Brilliant. A different way to get to Viviani's Curve is to perform a Rope Flow "Dragon Roll". Dragon Roll is a portmanteau of the phrase "drag and roll". The rope's mid-point will be a close approximation of Viv's Curve. You can see the "Dragon Roll" by looking at the first 30 seconds of inventor David Weck's YouTube video. There are thousands of people sprinkled around the planet who do rope flow regularly. I believe I was the first person to identify the closed curve that those dragon-rollers are moving around. Weck uses a figure-eight (i.e. a lemniscate) as a visualization tool in his "Weckmethod" movement studio. I believe the motion of the two hands follow a lemniscate -- but the two hands are out of phase with each other. I plan to do a more formal treatment of the "Dragon Flow" in Mathematica. A motion capture of both the mid-point and the hands during a Dragon Roll cycle would be a definite plus. That's a bit challenging, because torque is also a component in Rope Flow movements.