Bit Experts... What is this?

It's an eggbutt Pelham which is designed to be used in place of the double bridle to allow the use of one mouthpiece and two sets of reins instead of requiring both snaffle and curb bits to be carried in the mouth.

This one has a double jointed link mouthpiece and long purchase arm (upper cheek shank) so that the ratio of purchase to shank is 1 to 1. In other words, the length of the purchase (above the mouthpiece) is equal to the length of the shank (below the mouthpiece) which provides even distribution of pressure to the poll, curb groove, and bars when the curb reins are engaged.

The jointed link lies at an angle to the mouthpiece which makes it a version of Dr. Bristol as opposed to a flat French link. The Pelham is designed to be used with two sets of reins, although some people use bit converters (as you see on this one) between the snaffle and curb rings in order to use it with only one set of reins. A curb chain should be attached to the bridle ring on the purchases (upper shanks) in order for this bit to function correctly without over-rotating. It should be adjusted to contact the chin groove when the lower shanks are rotated backward 45 degrees from the vertical. By using this bit with only one set of reins on a converter, it really can't function correctly to allow for any refinement in communication.

I've used Pelhams to transition from snaffle to curb when a western horse is ready for finishing into a leverage bit. A western horse can be finished into the curb and ridden with one set of reins since the reins are kept slack and the horse is trained to respond to the loose neck rein for lateral cues. You can't maintain continual contact on a leverage bit. You also can't (or shouldn't) apply direct independent lateral rein cues to the shanks of a curb bit without confusing the communication and potentially damaging the horse's mouth.

If a horse is ready for refinement that a leverage bit can accommodate, but the horse doesn't neck rein on loose reins the way a western horse does, then either a Pelham or a double bridle with both a set of snaffle reins to accommodate direct independent rein aids and a set of curb reins (which are engaged only when more flexion or suspension or certain advanced movements are asked for) is used.

Since combining leverage shanks with a jointed mouthpiece creates painful and confusing signal, I would never use a jointed mouth Pelham, and I always used a mullen mouth Pelham with two sets of reins for transitions.

That's some sort of a full-cheek. Don't know about the link, though.

It is some type of french link (double jointed bit). I'm going to do some more research to see if I can find it. It almost looks like you could use it as a full cheek french link if you only use the snaffle ring.

Edit:

After looking around some, the only thing I can figure is that it is some type of gag. The only other option I've been able to find is a pelham, but the shanks are a bit too long. It looks awful to me. I wouldn't use it on my horse.

it is a full cheek dog bone snaffle bit

It looks like some sort of Dr. Bristol, designed to be flipped either way. If you flip it so the peice in the middle is slanted the same direction as the head (flush with the tounge), it just gives the horse something to play with.

If it's flipped the opposit way, so the edge of the middle peice is slanted in to the tounge, it applies tounge pressure. It also looks like it could be used like a pehlam.