That looks to me like a very early zig zagger. The screw in the back adjusts the width of the stitch.

My favorite foot is unfortunately no longer made. It is the adjustable hemmer, which was distributed by Singer with their machines up until the 1960s.

I have found this foot to be the most reliable for hemming, outperforming feet that were created for specific sizes of hems. I honestly can't tell you why, but it just works better.

I've noticed that the newer hemmers have a groove on the bottom of them. While this may help keeping hems straight, it does create a problem when hemming steep curves, like shirt tails and circular ruffles. Neither the narrow hemmer or the adjustable hemmer have this groove, which may explain why they both seem to work better.

I have also developed a method for making felled seams with the adjustable hemmer. The resulting seam is slightly narrower than 1/4", and is perfect for the side seams on shirts. I have not tried to fell an armseye with this attachment, though it could, conceivably, be done.