I have a reprint of this article that I purchased from Interweave a while back:
Hinged Ring with Cabochon
by Judy Hoch
Originally published in Lapidary Journal Jewelry Artist, September-October 2013
Here’s a pic of the back of the ring:
It may the the kind of thing you’re looking for. It (and similar styles) have been designed for fitting issues such as arthritic fingers, where the knuckles are enlarged.
Hope this helps, or at least can lead you to what you are looking for.