How can I repair the robot?

Hint 1 of 6:

If you haven't been trapped in a cage yet, you might want to read the "What
else am I missing here?" question first.  You won't be able to get
information on the robot until you've done what's mentioned there.

Hint 2 of 6:

In specific, when you escape the cage, your shadow can talk to the robot's
shadow to find that it's missing a piece.

Hint 3 of 6:

You then need to sacrifice another machine to get the appropriate part.

Hint 4 of 6:

Break the catapult as described in the previous question, and pick up the
gear for use in the robot.

Hint 5 of 6:

Look for an inventory item that will help you open the robot up so you can
repair it.

Hint 6 of 6:

Use the knife on the robot to make a hole.