The 3 Main Types of Catapults are:
Ballista:
The Ballista is a missile weapon that launches a large projectile at a distant target. The Ballista is very similar to a crossbow in the sense that they function very similarly. Two wood arms are attached to a piece of rope and the rope is attached to a winch that is pulled back, bending the arms of the weapon. When releasing the Ballista, the built up tension in the rope would send a large arrow towards the enemy with extreme accuracy. Unlike the Mangonel and the Trebuchet, it lacked alot of power. A smaller version of the Ballista is called the Spingald that was used in the past in more confined areas.
Mangonel:
The Mangonel is the most iconic type of catapult and is what most people think of when they think of a catapult. The Mangonel consists of a long wooden arm with a bucket, that holds the object that is being projected, with a rope or string attached to the end. The arm is pulled back and energy is stored in the rope and in the arm. When the arm is released, it would return to its upright position and come in contact with a block that would stop the arm but the object would continue to be projected towards the enemy. Although this weapon would have alot of power, it is the least accurate of all the types of catapults.
Trebuchet:
The Trebuchet was designed for max power and distance. The Trebuchet has a long arm that is balanced on a fulcrum and a short arm attached to a counterbalance. A sling was attached to the end of the long arm and then a rope was attached to the long arm and pulled down until the counterbalance is high in the air. The rope is then released and the counterbalance plummets down. The energy provided by the long arm brings to swing the short arm and when the long arm comes to a stop the projectile continues with the velocity.