ArsTechnica has a great article about the mechanical analog fire-control computers used in the navy and how they work. I think it's fascinating that people thought up these clever combinations of simple machine concepts. It makes me want to dig out my Kinect set and try to make a simple mechanical computer contraption...maybe I will!
The videos on the second page are definitely worth watching if you have even a passing interest in how simple machines with no electricity can compute mathematical functions.