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Whenever someone asks me how to make jump rings, I explain how simple it is. Wind your gold or silver wire tightly around a tube so that it looks like a spring, then slide it off. Then cut through it with a jewellers piercing saw, and as you cut, the rings fall off, and they will all be identical, and because you've used a saw and not cutters, they will join up perfectly.
The only problem is - what do you wind the wire around? A piece of knitting needle might do for one size, or perhaps a jumbo paperclip or a bit of wire coat hanger, but then you run out of ideas.
Well here is a set of tubes to make jump rings of sizes (mm) 4, 6, 7, 8, 10, 12, 14, 18. The steel tubes screw onto a holder to make them easy to hold whilst winding the wire.