This looks very much like one of the early 50's complicated add-on sewing attachments that came with my Aunt Ruby's brand new Necchi "top of the line" sewing machine--one of the new exports from a post-WWII Germany. Ruby bought every attachment they offered. My Gram had taught me to sew when I was about 7 on her old Treadle Singer Sewing Machine. Later, Ruby decided to teach me 'modern' sewing--electrically with a foot pedal! The Necchi--also a cabinet style with drawers and doors, had a hinged sewing table extension that folded over the top after the machine swung down into the cabinet. Anyway, these drawers were stuffed with boxed add-ons with pictures of the parts on the outside and detailed instructions of how to use them inside the box. I never got over to Gram and Ruby's (by then I was about 10, and we'd gotten a Portable Singer at home) to spend much time learning all the Necchi parts--I was more into gardening (3 sides of their yard were flower gardens with a vegetable garden in the far back).
This part looks very much like an ancient BUTTON FOOT. The forked arm that has 1 bent 'tong' fit around the needle screw and went up and down with it. The bottom part in the center that turns was driven by the fork, moving the material/button side to side to line it up with the needle coming down into the foot that was holding the button in place, while the needle/thread alternated stitching into the 2 button's holes. The doublefork in the center, attached to the outerside hooked like many parts around the main needle holder/driver below the tension, held on by a large-headed screw similar to the one shown on your foot. That screw probably held the part up in back as the metal was pretty heavy back then. That'd anchor the part horizontally from the side and vertically from the back, allowing the inside forked arm to be driven by the needle-screw's up/down motion, in turn, moving the portion on the center bottom side-to-side, allowing the needle to alternate holes in the button clamped under the foot. There are several levels/ layers of metal on the bottom of that part. It is likely that they somehow shifted back and forth--also driven directly or indirectly by the extended fork (like cog wheels in clocks).