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Imagine a person in a giant squirrel cage, climbing interior stairs that circle its perimeter. On one side, its axle has a gear that meshes with a cogged vertical beam. As the person climbs, the cylinder rotates and “rolls” up the beam. Going down the stairs would lower the lift, and a brake would lock
it at each destination floor.
With a light cage and the right gear ratio, one or more people should find it less arduous than using conventional stairs. To send it up to a waiting user, a motor or a fit, fluffy-tailed bellboy would be needed.
schematic sketch
http://www.geocitie...e/squirrelcage.html
[FarmerJohn, Oct 04 2004, last modified Oct 21 2004]
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Oh the fun you could have with a slinkey. |
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It's an interesting brain physics problem, though. Would it work? Would one's own weight, placed in an offset position inside the circular stairs, be enough to simultaneously roll the circle's edge down and the gear assembly 'up'? |
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It would certainly work, but you would be lifting the weight of the wheel as well as your own. Why not simply climb the stairs slowly? |
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[waugs] I was also wondering how I might be sure this could work, until I thought of a lever. With the short lever arm ending at the center of the axle, the fulcrum where the gear teeth mesh and the long arm ending at the weighted step, one could certainly lift any cage with suitable lever dimensions. When taking the next step, one puts force on the next imaginary lever arm with its fulcrum a few teeth higher up. |
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[Doc] Stairs are baked. This is half as baked and twice as fun. |
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Another advantage is the flywheel action of the cage, so
once you get it going, you feel like you're using less
energy. I'd hate to lose my footing with 2 or 3 others in
there with me. |
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Should work, as long as the following inequality is held:
x > G*r/P, where:
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G is the weight of the large and small gears, (assumed connected), r is the radius of the small gear, P is the person's weight, and x is the distance between the rack and the person's center of mass. |
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I'd laugh when someone trips and falls up 3 flights of steps. |
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Interesting. At first glance, it seems somehow counterintuitive that your weight can be used to lift your weight. But, it works with block and tackle arrangements. |
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Adding a ratcheting safety mechanism might be useful for keeping up travellers travelling up. And if the stairs were allowed to "freewheel" inside the cage, the trip down could be pretty fast. If not, the descent could still be fast, but not so fun. |
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