A mathematical model for a lateral harmonograph

A harmonograph is a mechanical device driven by one or more pendulums that produces aesthetically pleasing geometric designs. For a lateral harmonograph the pictures produced are 2D projections of 2 n phase space where n is the number of pendulums. The pendulums can be simple pendulums or conical pendulums. In this paper mathematical models for a 2-pendulum and 3-pendulum lateral harmonograph are derived. A small subset of parameter space is explored by analysing a number of simulations. The simulations demonstrate what the two models are capable of. A harmonograph is an excellent device to model and use as an educational tool as it can be used to engage mechanical engineering students with dynamics. It shows engineering students that a pendulum or multiple pendulums are a dynamic system that should be taken seriously and is far more interesting than an undergraduate student might superficially consider it to be.