As my cousin Reese says, Legos are a bit like potato chips. I had a lot of fun playing with the Lego parts in Reese's Robotic Invention System and I had to have just a little more, so I ordered a couple small sets, an 8229 and an 8213, that were the week's Lego phone specials. Mary looked at me a little funny since I'm 36 years old and unemployed, but hey, it keeps me outta the Star Trek conventions.
I built a little car with steering and rear suspension. Borrring. Then I built a trebuchet. Wheeee!
The scale was miniscule. A juggling ball, probably weighing a little more than a tennis ball, served as the counterweight. The ammunition was a quarter with a wire bread-tie wrapped around it. It had wheels to allow the frame to roll instead of having the absorb the forces of the massive counterweight. With the wheels, the counterweight would stop swinging almost immediately. Without the wheels, the thing would tear itself apart if dry-fired.
My first attempt tossed the quarter straight up behind the trebuchet about one foot in the air. Foo. Two loyal peasants crushed 'orribly beneath the gigantic boulder. The quarter was being released too early, and I got exactly the same result several times in a row.
I realized that I'd been holding onto the wheels when releasing. I kept my hands away from the wheels, and the quarter looped up and over and was driven into the floor about two feet in front of the trebuchet. Success, almost. "T'will take us 'alf a day to dig 'at boulder out'n the peat, Sire!" The interesting part to me was how repeatable everything seemed to be.
I added a little 1x2 angle piece to the end to make a 45 degree "finger" at the end of the throwing arm, and the quarter looped up and over and went about six feet. I kept making adjustments, and after lengthening the wire sling to almost equal the length of the arm, using a lighter projectile (a 24-tooth Lego gear) and going back to a 90 degree finger, the ammunition was being flung across the room and the castle walls were being torn asunder as the beseiged town prayed for mercy.
Here's a variation that occurred to me in which the counterweight is attached to a cam on the end of the throwing arm that is used to extend an appendage. The appendage starts out folded in, but as the throwing arm swings up and approaches the 45 degree release point, the cam moves the counterweight attachment point further from the appendage pivot point, increasing the force that is extending the appendage. This should create a "whipping" effect on the sling. On the downside, that appendage joint would probably have to handle quite a shock when it hits its fully-extended position. A hyperextension is a potential failure scenario. Another complication with the design is that a mechanical release mechanism of some kind may be needed. The traditional "finger" spike at the very end of the throwing arm can be retained, but an additional hook to drag the sling and payload out of the launch trough while the appendage is folded will be needed, along with a mechanism to retract the hook at about the time the main arm becomes horizontal. Okay, it's too complicated. Guess I'll have to pick up some more Legos and make sure...