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Create a plastic track, shaped like an inverted cycloid.
Place in this track a steel ball bearing.
Add a c-shaped electromagnet around the center of the
track, so that they can magnetically attract or repel the
ball when energized.
Add a sensor in the middle of the track; also, add two
more,
one on either side of the first on, and both
equidistant from it.
Add some electronics and a voltage source, so that the
electromagnet get energized when the ball triggers the
left or right sensor twice in a row. When the center
sensor
is triggered, the the electromagnet is turned off.
Each time the rolling magnet passes through the center,
the electromagnet briefly pulls the ball, adding
to it's speed.
If the ball were sliding frictionlessly, then it's period
would
depend solely on the radius of the cycloid; I honestly
don't
know how much effect there is due to the moment of
inertia.
Since there's friction involved, the ball shouldn't go flying
off the top edge of the track if you use a reasonably
small
voltage.
On the other hand, if the voltage *is* high enough to lift
the ball all the way past the top, then this could be used
as
a lift for a rolling ball kinetic sculpture. In this case, the
track doesn't need to be cycloid shaped; a parabola, or a
U
shape, or some odd 3-D shape, etc, will work... so long
as
the ball doesn't lose too much kinetic energy going back
and forth.
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//If the ball were sliding frictionlessly, then it's
period would depend solely on the radius of the
cycloid// |
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Ah, you're facing the classic escapement problem.
If the action were frictionless, you wouldn't need
the electromagnet/spring/weight to keep things
going. |
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As soon as you add a driving force (in this case, the
electromagnet), you change the period of the
oscillator (in this case, the ball). If the voltage
and timing of the pulse (relative to the ball's
movement) were constant, then the clock would
run at a steady rate, but this rate would differ
from the natural frequency of the ball. |
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For precise timekeeping, you would want to trigger
the electromagnet from a regulated source (eg, a
quartz clock). But then the whole mechanical side
of the device becomes a mere decoration. |
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On a related note, it should be possible to do
something very interesting using a tautochrone
curve. (A tautochrone curve is the same as a cycloid,
but the emphasis is on the tautochronicity. It's a
curve shaped such that a ball dropped onto it at any
point will roll to the end in the same time, wherever
it starts.) |
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