This is from the sustainable dressage website:
Another bit with this function is the drop-cheek
or baucher/fillis bit
. This bit can look deceptively like a gag-bit but it is not, since the mouth piece cannot slide on the bitring, which is a prerequisite for gag action. In this bit, the fastening of the bridle side piece is done further up the side of the head. This makes the bit lie flatter to the side of the head, because anything other than would have to fight the "lever" of the arm where the side piece joins. This effectively stops the bit from being pulled into the mouth from the side as well. And horses usually like this kind of bit.
Drop-cheek or Baucher snaffle.
Drop-cheek or Baucher snaffle upside down.
This bit is usually falsley described as creating poll pressure. Most baucher bits don't. In order for it to put pressure on the poll, the ring which the rein attaches to, needs to have a drawn-out oblong shape so that the rein stays at a certain position on the ring. If the ring is oblong, the rein will want to stay at one end, and thus pulls this end up towards the hand/rein. If the ring is round, so that the distance from the mouth bars to the rein is constant at all angles, the rein will slide.
It is also sometimes erroneously depicted upside down while called "hanging/dropped cheek". This use might be possible, but it really only turns into a strange jointed pelham without the lever effect. Just a rotating mouthpiece. It surely was not meant for this...