Each design of a jump ring chain or a chain maille weave requires large numbers of rings that are precise in size, are well shaped without any nicks or scratches, and have square cuts so they close without a noticeable gap. Here's the process I teach in my jewelry classes to make large numbers of uniform rings quickly and easily. There are three steps - finding the right size mandrel, winding a coil of rings, and cutting the rings apart.
Step 1: Getting the Right Size Rod
Jump rings are made by winding a wire around a rod or tube. Common sources are knitting needles, wooden dowels and metal stock from hardware stores and hobby shops. But finding the right size can be a problem. Minor changes in the size of the jump rings can make a big difference in the final "look" of the chain, so it's important to have a variety of mandrels to choose from.
Jewelry catalogs sell selections of straight rod mandrels for $50 or more, but my choice is from Harbor Freight. They have a set of 28 sizes, from 3/32 inch to 1/2 inch, for under ten bucks. It's called a Transfer Punch Set. The catalog number is #3577. www.harborfreight.com
Step 2: Winding the Rings
If you need just a few jump rings, it's easy to grab a mandrel and wind a couple of them. But when you need a large number, some form of winder saves a lot of time. A variable speed screw gun makes quick work of winding the coils.
To wind a coil, just bend a right angle on the end of the wire about 3/8 inch long and insert this into the screw gun chuck. Then wind slowly, keeping a tight coil. I like to rest the end of the mandrel on the edge of the table or bench pin.
One note of caution - if you are winding an entire length of wire, be careful as you get near the end of the wire. If the end passes under your thumb, it can cause a nasty scratch or cut.