Instructions on how to rotate the tower in Myst library and get the access key to unlock the cogwheel.
Get the Cogwheel Access Key
After you rotate the tower so that the line turns red on the cogwheel, you should go up the tower. There is a painting on the wall that shows the library door open, and there is another that shows a doorway with a set of stairs. Go to the portrait with the stairs, and click on it. The bookshelf will become a set of stairs that you can climb. Go up, then follow the path to the end, and open the elevator door. Go inside, then press the button to go up.
You can go up the ladder to see that the tower is looking at the cogwheels.
Then go down, and walk behind the elevator, and climb up the ladder with the
key symbol behind it. For the cogwheel, it gives you the following clue:
Go to the Clock Tower
This clue may remind you of the clock tower that you saw beyond the shore that you couldn't reach. Go there (check on the painting of the open door to open the library again) and check on the machine across from the clock tower. There is a large wheel, a small wheel, and a red button. Turning the large wheel will make the minute hand rotate, and turning the small wheel will make the hour hand rotate. Turn the large wheel 8 times, to make the minute hand of the clock tower point to :40, then turn the small wheel 2 times, to make the hour hand point to 2. Then press the red button to make a bridge appear.
Solve the Gear Puzzle
Cross the bridge, flip the Marker Switch upward, then go into the clock tower. If you pull the left-hand lever, the two bottom wheels will turn, but if you keep holding the lever, only the middle wheel will turn. If you pull the right-hand lever, the two top wheels will turn, but if you keep holding the lever, only the middle wheel will turn. You can pull lever on the wall on the right to reset the puzzle. Be aware that once the weight on the left reaches the floor, you can't rotate the wheels anymore and have to pull the rightmost lever to reset the puzzle and try again.
Pull the left lever and let go, so that the middle and bottom wheels say 1 and 1. Then pull the right lever and let go, then pull and hold it so the top wheel says 2, and keep holding it until the middle says 2.
When the wheels say 2, 2, 1, the cogwheel in front of the device will open.
Go to the large cogwheel that you saw near the docks of the island. You will see that it has opened. Look inside and you will find a book. Open it and click the picture inside to go to the Mechanical Age.