The automaton, also known as Da-vi, is found in Elemental Workshop IV after powering up the Cosmic machine. Once you solve the puzzle, he will be powered up by operating the draining machine and will move onto the next room to open the doors for you.
He is given orders in a rudimentary computer system that consists of an "address" and "command" block. The address block instructs the automaton where to go and the command block tells which action to perform there.
The book states that Vitruvius designed Da-vi based on a drawing made by an "old artist friend" of his, and then named it after them. The 'artist friend' he refers to is likely Da Vinci, who is the RuneScape counterpart of the real life artist and inventor Leonardo da Vinci. The drawing likely refers to the Vitruvian Man, which was drawn based on the writings of the real-life Vitruvius.