The pieces of machinery are, for the most part, in different wings of the tower. There is one piece on the very first level where you entered the Severed Hand. Make sure you get the piece off of the Swordsman who asks you to do his dirty work. You need to go back and talk to him after completing his quest.
I'm not trying to be vague to avoid spoiling, I just don't recall the exact locations.
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Most Subtle Official Straightman of the Laughing Hyenas -- Grammarian Brigade.