Watt's Curve

Watt's curve is a tricircular plane algebraic curve of degree six. It is generated by two circles of equal radius $b$, with centers a fixed distance $2a$ apart. A rigid rod of length $2c$ connects a point on each circle, and the midpoint of that rod traces out the Watt curve as both circles rotate. Depending on the relative sizes of $a$, $b$, and $c$, the curve can form a single loop, a figure-eight, or three separate loops. It takes its name from James Watt, who used exactly this kind of straight-line linkage in his pioneering work on the steam engine — Watt's parallel motion — to guide a piston rod in an approximately straight line using only pivoting links.