Just a wild guess but is it some kind of vise/clamp half… for pipes maybe… the two pegs anchored it into another part of the tool or surface, a chain or rope or all thread was passed through the clip shaped arms as they were tightened they drew in a similarly shaped piece from the other side until it was snug against the pipe?
If only we had the patent number, or even a patent date.
Can anyone see this as an obscure part from a "National" sewing machine or associated equipment? The company made some complex stuff in the late 1800s, including 'industrial' models and tables to support them with all kinds of weird attachments. They also made 'home workshop' equipment.
I wonder if it is some type of hardy for a vice?oops meant anvil not vice. but I can see Goldilocks I.D. as being plausible and it explains the side pieces also. Makes me think of the braces from Forrest Gump. run Forrest run.