Oh - you have a part I want!!!! It's that shiny sort of square with the round part on the end (sorf of off the bottom of your picture). that is an underbraider that will fit a Singer type rotary machine. It was NOT sold by Singer, but by Greist in sets for that style machine, which included New Home after the switched to side clamp, and before Free took over and put the name on their machiens - which are top clamp and take a different style underbraider.
Interesting what ends up with different machines -