At the 3rd level in the elven tower i got this "piece of machinery" where do I use this and how do I got further?

There are three other pieces of machinery that you need to get. They can be found in the rest of the towers of the Hand. You need to go up to the fourth level to access the towers though.

The stairway to the fourth level is on the third level just south and a bit west of the center of the map. Good luck!