any of the provided dimensions, only to detect differences so as to discriminate and sort a flow of similarly sized but distinct pieces.
Mike Halloran
Pembroke Pines, FL, USA