There once was a time when companies produced animal napkin rings using a plastic called Bakelite. Those vintage napkin rings can go for a decent price these days in antique stores. But there's no reason you can't design and 3D print your own versions! :-)
More info and pics: http://wp.me/p2hTaI-ho
3D print and put a napkin in them! Stand them on your table! Play!
Then - design your own!
Start with a 36mm diameter circle, make another, larger circle outside it, then remove the inner circle; instant ring! Extend out from the outer circle to make animal shapes, sprocket shapes, cars, planes, or anything you can think of.
When ready, extrude the whole thing 10mm, print on your 3D printer (I used 25% infill with 0 [zero] extra shells).