Jonathan wrote:
Thanks for the URL Jeff, and what you posted got me thinking. Fast up, slow down. That's what Georg always says! I came up with the device shown, that should be an easy test of Georg's theory. The red balls go down a straight incline, pushing along a toothed conveyor like a catepillar tractor. When they reach the bottom, they hop off the conveyor and onto the cycloidal path, and if they have not lost too must energy on the way down to the conveyor, they will quickly go back up and start over. I think that even if there were no conveyor, friction alone would stop the device from being perpetual.
Hi Jonathan,
The brachistochrone principle is something I once briefly looked into for the "Uncles Toy" PM discussed last week or so, except the opposite way around to the way you have it here. In the "uncles Toy" idea balls from the hopper ran down the face of the vertical auger (perhaps creates maximum acceleration similar to the brachistochrome cycloid) & at the bottom hit a geared paddle wheel & then position themselves on a conveyor lift back to the hopper. When the ball is at the bottom of the cycloid (or auger perhaps) it has its greatest linear kinetic energy because it is at its fastest velocity with greatest translational kinetic energy because it rolls. In the end I think the cycloid is just the most efficient energy saving track which allows maximum unimpeeded acceleration, or less frictional drag as the case may be.