OK, so the universal joint thing didn't work. But what about this thing?:
http://en.wikipedia.org/wiki/Peaucellier-Lipkin_linkage
The WP page describes a linkage which translates circular motion to linear motion (and vice versa). Note in particular the last sentence of the Geometry section:
"On the other hand, if point B were constrained to move along a line (not passing through O), then point D would necessarily have to move along a circle (passing through O)."
So, picture the blue line in the 2nd diagram going through B, not D. If B is driven along the blue line (which is a threaded rod), then D should move along a circular path I think.
So my question is: if B is driven at a constant rate, does D move at a constant *angular* rate? I'm guessing it probably doesn't, but it if did it might be a good system for a barn door mount.