Eureka! We're in the engine room! My analysis tells me that if you trace the spinning crankshaft all the way back to its source, you'll find Raleigh's treasure key and sabotage his machine while you're at it.
― Bentley, at the start of the mission[src]
Sly ventured through the machine-filled area until he came across a giant spinning furnace, which was spinning way too rapidly for him to make use of. Therefore, he had to take an alternate route, where he would be able to halt its rotation. With some skillful climbing, Sly grabbed onto a hook to a machine that carried him over to the furnace and stopped it in just the right place to allow himself to pass through and collect the treasure key.
I can't believe I pieced this one together. Try 2-2-7.