Two compartmented wheels are free to rotate on parallel axes, but one is offset so
that balls in the compartments can move freely from one wheel to the other. As the
animation shows, there are more balls descending on the larger wheel than are
ascending on the smaller wheel. The two wheels are synchronized by gears.
Of course animations don't necessarily obey physics. Perhaps this motion seems natural to you. Then click on the orange button and see it moving the opposite direction just as naturally.
To the right we show a static picture so you can count the balls and gear teeth and measure everything to convince yourself that the geometry is correct. It is.
This ingenious arrangement has elements in common with a number of other devices in this museum, inclulding some rather old ones. We won't tell you which these are just yet.
Computer analyist André Barata sends us this nice animation of a magnet motor. The three rotatable magnets engage the four segments of geared rack. The four circular arcs are guide rails to keep each magnet in position for strongest attraction for a certain time, until it encounters the rack gears, which then rotate the magnet 180°.
Note that the rotor has three rotatable magnets while the outer ring stator has four fixed magnets. I missed this subtle point the first time. Thus two rotor magnets are still being attracted to stator magnets while the other rotor magnet is switching polarity. Then another rotor magnet switches... And so on, perpetually. Simple!
The first drawing is provided to get across the inventor's conception of a special dedicated body, here called a "chain," that is able to be handled and stretched to longer length, thereby varying its linear density (mass/length). The chain consists of round weights connected by frictionless links. If put it on balance scales, the folded and the stretched versions of the chain weigh the same.
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| Fig. 1. Folded and unfolded chain showing equality of their weights even though their lengths are different. |
Fig. 2. The chain over pulleys showing how the links fall into place. |
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Take note of the heavy lines surrounding the chain in the right hand diagram above. They represent guide rails or enclosure to keep the chain on track. They will of course be as friction-free as possible, and for purposes of analysis we will consider them frictionless.
Also note that the chain passes over a smooth wheel at the top. It passes over a toothed gear at the bottom, which the inventor tells me helps keep the links properly aligned so they can open smoothly as they go around the bend, and be latched, so that they emerge at the lower right firmly separated.
This lower wheel is also the place where the inventor intends to extract the power that this machine will generate, and the inventor expects that he'll have to put some sort of a brake on it so that the chain's speed can be kept within safe limits.
The actual photo below shows part of the inventor's first prototype chain. We have flipped the photo left/right so that it matches the diagram above. The really ingenious mechanical features here are the links with hooks, which can keep the stretched chain in its stretched position until they fall out of position. But they do not interfere with the chain when it is in closed position.
The chain column on the right clearly weighs less than
the one on the left.
The clever linking arrangement keeps it that way, maintaining the
overbalanced condition. To understand this, consider the falling
chain column on the left, where the chain is compressed.
As it goes around the lower pulley, the
outer (larger radius) parts of the chain spread apart, allowing the
hook links to fall into place by the action of gravity.
The links remain
in place in the ascending portion of the chain on the right.
This maintains this portion of the chain in its expanded,
"low density" state. As sections of the chain
reach the upper pulley, and begin to go around it,
the links simply fall out of position,
permitting the chain to shorten to its compressed position as it
descends on the left.
You may at first wonder why the links on the left don't stretch out due to their own weight. But observe that they can't because they are stacked up against the links at the bottom that are restrained from "getting ahead" of the links of the expanded chain column at the right.
The latching hooks operate by gravity alone, without altering the energy of the chain by any significant amount.
This one should get your head spinning, but we hope not perpetually.
This hydrostatic
wheel was contributed to an English scientific journal in 1831. The inventor
supposed that the floating ball at B would displace liquid, and since "liquids
seek their own level, the levels at A and B are the same. But then there's
more water below that level on the left side, making it heavier, so the wheel
will turn.
The errors here are ones that any physics student should see. A floating object displaces its own weight of liquid, and so the weight of material in the tube is the same on the right as it is on the left. Also, water pressure exerts forces perpendicular to the container walls, in this case they are all radial, and can't produce a torque.
Our inventor with the restless mind says "Aha! Submerged bodies displace their own volume of water. If we can just keep that buoyant ball completely under water on the right side, then the left side will be heavier.
We show such
a system, with a buoyant can B completely underwater on the right side of
the wheel. We could even have vacuum in the can. Clearly there's more weight
on the left of the axle. The water levels are identical. Unfortunately only
water contacts the wheel walls, and that exerts force only perpendicular
to the walls, which is radial. Therefore it can't supply torque to the wheel.
But doesn't the water exert an upward buoyant force on the can B? Yes. And by Newton's third law the can exerts an equal downward force on the water. By Archimedes' principle, that buoyant force is equal to the weight of a volume of water equal to the volume of the can. So as far as the water is concerned, the pressures are the same everywhere as if the can weren't there, replaced by an equal volume of water.
You may have wondered what holds the can in position. If only the buoyant force acts on it, it will rise to the water surface. Something must supply a downward force on the can to keep it in position. That's a little tricky to engineer, to ensure the proper downward force on the can without affecting anything else in the system. But, in view of our analysis above, thinking about such engineering details is wasted effort. Even if we could invent such a can-securing device it wouldn't help our cause.
That was apparently
the goal of the person who sent me this drawing. He devised a way to support
the can that (he claims) does not exert retarding force on the system (that
he says is "unbalanced" and will therefore turn by itself). This is an
extremely diabolical and ingenious puzzle on several levels.
How it's supposed to work
Figure 2 (supplied by my correspondent) shows a flexible tube (52) running over two pulleys (50, 58). The tube contains water (64). Inside is an assembly that includes an air- or vacuum-filled can (56) and a stabilizing U-shaped wire (60). This wire and the four rollers (54, 62, and two others) prevent the can from rising due to its buoyancy, keeping it anchored in place. The roller (54) at the top of the can provides even better stability of the can, preventing it from dragging on the tube walls. Since water seeks its own level, the water surfaces in both arms of the tube will be at the same height.
Now it should be perfectly clear to anyone whose mind is not clouded by quantum mechanics that the system is heavier on the left side, so the machine should turn counter-clockwise. The inventor supplies this comparison picture to make that point perfectly clear.
Of course,
we showed above with the example of the water-filled wheel why the basic
premise is fatally flawed. But if one is simply presented with a full-blown
machine of this complexity one might not see that right away, buried as it
is in complicating details.
The same correspondent sends me a refreshing return to a purely mechanical device, with no water in it. Fig. 2 shows an assembly of two pulleys G1 and G2 and two gears, in a rigid frame. The two gears do not touch other, but the left one meshes with a vertical rack, as the right one meshes with the right rack. (A rack is a geared strip, with the gear teeth along a straight line.)
The right rack is movable, and an upward force acts to move it upward. Fig. 1 shows how this system acts like a lever, the weight W having a lever arm of 1 unit, the rack and applied force have a lever arm of 4 units. Therefore, assuming the lever weight is negligible, a force analysis shows us that an upward force of W/4 can lift a weight W. In Fig. 2 the same situation obtains, a force of 2.5 kg lifting a weight of 10 kg.
[We are expressing forces in the convenience unit "kilogram-weight" to avoid the necessity of including 9.8 m/s2 in each equation.]
Yet, by analyzing the geometry, when the rack is moved upward a distance d, the weight is lifted a distance d/2. So the work done on the weight is W(d/2) and the work done by the applied force on the rack is (W/4)d, only half as much as is done lifting the weight. So even if the weight of the pulleys, gears rack and frame isn't negligible, there's plenty of work left over for other purposes.
Readers are invited to submit answers.
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So, he says that he will use that fact by putting the platform on the edge of a round drum, counter-weighted with a load on the left side. Now, he says that the torque due to the weight on the platform will be communicated to the drum. The motor drives the drum to rotate clockwise, keeping the platform at a constant level. Now move the weight from A to B. This, he says, will give greater torque, communicated to the drum, to increase the effectiveness of the motor.
I have received many cockeyed perpetual motion machine proposals over the last few years, but this one deserves some sort of prize for its combination of so many dubious features implemented with so few moving parts. Most experienced physicists and engineers, and even students of these disciplines, would take one look at it and say "It'll never work!" "It's all screwed up!" But when pressed to identify one flaw that prevents it from working, one hardly knows where to begin:
Re: Answers left as exercise for the student. Send your answers to the address
shown at the right. The
earliest good answer(s) that arrive may be posted here, with credit to author.
I will post (at my discretion) answers that are simple to explain, clear,
correct, perceptive, and that stimulate thinking and further discussion.
Posted answers, whether written by me or by others, do not always represent
the final word on a given proposal. On several occasions perceptive readers
have noticed things we missed, or suggested simpler ways to explain something.
So don't hesitate to skeptically rethink given "answers".
While I welcome submission of new or innovative perpetual motion puzzles, I assume no obligation to respond in detail to all of them. In particular, I cannot be expected to analyze vague proposals, overly and unnecessarily complicated designs, nor ideas that are simply variations of classics found in the literature. I've already received proposals that fail for the same reasons already discussed elsewhere on my pages, indicating that the person proposing the idea hadn't fully understood these documents. Also, I choose not to include devices that would require advanced mathematics or physics for detailed analysis. I avoid posting puzzles unless I am reasonably confident what the flaw is, and that the flaw can be explained using elementary physics principles.
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