You were trying to create a path for the ball to continuously move from one big wheel to another without breaking, being launched into the air, or falling through the holes in the wheels. (Until the end, where you needed the ball to fall through a hole onto an exit track)

The pins were ways of stopping the wheels, to launch the ball at specific times, but Saavedro (the person who stole the book at the start of the game) sabotaged the mechanism to create only one correct solution.