Your washing machine probably used cheap nylon gears which self destructed. There are windmills older than 400 years old that still operate today despite using gears :)
This is false example - these windmills are actively maintained and repaired, how are you going to replace massive gears or bearings in space? Are you going to bring spare parts with you?
No, you will bring manufacturing capabilities with you. Decently sized warships carry a machine shop for a reason. A generation ship will have to be totally self sufficient, this will include not just food, air and water but also being able to manufacture pretty much anything they might need.
