I beat all of the levels, but I don't think I beat any of them the "right" way. The first level I beat with a single wheel, and that was the only one that I completed without breaking the game.
I discovered a bug where a single battery connected to a plank would power all wheels, even if those wheels aren't connected to anything. So I exploited the hell out of that to complete levels by spamming crazy amounts of self-propelling wheels.
I had a lot of fun while breaking your game, though.