How does the Half-A-Gear puzzle work?

Hint 1 of 4:

The object here is to pull down the correct combination of levers to create a
long enough piston to push the gear until it is no longer visable.

Hint 2 of 4:

If you're on the right track, pulling down a lever will make the piston
longer.  But if the piston gets shorter after you've pulled down a lever, at
least one of the levers is wrong.

Hint 3 of 4:

Label the handles 1 to 7 from left to right.  Pull down handles 1, 4, 6, 7.

Hint 4 of 4:

Correct positions of gears: down, up, up, down, up, down, down.