This method works OK if you only have to add a small amount, 1/2 inch or less to each side, or if the armhole is for a dropped shoulder style. But I've found the Palmer-Pletsch method, which involves an additional pivot line from armhole curve to bust point provides better fit, especially for regular armholes (fitted close to body for set in sleeves or sleeveless styles). The Palmer-Pletsch method adds a dart for the best fit, but one can omit the dart by reshaping at the hemline; this, of course, works best for a loose-fit garment. If it is fitted garment, the dart is a must.

Also, the method described here does not allow for extra length in front to go over a large bust. Without that addition, the front will pull up so that the hemline does not remain parallel with the floor.

My first thought when I saw it, is that it's a ruffler, but it's much smaller and not as long as a ruffler, and doesn't have a part that moves forward/backward to push the fabric into gathers or pleats. It could be a shirrer, but I don't think so.

I think the grooves on the bottom of the foot have something to do with it's function, perhaps to grip the fabric to keep it from shifting.

As the fork goes up and down, the small bar moves from front to back, and back to front, causing the can-opener gear to move, right. What other movement happens? That is, what does the gear's movement do? I studied the 1st and 3rd photos again (fork up, then fork down, side view), and I can see that the foot part (that touches the fabric and that the needle goes through) moves right to left at the turning of the gear. (this is why the round circular thing on the bottom moves 'up and down' in the photo (left to right when the foot is upright). So as the foot grips the fabric, it moves the fabric back and forth creating a zig zag. That is, the needle doesn't move sideways as on modern zig-zag machines, but simply sews straight, while the fabric zigs and zags.

I don't think it's a buttonhole foot, as the screw in the back doesn't have enough length to adjust for long or short buttonholes. Instead, that screw probably adjust the width of the zig-zag.

The suggestion that it is for sewing on bias binding is interesting; I can't see how that would work, but then I've never used a bias-binding foot.

I'm sticking with the zig-zag attachment for a straight-stitch machine.