What about mandrels?
You’ll insert a mandrel into the winder, then coil wire around the mandrel to make jump rings. The diameter of the mandrel determines the inside diameter (ID) of your jump rings. Just remember that when you cut the coil into jump rings, the saw blade will remove a small amount of material as you cut; because of that difference, the diameters won’t be an exact match.
Here are some items that you can use as a mandrel:
Calibrated steel mandrel sets:
These are commercially available from most jewelry supply companies. They often come in specialty shapes.
These allow you to saw the coil into jump rings while the coil is still on the mandrel.
The short, double-pointed variety work well, in aluminum, plastic, bamboo, or wood. Make sure not to dent hollow aluminum needles, or you’ll have a hard time removing your coil.
Nails or other hardware:
For safety, just make sure to blunt the ends of any nails before you use them for coiling.