Clamp-on 360° swivel hobby vise
3" spring clamp
Screws and other hardware
Step 1: Research and Planning
I kept coming back to the idea of the classic swing-arm lamp that clamps to a desk or drafting table. Using one of those as the core of my project would take a lot of the mechanical fiddling out of the process. I was concerned that it wouldn't have the juice to hold up the work, though, so I went searching through instructables to find other folks who had re-purposed these mechanisms.
That turned out to be surprisingly tricky. At first I thought I was looking for "Tensor" lamps, but that is a completely different technology. The lamps I was picturing were usually called "swing-arm lamps", but non-US 'iblers more often called them "Anglepoise lamps". I also saw people calling them "balanced-arm" and "floating-arm" lamps.
In the end, I created a Guide to pull all of these projects together, so you don't have to. You're welcome. :-)
I determined that one of these lamp arms would probably hold a bead loom or mid-sized embroidery hoop with no trouble. The Edmunds model is heavier-duty, but people use those to hold big embroidery frames loaded with a yard or more of fabric. My wife doesn't do anything like that. At least, not yet.
I also knew I would need a means to adjust the angle at the end of the arm. I decided to keep my options open, but I liked the look of this multi-directional hobby vise. The whole thing would be too heavy for my purpose, but I thought I could cannibalize it for the ball-and-socket joint.