With the underbraider, it depends on which style you have. They mount to the base of the machine, so the shank does not matter.
Most puzzle boxes come with this style - (I messed this up -edited to fix) one for the 27 on the RIGHT and one for the 15 on the LEFT. The screw is in a slightly different location, and the 27 hooks to the back of the feed dog opening, the 15 has a small pin that slips into the hole on the needle plate.
Here are several others - Obviously the smaller half moon will only fit on the 27/28 or 127/128 models.
Here are the rest being modeled by a 201. On all of them, there is a pin or hook that holds into the hole on the needle plate. The half moon one lines up, but did not want to lay flat. It fit fine on a 66.
I did not switch out the foot - the quilter or an underbraider foot works with it.
The puzzle box 27 stlye would not fit. I had them mixed up at first, but then I opened up the 27 and it has NO HOLE in the needle plate.
BTW - all those that fit the 201 also fit the 66 and 15 I tired them on - i