I'm surprised that this was a mystery! My mother's Singer Touch and Sew machine had one of these (admittedly with some plastic areas) in the 1970s. It is called a walking foot. The large lever at the top fits around the screw that holds the needle in place. This lifts the foot away from the fabric after each stitch as the needle rises, allowing the feed dogs to move the fabric. As the needles comes down, the foot presses onto the fabric again so that it is held firmly as the needle penetrates the fabric.

It is not only for use on heavy fabrics, although it is wonderful for that. It is also useful for matching plaids and for stitching slippery fabrics as it stops the top piece of material from sliding over the bottom one.

I remember that my mum used it a lot and it was her solution to all difficult fabrics that used to make her curse...