I have, as art that I built for fun, a new manifestation of an inverted cycloid. If you remember from calculus, a cycloid is the path that a point would take if put on the edge of a disc and rolled. The hopping motion of the point is a cycloid. Gauss (I think) figured out that a perfect pendulum would take this path inverted. In otherwords, the circular path that a normal pendulum takes doesn't give it a regular period from crest to crest. If the weight were to follow the path of an inverted cycloid, it would always take it the same amount of time to swing from side to side, regardless of how high it is swinging.
Building on the concept, I created two steel plates that, when put side-by-side created a gap in which a ball bearing could roll. I came up with the horizontal formula for the curvature of the gap such that the vertical movement of the ball was that of an inverted cycloid. It works great and is now art in my apartment.
Major geeki/nerdiness. Aaaaah thankyou.[/QUOT
huh?