Normally, if you cannot turn a gear by hand, you use the Multi-Tool. (Get this from the Cantina at the start of the island.)
At the Giant Fan in the annex, you must exit the Mech and ride the turning blades to reach the stuck gear at the top. Normally, you would have needed the Multi-Tool to discover the number "0516" at the Mayor's office. However, if you learned the number from somewhere else, you may find yourself at the Giant Fan without the Multi-Tool. You should exit the Mech, walk back to the Cantina, get the Multi-Tool, then use the Teleporter to return to where you left the Mech.
Where a gear is not turned by hand, you would use the Multi-Tool, available at the Cantina when you enter the island.
its in the museum on mainstreet of steamworks island :)
The name "Gear Works" may refer to the Poptropica island called "Steamworks Island." -- Gear Alley is the left side of the island away from Main Street -- Gear Shop is the common room (multiplayer) on Main Street (see the related question below)
You use the steam battery in Gear Alley. On number 5.
It's Steamworks Island #14th Island
(The solution is at the related question "How do you beat Steamworks Island")
the crab on steamworks island is next to the living quarters
You go to Steamworks and head to the museum and there is the Deogen
steamworks island
There is a video walkthrough at the related link below. There are written WikiAnswers solutions at the related questions, as there are for all Poptropica islands. (How do you beat Steamworks Island) (What is the walkthrough for Steamworks Island)
Steamworks island
You put oil on the gears which are in the middle.