This is the curve of "quickest descent".

I have drawn the three Trochoid Curves upside down from the normal orientation primarily because of the mechanical device I devised to generate them. I chose to attach the top of a transparent screen to the green rack and let it hang down - gravity gives it some stability - as opposed to attaching the bottom of the screen to the green rack and having it stand on its edge. In the latter position, I would have had to stabilize the top before the tracing point could effectively maintain contact with the screen and trace a curve. Also, the "curve of quickest descent" is easier to understand with the curve drawn in this position. I will add an explanation of how this curve is the fastest path for an object to take from point A to point B when point B is lower than point A, unless the object is falling straight down. Conventional logic lends itself to believe the fastest path would be a straight line, but this is not so. Study the cycloid curve and think about this. If you are like me and get involved in things and forget to check back for delayed answers, email me right now to notify you when I have updated this page. If I had the graphic and explanation ready now, I wouldn't keep you in suspense. Bear with me. Or, if you want to prepare an explanation for me, with or with out graphics, submit it to me and I will use it and give you credit on this page. Of course, the explanation has to be correct. No heavy physics, please. I need to be able to understand the explanation.