My son is very much into LEGOs (and to a lesser extent, so is my daughter). I'm pretty sure that by age five, he has more blocks than my two brothers and I ever had growing up. One of his kits, the Klutz Crazy Action Contraptions, has a relatively-small number of pieces, including bricks, gears, and a few rubber bands; but their detailed instructions allow even a five-year-old to build a variety of gravity and rubber-band powered machines! Combine that with my engineering mindset and… well, you'll see.
And then I discovered the Lego.com Digital Designer, which you can download and use as an infinite LEGO kit, and to document your physical designs. So I have been able to capture creations so we can re-build them later. :-)
I love the physics of siege engines. Before moving on to the trebuchet, I decided I'd start with a catapult. I had seen in the other contraptions the power of a rubber band, and decided that would be the best choice (rather than torsion in the throwing arm, which would be rather hard on a LEGO structure).
(The LEGO Digital Designer doesn't have rubber bands, unsurprisingly.)
My daughter gave me a trebuchet kit (non-lego) for Christmas, and when I saw the finished product, and saw my son playing with the Contraption kit, I knew I'd eventually make the trebuchet. Here it is. :-)
(The LEGO Digital Designer doesn't have floss, either. Also, sometimes it's CAD wouldn't let me place things, like the half-bushing, in a location where I know it fits.)