When trying to communicate some information, it's nice to be able to use words that mean the same thing to all parties.  For those of you who might be a bit befuddled about a "CW" or what a "30 degree pin angle" is, perhaps this page will help. A lot of images, so be patient and let them load.
 

Frame Base
(Sometimes with a floor on it.)
Tower or A-frames
Outriggers
Axle Housing
(At the top)
Trough
Axle
Beam or Throwing Arm
Sling and Pouch
Counter Weight (CW)
and Hanger
 
 
Release Pin
 Trigger and Release/Haul Down line
 Slip Ring
 
 Here's are two simplified Trebuchets.  Two?  Yes, because one is a FCW and the other is a HCW.  See, you needed this page after all!
 A FCW is a Fixed Counter Weight and a HCW is a Hinged Counter Weight.  This refers to how the Counter Weight (CW) attached to the end of the Throwing Arm, Fixed being simply that, Fixed, like an ax head on a handle.  The Hinged Counter Weight (HCW) uses a Hanger to support the CW from the short end of the Throwing Arm.  The Hanger can be rope, chain, wood, anything that will hold the CW at a fixed distance and will pivot around the end of the short arm.
 
Fixed Counter Weight
Hinged Counter Weight
Long / Short (Sling / CW) Arms
The Throwing arm (also called the Beam) is often referred to as if it was made of two components.  The two terms are used in discussions mostly as a way to reference which end of the Beam one is talking about.  Simply put, the Long arm is that section of the Beam that runs from the axle to the Release Pin.  The Short arm is from the axle to the where the hanger connects to the other end of the Beam.  Some say "Long arm" while others say "Sling arm", or "Short arm" instead of "Counter Weight arm".  It's up to you.
 
Tuning
This is the art/science of adjusting the variables of a Trebuchet in order to obtain the desired results, whether this is efficiency, distance or attempting to hit a given target.  Most Trebuchets are built in a way that limits how many things you can change, at least easily.  Sling length, hanger length, payload mass, CW mass and cocking angle are the usual variables to play with. Beam length and the ratio of the long/short arms (of the beam) are two more variables, but these can be very difficult to modify easily, especially on large machines.
 
Stall Point
This is something that will be found on either the HCW Trebuchet or a FCW Trebuchet that is on wheels.  It is a factor that many people either look on as a trivial item or are unaware of it.  In fact, it is a very important feature that can add a large percentage to the distance your machine can throw.  It is also one of the more difficult things to tune your machine for, mostly due to the speed of events.  In the graphics below I've exaggerated the motion a little bit for clarity.
 
 
Here is a model Trebuchet in the cocked position.  Note the relative position of the CW to the vertical support pole.  (Most of the frame work has been stripped away for clarity.)
As the beam rotates, the horizontal distance from the end of the short arm to the pivot is getting longer.  This causes the CW to start moving towards the right.
As the beam goes through horizontal, the CW is still moving to the right, but it's still gaining some speed in that direction as well as moving downward with the end of the short arm. The horizontal distance between the end of the short arm and the pivot is now at maximum.
Now things start getting more interesting.  The horizontal distance between the end of the short arm and the pivot is now getting shorter, but the CW still has velocity towards the right.  It will start slowing in that direction (right) but it's still headed that way.
In the meantime, the sling has been whipping around, gaining some nice velocity and is approaching the release point.  But now things gets critical in their timing.  The CW has reached its maximum horizontal movement to the right at the same time that the CW, hanger, beam and sling all line up (or close to it.)  Despite the poor angle for it to be turning the beam from, there is enough energy applied by the CW to give the beam a real nice 'jerk' when it's needed most.  In a properly tuned machine, the CW will actually stop at this point (for a split second) before starting to swing back to the left and completing its downward motion.  But as the payload is already gone, this is wasted motion/energy. 
Unless you have a quick eye, it can be very difficult to judge when the stall point is taking place relative to the release of the payload.  Many people use a video camera to shoot the action, then play it back at slow speed to pick out the moments of interest.

Here is a picture from a newspaper that happened to catch the Trebuchet of Rob Kohler, just at the stall point.  Notice the wonderful alignment of the CW, Beam and Sling. The projectile hasn't quite left the pouch although the slip ring has come off the release pin.  An excellant example of release at stall. (Thanks Rob!)

Variables
A lot of analysis has been done on Trebuchets.  Over time the various angles, masses and linear components have come to have labels that are commonly used.

 
 
L1 = From pivot center to the end of the Beam where the Hanger/CW is suspended from.
        (Also refereed to as the short arm or counter weight arm.)
L2 = From pivot center to the end of the Beam where the Release Pin is.
        (Also refereed to as the long arm or sling arm.)
L3 = From Release Pin to center of mass of Payload.
L4 = From end of short arm to center of mass of CW.
L5 =  Vertical distance from ground to Beam pivot point, sometimes known as the axle height.

mb = Mass of Beam
m1 = Mass of Counter Weight
m2 = Mass of Payload

(0,0) = Origin for X,Y plots
(X1,Y1) = Position of end of short arm.
(X2,Y2) = Position of end of long arm.
(X3,Y3) = Position of center of mass of payload.
(X4,Y4) = Position of center of mass of counter weight

Psi = Included angle between Beam long axis and from Beam end to center of mass of Payload.
Phi = Included angle between long axis of hanger and long axis of Beam.
Theta = Included angle between short arm and a vertical line from the Beam pivot point downward.

(Myself, I don't care for the angular labels and would prefer references of Theta 1, Theta 2 and Theta 3.  It's more consistent with the other labels and doesn't confuse the Psi and Phi labels with other Engineering labels. But hey, that's just me...)
 
Pin Angle
The angle that is subtended by the Release Pin in reference to the long axis of the Throwing Arm. An important feature that, along with other factors, helps determine what angle the payload is released at. In this view the Throwing Arm is at horizontal, but it's important to understand that the Pin Angle is relative to the Throwing Arm, not the ground or the frame of the Trebuchet, so no matter where the Throwing Arm is, the Pin Angle will remain the same.
 

Cocking Angle
With the Trebuchet cocked, ready to fire, the Cocking Angle is referenced to the frame base and is subtended by the long axis of the Throwing Arm.

Hanger Angle
This is a simple one, but is referenced differently.  It is that angle between the long axis of the Throwing Arm and the long axis of the Hanger. I haven't included a graphic for it but will if pressed into it.

Prop Angle
This is the same as the Hanger Angle, but since there would be a device (the Prop, not shown here) that holds the Counter Weight in a new position it's called something else.  The long axis' of the Hanger and the Throwing Arm are still the reference lines.  Propping is not often used but is spoken of often enough to include it here. Refer to my Theory page for more about Propping.