I tried... I really did... But I can't get it to work. But I did find someone else who has tried... (
performs handball)
Simanek's Silly Slinky Device
[New, November 2005] Back in the 1950s when I was an undergraduate student, some of us would relax from the rigors of homework by inventing mechanical devices as challenges to each other to figure out why they can't work. I found this one in my classical mechanics notes from those creative times. Here's the description designed to put the best face on it.
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.
The internal forces are clearly balanced, so we need not consider them. Obviously the 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!
More power! The expected power output is proportional to the weight difference of the two vertical portions of the Slinky Spring. Therefore the power can be increased by increasing the length of the spring and the distance between the pulleys. This improved version is shown in the second figure. There is no limit to the improvement that can be gained in this way.
Even unworkable devices should be well-engineered.
Suspended springs do not have uniform spacing between loops. That isn't shown in the picture, but it isn't an issue affecting the performance of this device. What's important is that there be more spring loops on one side than the other at all times and the belt (C) functions to maintain that condition.
What an elegantly simple concept! If we build it, will it turn? As usual, we allow you to use perfect components, frictionless bearings, etc. Discussion and solutions are invited.