One of the designs I like best is to use a piece of flexible wood (or maybe bamboo?) as a bow which bends and provides the spring power of the wood lathe. See the designs below to see what I mean.
#1. The Treadle Wood Lathe
This design is a bit more complicated, but works like a foot treadle sewing machine. Pros and Cons: The wood being turned remains in a constant circular motion.
|A Very Large Treadle Wood Lathe
#2. The Bow Powered Wood Lathe
I have seen similar designs elsewhere. The downward stroke of the foot spins the lathe in one direction, and then the bow + string pulls the lathe the opposite way, creating an alternating direction every downward and upward stroke. Pros and Cons - Conserves energy, but that alternating direction thing requires some timing on your part to maximize energy and speed.
#2B. Alternative Bow Lathe Design
Less efficient but it works. This is hand-powered, so it would be easier if you had a friend working the bow.
#3. The Wind Powered Wood Lathe
This is actually just a variation of the Bow Lathe, but instead of the power coming from your foot, you are attaching something to the bow that blows in the wind easily, causing the bow to move whenever the wind is gusting. This "gust powered" wood lathe in theory only works on windy / gusty days.
An alternative to this would be to use a windmill or vertical axis turbine (shown below) to power your wood lathe instead. The turbine then turns a bicycle wheel which is rigged up to your wood lathe via either bicycle chain or a rubber belt.
#4. Hydro Powered Wood Lathe
I couldn't find any examples of this, but in theory someone could build one if they really wanted to. This just need a river on their property and to make an overshot water wheel.
#5. Bicycle Powered Wood Lathe
A fairly simple design... but this requires you have a friend who is willing to do the pedaling.
Check out this giant lathe.