Saturday, March 31, 2012

Some failed experiment(pmm)

¤Simanek's Silly Slinky Device¤

Two identical gear wheels (A and B) are connected by a frictionless chain drive (C). Obtain a Slinky (TM) toy or two, and make a chain of them to wrap around the outside of these wheels as shown. The coils of the spring engage in the gear teeth, which prevent the coils slipping on the pulleys.
... The design allows either one or two coils to fit in the gaps between the teeth. we show two coils per gap at the bottom, and one coil per gap at the top.

We have arranged things so that the coils are closer together on the right than on the left. We show a compression ratio of 2, but it can be anything you want. The chain drive (C) with ratio 2:1 keeps the lower pulley rotating half as fast as the upper one, maintaining the chosen compression ratio.

forces are clearly
so we need not consider
system is heavier in the right, since there are twice as many spring coils, so we expect the slinky and upwer wheel to rotate clockwise. As it turns, the compression ratio will be mainatained, and the unbalance maintained continually. The coils are expanded as they go around the top pulley, and compressed as they go around the bottom pulley, as indicated.

Of course, good engineering design will require two locked coaxial gears at the top and also at the bottom, to provide for proper tracking to give the spring lateral stability, otherwise it would fall off the gears. If you actually build one, its friction will prevent its motion. But it does move freely if either pulley is driven by hand, and it does does maintain the condition of overbalance no matter how far you rotate it. Now reduce the friction to zero and watch it go!

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