Let me see...
- Gunnar gear. One gear is being used as a coaster. Find Dagny's note (inside a bottle in the hold), and you will be able to take the gear. You have to do this when Gunnar isn't there, so that's either when he goes out sailing for the first time, or when he's kicked out of the pub. Or at the very end of the game, I suppose, when all the characters pretty much disappear.
- Langspil gear. Solve the triangle puzzle in the captain's quarters to learn that the langspil is worth investigating. Look at it and solve its puzzle for a gear.
- Lion head gear. When you learn that Dagny wasn't kidnapped, she gives you the lion head. You can solve the lion head puzzle on the figurehead for a gear. Do you have to read Soren's email about the lion head before Nancy tries to solve the puzzle?
- Crow's Nest Gear. Read the book in Magnus' house, and you can solve the puzzle in the crow's nest by Soren's.
- Not Actually A Gear. The final gear is a crank that you get from Elisabet, after solving the bilge pump puzzle.
I don't really know what triggers the bilge pump puzzle, which gives you the final gear. Both times I've played the game, that happened after I put two or so gears on the gear cupboard.