As is well known, there was little concern in Apollonius' Conics about the actual "mechanical" construction of the conic sections. In fact, it is not entirely clear whether there ever was an interest in Classical Antiquity in any tool that would draw a given conic section in the same way one can draw a circle with the help of a compass. There certainly was an interest in such a tool among Muslim mathematicians. In Renaissance Europe, a number of mathematicians suggested various mechanical ways to construct the conic sections as well--although no actual drawing devices seem to have been built. In this talk I will outline the most important proposals for the mechanical construction of the conic sections and sketch their historical context. I will discuss one particular construction in more detail and pursue its history from the early 17th century to the mid-20th century.