Building a trebuchet to break a siege was no small expense. It required a good many nails, about two miles of quality rope, enough lumber to build a small house, and most difficult of all: expert engineers.
A typical starting point for construction of a trebuchet is the frame. This process was not as simple as it might at first seem because the frame of a trebuchet has to withstand a variety of forces which can change during operation. Most structures are not designed to move hundreds or thousands of pounds of something, and in medieval times, such a construct was nearly unprecedented.
After the base frame was in place and the A-frame was up, the throwing arm and counter-weight basket had to be affixed to it. The precision with which the fulcrum was made had to be precise to prevent the rotary motion of the arm from grinding in such a way that it would reduce the energy the engine could put into a projectile. This part of the machine was critical because trebuchets could have a weight basket with a capacity up to multiple tons.
A simple machine would provide mechanical advantage which would allow a small group of workers to lower a trebuchet arm into a firing position. The throwing sling would be setup with a projectile inside and a loop of rope would be placed around the firing pin.
When the device is triggered, the counterweight falls quickly and sweeps the throwing arm in an arc toward the target. The sling containing the projectile moves due to centripetal force and somewhere near the top of its path releases the projectile.
The physical principles behind trebuchets are fairly complex, and it is worth noting that a trebuchet’s maximum range is determined by several factors: the capacity of the weight basket, the length and ratio of the throwing arm to the fulcrum and distance from fulcrum to basket, the length of the lead rope on the sling, and the angle of the firing pin affixed to the end of the throwing arm.
Pictures are courtesy of http://medievallifestyle.com/siege-engines/trebuchet.html