That's right, the back roll creates the arc. There's no gear ratio as such, other than a fairly big wheel to pull round.
The gears, or maybe I should call them cogs?,that link the two front rolls determine everything. I.e. the diameter of your rolls has to be equal to, or slightly greater than the distance across the cog between teeth, and the length of the teeth determines the thickness of material you can put between the rolls and have them engage and drive.
The most common use for my rolls is putting a gentle curve in 16swg mild steel when I'm making fireplace canopies, but I also use it for flat bar up to about 1/4 X 2"
Because of the size of the rolls it won't roll very tight circles ( maybe 18" min, and it leaves a flat bit maybe 3", but that's less of a problem if one feeds in the material from one end, then the other.
So it has it's limitations, but cannibalising the mangle saved so much work it was worth doing them that way.
I do have some plans to make a set from scratch I could probably scan for you, If I'm feeling really kind!

Will Jones, www.ironwill.org.uk

You don't have to scan them, I have a set of plans that I can scale up to meet my heavier gauge material. Really the part that I have to do the most research on in the gearing and getting the carrier bearings figured out for the rollers. I was wondering what you used for the idler wheels on you ring roller, that is a really cool piece. I will make one for myself.

CW

Got lucky there. on a previous trip to the scrap yard I picked up a bunch of big clevis pins, along with some thick walled tube that just fitted over them. Sometimes that cr*p you pick up/don't throw away really does come in useful someday!
The great thing about that tool is the polyurethane tyre doesn't let the metal slip. You have to get as big and heavy a washer on the back as you can to prevent the castor from tilting under pressure.
Will Jones, www.ironwill.org.uk

You are right about the scrap yard, I wish my shop were closer to the scrap yards so I didn't have to make a special trip to go there. Oh the treasure you can find. Do you have any problem keeping the piece square in you ring roller.

CW

Not much. I think because the castor is slightly convex it helps . Biggest problem is it really needs one person to turn the handle, and another to support the stock as it comes out, and there's only one of me.
I too am a long way from a decent scrapyard now. Doh
Will Jones, www.ironwill.org.uk

P.S.You're right, making your own tools takes time, and sometimes they don't end up perfect, but every single time you use a tool you've made, you get a kind of warm fuzzy feeling inside.
Will Jones, www.ironwill.org.uk