The trebuchet, a siege engine of the Middle Ages, first appeared during the 12th century. Though they were most common in Europe (and used often during the Crusades), trebuchets were actually invented in China. The word "trebuchet" comes from the Middle French word "trebuch" meaning to overturn or to fall. While often assumed to be nothing more than large catapults, they are far more efficient and quite capable of bashing down thick stone walls. Trebuchets were used for hurling boulders, flaming objects, rotting animals, and hostages.
Trebuchets operate on very simple physics - the class 1 lever. This kind of lever is shown in a seesaw. The fulcrum is at a middle point, with a counterweight on one end and the object to be launched, called the load, at the other. When the trigger is pulled, the counterweight drops, the throwing arm rotates around the fulcrum, and the load is launched in a parabolic arc. The load is not placed on the throwing arm, though, but in a sling, and therefore the load is launched with some help from centrifugal force.
The load is placed in a sling attached to the back of the throwing arm. One end of the sling is firmly attached, the other is simply looped over an almost straight hook. The hook is bent up or down slightly for desired release time.
The counterweight on the trebuchet is much heavier than the load, and attached very close to the fulcrum. The weight can be fixed or hanging. Fixed weights allow for fast throwing with less arc and greater consistency, but can often simply send the load barreling into the ground. Hanging weights are less consistent, but have greater arc and will often go farther, but will send the load straight up when they are feeling temperamental.
Trebuchets, though they require a large counterweight, are a more sensible and efficient weapon than the more well-known catapult. The catapult is a class 3 lever, with the force in the middle. When the trigger is pulled, the force sends the throwing arm up until it hits a bar. The catapult has two faults. First, there is the problem of the throwing arm splintering under too much weight, as it needs to be bent back. Second, there is the problem of the throwing arm breaking the bar placed there to stop it. Trebuchets have neither of these problems.
I recently built a trebuchet for the purpose of seeing what these siege engines could do. It was small: it had a 20 inch throwing arm and a 4 pound counterweight. I used a fixed counterweight 2 inches from the fulcrum. Using a glass marble of 1-inch diameter and a 6-inch sling, I managed to send the marble 41 feet, or 492 inches.