I used to have a friend who would make chainmail. He had long coils of steel which looked like springs but I don't think they were actually springy. He'd nip off individual rings from them, weave them into whatever he was currently making, then bend them closed.

If you were actually going for historic accuracy, or planned to use it for armor then you would weld the rings. Generally people don't weld them since it takes a lot of time and effort. They are just bent closed.

"Designed" is a strong word. I crank these out, literally, on a wire winding jig that I made out of scrap wood and bits of steel rod a couple of decades ago. Since these are aluminum and I wouldn't drive myself bats doing so, I cut the rings off of the coils using a jeweler's saw. (You can do this with steel wire if you really want to, but it takes forever and you'll burn through a lot of saw blades. Most people just use wire cutters to make steel rings, which are uglier but the process consumes significantly less of your life.)