I had a request to discuss the Bevel cheekpiece, so let's do it!
This cheekpiece is fairly straightforward to understand. The cheekpiece attaches in the upper fixed ring, and the reins in the lower. When the reins are engaged, the bit rotates backwards and the mouthpiece engages, creating a gag action. That means that the mouthpiece will slide up the bars of the cheekpiece and climb in the mouth freely. This bit has minimal poll pressure due to its complete lack of a curb chain, so the only poll pressure is the pressure of the stretching lips and balling tongue. The lack of curb chain also allows for over-rotation, meaning it can continue to rotate and climb well beyond where it would sit balanced.
Overall this cheekpiece is a mild gag, but still not ideal due to its lack of curb chain and conflicting actions (up on the mouth, down on the poll).