I study medieval woodworking a lot, and I've always wanted to try out the medieval style lathe. The major difference between this type, and the modern lathe is that the motion is reciprocal, rather than continuous circular motion. That, and the fact that it is totally human powered. The back and forth motion of a "spring pole" type lathe has been used well past the 1600's era that I study, and in many places is still in use today.
The whole idea behind a Spring Pole lathe is that you would pinch a piece of wood between two points, wrap a cord around the wood, and pump down on a treadle while putting your cutting tool to the wood. On release, the springy pole attached to the top of the rope would pull up, spinning the wood backwards, and making it ready to be pushed down again and cut.
Here is my build process as posted in my woodworking blog: http://wood.box23.net