This style has one foot (upper right above the needle case and below the quilt guide) that attaches to the machine - and these slide into it. This is a much less common set, most are the more typical where each can be attached to the machine by themselves.
I have this set for the 66 back clamp and the 27. I would expect there is a set made for the 15.
While the tucker and ruffler were used with other sets, including the later puzzle boxes, this particular type of underbraider and shirr plate - I've only seen in this type of set with the separate attachment foot. The more typical puzzle box shirr and underbraider are sort of similar in shape, but are much "plainer" looking than these.
There are a lot of variatoins in attachment sets in the earlier years, but not so much in later years.