This sophisticated linkage has, like a Swiss knife, a wide spectrum of uses. It draws not only circles but also ellipses and straight lines. Just turn the crank. By sliding the blue pencil along its rod, you get a circle at one end, a line at the other, and the full range of ellipses in between.
This Demonstration connects two similar isosceles trapezoids and a rhombus. The equation of the curve is not hard to establish.