Da Vinci’s Cam Hammer

This is Da Vinci’s design for a cam-driven hammer. Here is a model that I built out of wood using a hand Dremel tool, glue, and wood from this kit. The hammer can be also interpreted as an information machine, and there are ways of using this as an analog model to investigate mathematical and computing principles. We can ask system theoretic questions and pose challenges: (1) How would you use Da Vinci’s hammer to capture the concept of number? (2) Define the states, state space, inputs, events, and outputs for this mechanism. (3) What is the cause-effect chain of the machine? (4) Map the continuum of state space to make it a finite state machine. (5) Is there a control loop in this machine? If so, what are the beginning and ending loop values? (6) Define a mathematical function being dynamically represented, and (7) define the mechanical advantage using the lever concept. Answering these questions and addresses the resulting challenges can be more interesting than having students move alphabetic symbols around, plus they can learn a little bit about history.