The cylindrical part of a hinge is called a knuckle.
In some areas it is also called the barrel.
A knuckle.
hinge
Hinge joints include a cylindrical bone end that fits into a groove, called a trochlea, on the other bone. One example is your elbow.
Cylindrical.
It got its name because it acts as a hinge, only opening and closing a certain distance. Your elbow is a hinge joint. Think of your elbow as a hinge on a door in your house. The door is your forearm and the door frame is your upper arm/body.
The pin that slides into a door hinge is called a hinge pin. It is usually removable to allow for door removal or adjustment.
The theorem emulates the action of a hinge. As the angle of the hinge is increased the distance between the free edges increases.
rouleau
Don't know what a "bushy" is but maybe you're thinking about a bushing. A bushing on a car is usually a cylindrical "sleeve" that's used if you want to attach one part to another but still allowing them to move a little. Think of it as a hinge lined with rubber. A regular hinge would seize and jam unless the halves are perfectly aligned, but with a rubber sleeve in one half, the parts have some degree of freedom to move.
The butt end of a hinge is the part that attaches to the stationary frame or door jamb. It typically has screw holes for mounting.
Synovial pivotal hinge
A cannelure is a ringlike groove, such as the fluting around the cylindrical part of a bullet.