Square-Hole Drill in Three Dimensions
One can combine the use of a Reuleaux triangle to make a square-hole drill with an Oldham coupling to make a drill that has one end following pure circular motion, while the other end has a cutting tool that follows an exact square. This idea appeared in a 1939 note in Mechanical World, with no author given, and was recently popularized in the book How Round Is Your Circle?; the authors made a working device along these lines. More details of the square-hole drill portion can be found in the Demonstration "Drilling a Square Hole".
Reference: J. Bryant and C. Sangwin, How Round Is Your Circle?, Princeton, NJ: Princeton University Press, 2007.