Bit shank

Bits that have shanks coming off the mouthpiece create leverage and place pressure on the poll via the crownpiece of the bridle, to the chin groove via the curb chain, and, especially with a "loose jaw" shank, may also touch the sides of the mouth and jaw.

The purchase of the bit is the upper portion of the cheek that extends from the mouthpiece to the headstall rings.

The length of the shank determines the degree of leverage put on the horse's head and mouth.

The relative ratio between the length of the purchase and the lever arm also affects the amount and type of leverage that is applied to the chin and poll of the horse (producing 1:3 ratio of rein to chin+poll forces in case of the typical curb bit).

Therefore, the horse has more "warning" of a rider's hand movements in a long-shanked bit, allowing it to respond before any significant pressure is applied to its mouth.

In this way, a longer shank (up to a point) can allow quieter communication between a well-trained horse and a rider with soft hands, without increasing severity of the mouthpiece.

Those that have a nose-out head position when working, such as cutting and roping horses, more commonly use a more curved shank.

In reality, the design simply allowed the horse to comfortably travel with its nose well ahead of the vertical.

An S curve in a shank does not have a major effect on the angle at which the rein engages, but may alter the balance of the bit at the point the lever arm joins the mouthpiece.

A classic "Santa Barbara" style bit shank, designed for western riding and decorated with silver for use at horse shows
Parts of a curb bit and its shank. (Click on image to enlarge)
This photo shows all possible elements of a western shanked bit, including loose cheek, "slobber bar," mouthpiece, curb rein ring, snaffle rein slot, and curb chain that applies leverage to the chin groove.
A shank on a spade bit in a horse's mouth.
This photo shows all the elements of an English shanked bit, including cheek, rings for both snaffle and curb reins, a small attachment point for a lip strap, curb hooks for a curb chain, mouthpiece and curb chain
A fixed shank, common shank length, show-legal
A short shank has less leverage than a long shank and is generally considered milder. Here, a loose-jaw shank that lacks a shank "hobble" or slobber bar, allowing maximum movement and warning to the horse. A bit like this may be used to transition a horse from a snaffle to a curb, either as shown, or with a second rein added to the upper snaffle ring.