The most accurate catapult is the trebuchet, which uses a wooden frame, a long beam that acts as a throwing arm, and a counterweight that outweighs the payload. The payload is placed in a pouch on a sling that releases from a ring at the end of the arm.
The mangonel is another type of catapult, and requires a wooden frame, a cantilever-type spring and a torsion-type spring, two lengths of rope, a long arm beam and an attached bucket that holds the payload. There is also a crossbar that the arm hits after it is launched to propel the payload forward so the arm doesn't wind all the way around, throwing the payload into the ground.
The ballista catapult is designed much like a crossbow. The materials needed are a wooden frame, a wooden arm with a hollowed center that a winch system cranks backwards, a bow string and a twisted rope in the winch system. The winch system also needs a metal or wooden crank and rods that draw back the bow string and the payload.
When the materials are calculated correctly, catapults are capable of using stored energy to launch a payload a very long distance. While the trebuchet was the most consistent of the types of catapults, the mangonel is the most recognizable type, as it was used for targets that were lower to the ground in linear warfare. The trebuchet was great for launching a payload at or over a wall.