h a l f b a k e r yNice swing,
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Yeah, you're probably right bigsleep. |
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I was hoping that the moment of inertia of the top pendulum would compensate for the change in centre of gravity. |
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Clever. The balls act as gears, right? (It would fall over in an instant, but it's still a nice idea. If you put an arrow pointing to a battery, you could get investors for it.) |
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yep, the balls act as gears. |
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So this idea probably doesn't work, but it poses the question: is it possible to increase the stability of a vertical object with passive moving components? |
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Could the ball gear arrangement get out of whack due to a non centre-returning sequence of big pendulum movements? I suspect so. |
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It could be a tiny, tiny segway for lego people! |
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//Could the ball gear arrangement get out of whack due to a non centre-returning sequence of big pendulum movements?// |
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yep, probably. This could be overcome by concentric ribs on each ball which act like gear teeth. |
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//is it possible to increase the stability of a vertical object with passive moving components?//
Yes, give it bigger feet. |
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Other passive ways of increasing the stability include: a) attaching a helium balloon and b) making the centre of gravity of the object below the supporting surface. (although I wouldn't consider either of these to be 'passive moving' elements) |
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I think the main problem with this idea is that it will take at least as much energy to stop it toppling than it can extract from toppling (and frictional losses will push it in favour of toppling). |
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I'm wondering if it could extract as much energy as it would use if the surface wobbled (rather than being stationary)? |
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Like an iceberg, this might balance if it semi-floated in water supported in the center of some sort of innertube. Also, if you put this in some wave waters, this could add some energy to the weights and cause them to roll around so that the [whatever the dipole moment for mass is called, net(mi*ri)] relative to the center ball is always pointing against gravity. |
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/yep, probably. This could be overcome by concentric ribs on each ball which act like gear teeth./ |
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If the balls are different sizes that won't help. |
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//If the balls are different sizes that won't help// |
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this is not immediately obvious to me. Could you elaborate? |
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I was probably premature in my pooh-poohing. For now, I retract my assertion re: out-of-whackedness. |
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One sphere on the top which can be rotated in two directions independently. Much like an unbalanced person 'windmills' the arms, the sphere is temporarily rotated to bring the system to the vertical. |
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An external power source could be used, but another novel idea would be to allow the sphere to drop slightly down the shaft. |
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Alas, the illustration for this idea was lost (the image
hosting site disappeared and I don't have the original
on my computer). I posted a similar idea: 'mirror
lever' with vaguely similar illustrations if interested. |
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Anyway, this idea has bubbled to the top because I
just added a link to cool art by Dan Graybe which is
tangentially related. |
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//poses the question: is it possible to increase the
stability of a vertical object with passive moving
components?// |
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That is a brilliant question. [+] |
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I think [xaviergisz] answered it with a very nice line of reasoning above: |
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// I think the main problem with this idea is that it will take at least as much energy to stop it toppling than it can extract from toppling (and frictional losses will push it in favour of toppling). // |
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But I'm glad this came back up because that is an intersting question (and answer). |
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//the main problem with this idea is that it will
take at least as much energy to stop it toppling
than it can extract from toppling// |
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I'm not sure that's a rigorous argument. If I take a
very long, thin heavy rod with a well-squared end,
I can balance on a level surface, as long as nothing
disturbs it. In that case, it takes no energy at all
to stop it topping and releasing its energy. |
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To be clear: I think the energy argument is the
right one, but I don't think it's as direct an
argument as the one proposed. |
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I don't know that the energy argument is correct, I
would be more inclined to look at the center of
gravity. |
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Without an outside force, no purely internal
motion can shift the center of gravity of an
object. If one part moves in one direction,
another will move in the opposite direction, and
the center of gravity of the total object remains in
place. Please note that a stable/balanced object
that moves can receive that outside force as a
reaction through it's base. |
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Once the center of gravity is not above the base,
the object begins to tip, and it can no longer
experience a reaction force from it's base. As
such, any action may cause it's arms to move, but
the center of gravity will remain on it's tipping
path. |
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Yeah, that sounds right to me. |
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But it's still interesting to examine possible
solutions and see why they fail, just as it's
interesting to pick apart the reasons why perpetual
motion machines fail. |
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[MechE] // Without an outside force, no purely internal motion can shift the center of gravity of an object. // |
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I agree that is true, but in this case we do have a point in contact with the ground. I assume that this point has friction so it can resist horizontal forces. For stability on one axis, consider a flywheel with a horizontal axis pointed towards you that is supported by a single foot with a sharp point on the end. Assume it starts at rest in unstable equilibrium. If a clockwise torque is applied to the flywheel, there will be a counterclockwise torque on the foot, which will cause the whole contraption to tip left. If the flywheel is stopped very soon, the movement will mostly stop, but as soon as it had started to move, gravity started putting torque on the system as well, so it will continue tipping to the left even after the flywheel is stopped. If we notice this tipping soon enough and spin up the flywheel in the counter-clockwise direction fast enough, equilibrium can be regained. |
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[Max], regarding your long rod with the square tip, that is not balancing on a point as this idea requires. The base has a finite width, so tipping will lift the CG, requiring some finite amount of energy to get it tipping. There is no such thing as a perfect point contact, but there is also no perfect initial condition or perfect lack of disturbance, so I think it is valid to say that with a single point of balance below CG, energy will be needed to stop it from toppling. At any point in time, I think that energy will be equal to the amount of potential energy cashed in by the lowering of the CG. Consider if an object almost balanced on a point starts to tip then hits a wall with a perfectly elastic collision. It will bounce back to its original position (ignoring air friction). One shortcoming of [xaviergisz]'s explanation is that using only components attached to the device, it may not be theoretically possible to capture 100% of the energy as the device is tipping, even ignoring friction and other losses. His limit is valid, but I'm not sure if there might be an even tighter limit for a device with no stored energy. |
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My flywheel example is one way that an active device could maintain balance on a point (add a second flywheel to handle the other axis). If we have perfect motors, generators, and battery systems (with some initial charge), I think we can always get back to the initial state, so there is no inherent loss of energy, but I suspect that once it starts to tip, it will need to borrow some energy from the battery to get back to equilibrium. And of course with real world losses, the battery would eventually run out of energy. |
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One thing that might look almost as good is if the energy was stored as potential energy using a weight, either sliding or swinging. If a device like this was designed very well, it might require very little energy when there was very little disturbance. To start it, dangle it from a centered lift point that holds the weights in the max position, and then drop it from about 1mm above the surface onto a rubber pad. This way it starts very close to equilibrium with the weights storing as much energy as possible. As it fine tunes its initial equilibrium and compensates for air currents while you place the glass cover over it, the weights fall about half way. It then stays practically motionless for several minutes. A time lapse camera would show the weight falling very slowly. As soon as the AC turns on, the continual vibrations require constant compensation. The weights start falling again, and it tips over 10 seconds later. Okay, maybe that would be very hard to achieve as well, but I think it's theoretically possible and would be really cool. |
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[scad] agreed, but my point was that there is no
direct link between the energy needed to keep
something balanced, and the energy which would
be released if it topples. I can balance an
arbitarily large mass on the end of an arbitarily
thin (though not infinitely thin) rod, and prevent
it from toppling through the action of an arbitarily
small force. |
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In fact, no energy need be expended to keep the
thing from toppling. If I lean the rod against a
wall, it will stay there, leaningly, for as long as I
choose to leave it. |
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[max] in all those cases you have to go uphill a leetle teeny beet bit before you can zoom all the way down. |
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Gravity is working on both weights concurrently
making an inertia. There is no extra energy to over
compensate for losses. |
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//in all those cases you have to go uphill a leetle
teeny beet bit before you can zoom all the way
down.// Not in the case of a rod leaning on a wall. I
f the wall were not there, it wouldn't require an
activation energy for the rod to fall. |
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I think removing the wall might take some activation energy. |
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To answer the original question "can a passive
mechanism help balance a toy", the answer is
"yes" in a simple sense. |
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If I balance a wooden rod on its flat end, and
nudge it very slightly, a complex mechanism helps
to keep it upright. That mechanism involves the
fact that the centre of gravity shifts relative to
the base, putting more compressive force on one
side of the base than on the other. Then the
electrostatic repulsion between the atoms on
that side increases as a result of the compression,
tending to push those atoms apart and thereby
providing a restoring force. |
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This natural tendency of a column to right itself,
up to a point, is actually a very complex, multi-
step process and, if it didn't exist naturally, it
would be considered quite remarkable. For
example, if there were no solids, and if we and
our surroundings were entirely liquid, we would
marvel at this new nano-engineered material that
resisted tipping, deformation and other forces. |
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So, the question is not whether passive
mechanisms can stabilise a balancing toy. The
question is whether the natural properties of
solids are the only or best way of doing so. |
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Aren't you just fighting geometry again? |
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Well I'm betting against you again I'm afraid. The odds on offer are not very profitable though. |
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[MechE] // Without an outside force, no purely internal
motion can shift the center of gravity of an object. // |
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True. But internal motion can cause a rotation about a
fixed point, as every person can prove when they lose
balance and windmill their arms to regain balance. This is
why I suggested a kind of gimbal system as a way to rotate
the C of G to the balance point. |
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// To answer the original question "can a passive mechanism help balance a toy", the answer is "yes" in a simple sense. If I balance a wooden rod on its flat end... // |
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[Max] I think your definition of the original question is different than mine since the idea started with: // This is a toy that balances on a point // |
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In your first post you summarized the question as: //poses the question: is it possible to increase the stability of a vertical object with passive moving components?// If you apply that to something balanced on a point (and are trying to increase the stability from unstable to stable), I think the energy argument is enough. If you apply that to the general case where you might want to increase the stability of an object that is already stable, then I agree that the energy argument might not apply, or at least might be much more difficult to apply. Actually, in the case of an object with a flat base I'm not yet convinced that it isn't possible to increase the stability by adding some movable passive gizmo (removing other mass to avoid cheating by changing the CG). |
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I've heard of all sorts of ideas for stabilizing skycrapers against earthquakes, but I'm not sure which of those apply since those engineers don't consider it cheating to cange the CG or use active systems. Also, stability against shaking seems different than stability against the base being tipped and held at an angle or being moved a significant distance. |
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// Also, stability against shaking seems different than stability against the base being tipped and held at an angle or being moved a significant distance.// |
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Shaking is oscillation, which - if it's simple harmonic motion - is about a fixed point. There is no enduring displacement from the rest position. |
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"First law: When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force" |
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Objects have an innate tendency to move to their position of lowest potential energy. If, by displacing an object from static equilibrium, you offer the opportunity to decrease its potential energy, it will take it. Knock a table, and the balanced pencil will fall ... but apply a consistent periodic oscillation and it can continue to balance. |
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//the idea started with: // This is a toy that
balances on a point //// |
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Ah, but nothing ever balances on a point, even if
it is stabilized. If it has finite weight but balances
on a point, the force at that point will be infinite.
A pencil, tip downward, rests on a small area but
definitely not a point. If you were able to balance
a pencil on its tip, the reactive mechanism I
described would be responsible for keeping it
there, even though it would only operate within a
very very small range of displacements. |
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// If it has finite weight but balances on a
point, the force at that point wil be infinite. // |
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… and thus by inference the object gains
infinite potential energy just by having a
"perfectly" sharp point created on it … |
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<Rummages in desk for pencil sharpener> |
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How did you manage to copy-and-paste, yet lose an
'l' in the middle? Is the Borg RAMPack wobbly again? |
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We sometimes experience difficulties
interfacing with your primitive technology - in
this case, the cable for the cassette recorder
got tangled round the 16k memory expansion
module and because the edge connector is
only tinned rather than gold-flashed (Thank
you, Sir Clive … cheap as always), when it got
nudged by an errant copy of Practical Wireless
there was a glitch and the 'l' mysteriously
disappeared. |
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It's probably got stuck in the Teletype tractor-
feed … |
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// Ah, but nothing ever balances on a point, // That is true. But for the purposes of baking this device, the point would have to be small enough to look like a point, and as such would not have enough width to practically make any difference. |
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Since we are not taking advantage of the fact that there is more than one point touching in the design of the system, it seems valid to simplify the reasoning for why this can or cannot work by treating it as a theoretical point. |
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