A similar machine at work:
As we have received a lot reactions and feedbacks on the 3DPlot utility we released in February 2012, I have decided to use a similar principle and make a "guilloche-engine" in AutoCAD. My first attempt went through modeling the scheme of a true machine using the parametric constraints on AutoCAD geometric objects but this way has proven to be too difficult.
A more reliable way - similar to that used for 3DPlot - is using hypotrochoids, epitrochiods and other parametric curves. The resulting 2DPlot add-on application for AutoCAD can assist you in drawing any parametric curve defined by a mathematical expression (equation) of the type XY=f(u). The examples included in this LISP routine show interesting and visually pleasant artistic curves which can be used e.g. for decoration on diplomas, printed stocks and other materials. You can export them from AutoCAD to other software, e.g. for DTP, in any precision.
Try yourself both the 2DPlot and 3DPlot utilities for free and create drawings like this: