Reuleaux triangle or how to drill a square hole

And you know you can drill a square hole - sounds unlikely, but it is nonetheless. Yes, there are actually drills that allow you to drill square holes. To tell you the truth, a square comes out with slightly rounded edges that need to be filed, and yet a square hole can indeed be drilled.

And the Reuleaux triangle helps to cope with this difficult task. The figure was named after the German mechanic Franz Röhlo. He was probably the first to investigate the properties of this triangle and use it in his mechanisms. To tell the truth, the unusual properties of this figure were discovered long before Reuleaux, and Leonard Euler and even Leonardo da Vinci disputed the palm of the German. Oh well ...

For the first time, Harry Watts, an English engineer who worked in the United States, managed to make a mill for drilling square holes. To do this, he used a square-slotted guide template, in which the drill, inserted into the "floating chuck", moved. The chuck and drill were patented by Watts in 1917. The new drills were sold by Watts Brothers Tool Works. How exactly a square hole is obtained using such a drill can be seen on the video below, where Reuleaux's triangle rotates around a slightly movable axis.

So, a drill with a cross-section in the form of a Reuleaux triangle (see illustration) and cutting edges coinciding with its vertices allows you to get almost square holes. The peculiarity of such a drill is that its center does not remain in place during rotation, as is the case with traditional twist drills, but describes a curve consisting of four elliptical arcs. Therefore, the chuck in which the drill is clamped must not impede this movement.