On Oskar's Gear Shift, without telling me the solution, is it possible, ignoring small gears, to move a SINGLE LARGE GEAR by a SINGLE TOOTH ROTATION leaving the other large gears unchanged (solved)?

Long version follows:
I'm finally getting around to solving a Gear Shift that was scrambled by friends who found it on my desk at work.

I don't want to look up the solution, and I'm only asking this question here on the chance that something mechanical was popped on this puzzle by one of my friends putting it into an unsolvable state.

Currently I'm just working on the large corners ignoring the small ones to nail down my strategy.

I have a situation with only one of the large corners off by one gear. The more I understand the puzzle the more convinced I am that you can't move one large corner by one gear tooth, or any odd number, using legal moves.

So my question to those who know is this:

Without telling me the solution, is it possible, ignoring small gears, to move a SINGLE LARGE GEAR by a SINGLE TOOTH ROTATION leaving the other large gears unchanged (solved)?

No, the big corners, when all the other big corners are solved, can only be moved in increments of two teeth.

That would be why this has been such a painful solve. OK, thanks a lot Luke, I'm going to pop it back into place.

My coworkers are dangerous around puzzles...

EDIT-- And I now have a reliable solution. *PHEW*, A very fun puzzle.