I solved this puzzle with a lot of blood, sweat and tears (well, mostly sweat and tears). I couldn't figure out the directions in the walkthrough, and just by experimenting managed to do it in about an hour.
By turning and straightening, over and over you have to get the far left plate to turn on its side, then the second from the left, and so on until they're all horizontal. Then you can slide them out. I know this explanation probably doesn't help, and I almost gave up several times, but I finally DID IT! The tartan plaid was a piece of cake compared to this puzzle.