. I imagine the hard part is keeping the swing at a steady rate. Anyone have experience with this kind of thing?[/QUOTE]
My experience is looking at home made things.
The spring typically is called [I think] a "constant force" spring.
It is a very long flat stripwrapped into a coil, so it has the outline of a thick disk . The application uses only a small part of the total , er, winding. That means the force at release is very close to the force at the end of the swing, so speed is pretty constant.
A short spring, like a rubber band, would provide full force at the start and zero at the end, and obvious exposure variation. If one leaves some room between the initial position and the opening of exposure, the acceleration from zero to full speed will not significantly affect exposure. You can find the type of spring to which I am referring in industrial catalogs, etc. McMAsters-Carr probly has them, or google spring.