Toad Elevating Moment

[MrVibrating]

last thought tonight - i haven't exactly done the vector math but after a little more thought i've an inkling of a possible torque from asymmetrically extending and retracting masses spinning in the radial plane, while rotating in the axial plane with the wheel....

..or, possibly tracing MT119's snake as a trajectory, take a winding path up and a straight line back down, ie. restricting the perpendicular-CF interaction to alternate radial strokes, in vs out, say...

[MrVibrating]

...ookay, had another little look at this idea tonight, and it still looks potentially interesting.


Notice how in this demonstration:
http://www.youtube.com/watch?v=cquvA_IpEsA
..the gyroscope maintains an orthogonal, axial rotation.. the circular path it traces out could be the rim of a wheel...

So, gyroscopes can apply a kind of reactive torque against a rotor. This is potentially useful (Wolff's description of the wheel's constant speed whether raising or lowering a load is consistent with an inertial reaction providing its torque).


Now however, consider also that this constant precession incurrs an addisional CF component in the radial plane, about which it's rotating; hence, the gyroscope can be accelerated by the CF its rotation in a perpendicular plane creates.

For instance, suppose the gyroscope rides up and down its shaft on a screw thread - as it spins about its axis it causes precession, rotating the wheel. This generates CF, and this radial force pulls the gyroscope outwards towards the rim, accelerating its spin as it winds its way up the thread. Much like the rifling of a barrel spinning a bullet...

And that looks tentatively like the makings of a positive feedback loop, to me.

The gyro accelerates the wheel, creating CF, which accelerates the gyro, accelerating the wheel, raising the CF and accelerating the gyro. This then accelerates the wheel, boosting CF and accelerating the gyro. As you can see, this paragraph goes on forever...

I'll cut it short only to note that at some point we'd obviously have to retract the gyro, so that it can be fed outwards again, however even this action causes an acceleration of the wheel, by drawing the center of mass inwards. This RPM rise increases the CF, which accelerates the gyro, accelerating the wheel....

Rinse, repeat and goto 10.







I'm unsure how to sim this in 2D - clearly the parts would need drawing and animating in exploded form, perhaps using variables to plug the output force from one mechanism into the input force for a dependent mechanism, albeit not physically connected in the sim...? Is this possible?

It'd be a lot of hassle to build a real rig for a negative result...

[MrVibrating]

Right, had another quick read and the angular precession i'm thinking of using as torque depends upon gravity; its downwards force is effectively translated into an angular force about the axis:

http://www.gyroscopes.org/behaviour.asp

Which is great for a horizontal wheel, except ours is supposed to be vertical....

This is where i can get in a right muddle trying to do mental rotations, but at first sight it would seem:

- the radial center of rotation i was considering for the gyros (rotating about the spokes) isn't going to convert the gravitational force into torque via precession

- if there's anything to this line of enquiry, it requires a slightly different orientation



Continuing on regardless then, has anyone else noticed that you can see the ink of MT142 through the paper of MT136, and vice versa? This weems to suggest 142 is indeed part of MT... and also, taking as read the suggestion that MT portrays the progression of ideas leading to the breakthrough, that the last thing B. was playing with was precisely this.. converting precession forces into torque.


As noted earlier, this scheme has a number of attractive qualities not found in other systems:

- we can only vary the effective value of mass/gravity via balancing, and varying the translation angles relative the the gravitational vector. These attempts all come up against basic symmetries, thus far.

- whereas interacting inertial moments have the properties of poles and dipoles, like magnets, and can also likewise push and pull each other up and down their curves - varying angular momentum in precisely the same manner as field density in magnets.

- hence what i'm suggesting is to contemplate angular momentum L as being somewhat analogous to magnetic field density B

This really opens up the field of possibly-useful mechanisms - ie. ones in which the net energy of the system is a potentially non-linear function of the interaction pattern, rather than a linear function of the initial PE.

Earlier in this thread i considered the problem of whether it's possible for a mass to leave a rotating system without taking away its share of the system's energy with it, concluding that it was, in principle... and i think this may be a related mechanic.

So if the hypothesis is valid then there's some way of arranging two or more moments that can be made to selectively boost each other's magnitude, at little or no cost to themselves. In other words, there's some kind of orthogonal torque moment that's incidental to the system's initial input energy.

I previously built MT142 as a Mecanno model, but i only checked that the parallelogram was, indeed, at equilibrium. It seemed axiomatic that the paired pendulums themselves were likewise at equilibrium, so i omitted a full implementation of them... i made one pair, just to play with, but they're basically energy-neutral, balancing eachother out. Hence i was unable to inspect any angular momentum interactions between their orthogonal planes of motion - which, given the above points, is surely their intended purpose.

A model would be possible in WM2D however. Obviously MT142 almost certainly won't self-sustain, however if it WAS the penultimate failed attempt, then perhaps it does encompass some interesting behaviour or principle, key to the finale, "MT143"...

[MrVibrating]

I'm about to say a crazy thing, so bare with me...



It's obvious what this most recent escapade has been leading up to... Can we substitute CF in a vertical wheel for G in a horizontal wheel, thus translating CF into torque via precession, rather than gravity, as in the previously linked examples?

Like i said i'm not great at these kinds of mental rotations, but a straightforward substitution of vectors leaves us with gyros oriented in the axial plane, rather than radial as previously supposed.

It really is that simple, i think... if the gyro's spinning in the same plane as the axle, then the outward centrifugal force is translated into an orthogonal torque moment, causing the wheel to rotate.

This is a cinch to model in 2D, so i'll have a go later, see what comes up... That, and i wanna try a full 2D implementation of MT142, as i've said, i've checked it for static equilibrium, but my suspicions ATM center on a dynamic equilibrium between interacting CF moments, so i want to see how the trapezoid behaves when the over-and-under pendulums are animated...

[MrVibrating]

I already know how to do this electromagnetically, courtesy of Steorn (their famous "fast-in, slow-out" Sv interaction destroys classical energy by moving it into the vacuum). And it was that realisation that inspired me to redouble the search for a mechanical corollary.

And for now, i remain optimistic we'll find one....

Thanks for the thought provoking discussion MV.

I have proposed the exact same mechanism in mechanics and it is the same as Bessler documented.

JB's statement "These weights are themselves the PM device, the essential constituent parts which must of necessity continue to exercise their motive force (derived from the PM principle) indefinitely -- so long as they keep away from the center of gravity" MT p. 20 is the exact embodiment of your idea as well.

JB states it again in GB 56 as The causative principle of the movement, its ponderous impetus.

Ponderous meaning:

1. of great weight; heavy; huge
2. (esp of movement) lacking ease or lightness; awkward, lumbering, or graceless
3. dull or laborious a ponderous oration (from the freedictionary.com)

The idea being that a smaller fast moving mass attached to a ponderous pendulum mass can cause the much heavier lumbering mass to continually perform work in the process of seeking equilibrium and never find it.

The “fast in, slow out� concept is exactly what JB is referring to here and by leading the ponderous mass of a central heavy pendulum with lighter, faster masses we cause a continuous differential of PE to be created in the lateral direction rather than the vertical. This differential is created in the Rotational PE (torque) of the primary pendulum.

We know that any displacement of mass in the vertical direction is useless to our cause as this is conservative. But a lateral displacement can be created essentially work-free.

We can witness this process occurring on any weekday one should choose by visiting a local primary school during class recess as we observe playground swings in constant use. The same work-free lateral disturbance causes the child to swing higher and higher with no work input.

The same cannot be said for CF driven examples as there are none. There are no examples in nature of CF creating or increasing the energy of any natural process. CF is always a dissipative exercise, never a creative one. And is totally confirmed as a conservative force by the 1st law of thermodynamics.

I have documented the exact process you propose in the thread “Rotary Analogue to Milkovic Secondary Oscillator� http://www.besslerwheel.com/forum/viewtopic.php?t=4894

The physical process of MECHANICAL RESONANCE can then easily lift 4 lbs with 1. By initiating a continuous work free disturbance of the lateral CoG we create resonance in the primary pendulum that repeatedly lifts the heavy pendulum mass. Resonance is a natural process employed in thousands of mechanisms, both natural and manmade. In the demo heavier exciter weights have been used to speed up the process but by using lighter weights, the 4/1 ratio can be achieved.

In AP p342 JB says "one pound can cause the raising of more than one pound". Mechanical resonance is the only known physical process by which a heavier weight can be raised by a lighter one. In our swing set example the child's entire body is being raised by simply shifting the lateral CoG of the lower legs fore and aft.

Why not attempt to improve on a process that is already known for doing the job rather than trying to invent new techniques that no one has ever observed in physics?

The improvement in this resonant process is that it has been made work-free due to vertical counterbalancing. Each exciter weight follows a closed loop path which we know is conservative but by combining the vertical CoG of all four exciters, we maintain a strictly linear, lateral translation of the horizontal CoG requiring no vertical PE to be consumed.

No the process has not been close-looped as I am just now constructing the POP. If the loop can be closed electronically then the mechanical loop will be attempted.

Other characteristics are that the closed loop process can operate in either direction, can be precocked for a gravity assisted start, creates prodigious torque from startup, requires no unreliable latching mechanisms and can easily be converted to rotary output.

Hiya CC, i remember you from the Steorn forum, long time no see.. and glad you're on the case here... :)

You're right, MT20 does seem similar in terms of the relative inner and outer displacements, although MT119 has the paired displacements on opposite sides of the axle, whereas MT20 has two pairs on opposite sides in conjugate phase..

TBH, i've little idea how to intepret MT119, besides what i saw as a striking resemblance to the relative displacements of an asymmetrically-fixed scissorjack.

Another, alternative, interpretation is that the tighter and looser sections correspond to expanded vs retracted jacks, or at least their relative weight positions, if using pulleys or whatever instead.

As for a smaller mass manipulating the motion of a larger one in any useful way, i'm unsure - but i'm more than ready to be surprised... i tend to frame this kind of problem in terms of their relative inertial responses, in a zero-G environment - as when considering "inertial thrusters" and the whole N3 issue... in which you always come up against mass constancy. But adding in CF and G complicates that picture i guess, perhaps there's more to it, as you suspect..

Right now i'm in gyro mania, unfortunately, so i read gyro clues into everything.

Ponderous - like a gyro? Needs to stay out of the center of rotation - because there's no CF there..? See, i can't help it...

You're right of course about orthogonal translations being free with respect to the vector gradient, but again, when we get to the whole kiiking thing i tend to get more sceptical - i followed JC's thoughts on the matter and couldn't see a gain there either.

The only "in-principle" gain mechanism i can see in swingy stuff is the theoretical possibility of taking an asymmetric swing - such as a pendulum wrapping around an obstruction between the fulcrum and weight - so that it gets longer and slower in one direction, then shorter and faster on the return swing.

That in itself's useless of course, but if however we could separate out the force and distance components, swap them over and recombine them as odd pairs, we'd end up with a high-force high-displacement 'super' swing, and a low-force low-displacement 'afterbirth' swing. Then you'd just keep the former, and discard the latter. Easy OU.

But a practical implementation seems improbable... if not impossible... dunno...

Ditto re. CF being conservative - the first law says all classical field interactions are conservative, and remember that just because the work done in boosting the swing may not come at the expense of a vertical displacement, it still needs some kind of input energy - yes, off-axis translations have lower energies that those parallel to the vector, but you're still doing work pushing sideways upon a swing... and likewise WRT resonant systems generally.

You seem to be addressing this though with your counter-balanced lateral exciters..? I can only build a foggy mental picture out of that but it sounds interesting... :) I guess i'll have to read your thread, when i get time...

As i was saying after you though, what appeals to me about CF is the specific case of interacting CF components, and the possibility - or not - of a positive feedback loop between them, not altogether unlike magnets pulling each other up their B/H curves in attraction. IOW, it's not CF per se that i'm considering, but rather how multiple CF moments add or subtract from each other in various planes.. It's no doubt futile as you suggest, but i just need to check for myself to see the clear picture...

[MrVibrating]

MrVibrating:

But MT119 is so abstract as to seem surrealist - what is this metaphor of a snake yakking up into its own arse supposed to mean? Clearly there could be no sane expectation that the fluid motion would self-perpetuate.

Well, actually then it was more of a problem in Bessler’s time and still confuses people today. That is the weight of the bigger volume of fluid (the big bottom) would influence hydrostatic pressure and cause a siphon to work continuously. This is directly related to the hydrostatic paradox which Pascal had worked on 50 years before, that volume and hydrostatic pressure do not affect each other but rather only influenced by height.

Hydrostatic Paradox :-
The seeming contradiction that the weight of the fluid poured into a vessel can be different from the force of the pressure exerted by it on the bottom of the vessel. Thus, in a vessel that is wider at the top, the force of the pressure on the bottom is less than the weight of the fluid, whereas in one that is wider at the bottom, it is greater. In a cylindrical vessel both forces are the same. If the same fluid is poured up to the same height in vessels of different shapes but the same bottom areas, then despite the differences in the weight of fluid poured into the vessels, the force of the pressure on the bottoms is identical for all the vessels and is equal to the weight of the fluid in the cylindrical vessel. This follows from the fact that the pressure of a quiescent fluid depends only on the depth under a free surface and the density of the fluid.
The hydrostatic paradox is explained by the fact that, since the hydrostatic pressure is always normal to a vessel’s walls, the force of the pressure on the inclined walls has a vertical component that compensates for the excess weight of the volume of fluid in a vessel that is wider at the top than a cylindrical vessel with the same bottom area and compensates for the lack of weight of the volume of fluid in a vessel that is narrower at the top. The paradox was discovered by the French physicist B. Pascal.

http://en.wikipedia.org/wiki/Pascal%27s_law

Thanks, i hadn't heard of the hydrostatic paradox, and having now read up on it, can say that i didn't personally fall for the fallacy - i've previously considered hydrostatics in terms of buoyancy, and that must've got me off on the right foot, somehow..! But you're right, that does seem to be the main thrust of these images.

I don't think that entirely dispels my previous suspicions though - the apparent correlation between the serpent's upper and lower body and scissorjack-type asymmetric displacements still seems valid, and ditto WRT to the axle at G. Hence the cone shape may still be a metaphor for the CF gradient, if disguised as an unrelated issue in hydrostatics...

Obviously MT117 and 118 also better fit your interpretation than mine, still, the relationship between the cone shape and the CF gradient shape isn't something i'll dismiss entirely, just yet (i've so little else to work with ATM!)..

[MrVibrating]

- and if you rotate the darned snake, you'll have a spiral tube water pump (http://lurkertech.com/water/pump/morgan/blair/002.htm)

ruggero ;-)

Yup, a lá MT120...!

You've gotta admit, going by the numbering of MT, CF is one of the last things he was playing with before the Eureka moment...

[ruggerodk]

Rights MrV...and that made me wondering:
Not one single time does JB mention CF!
Not in AP, not in MT, not in TP.

Why is that?

What did they call CF in those days?

Ruggero ;-)[/quote]

[eccentrically1]

huygens coined the term in 1659

http://en.wikipedia.org/wiki/History_of ... _and_Hooke

[MrVibrating]

just to recap, the precessional torque i'm on about in that video occurs at 1:45

http://www.youtube.com/watch?v=cquvA_IpEsA

..and this link explains why this torque occurs:

http://www.gyroscopes.org/behaviour.asp

and what i'm suggesting is to replace the G vector that's causing this precessional torque, with CF instead, for the same net result of torque about the wheel's main axle.

The allure of this config is that each type of effect causes the other;

- the wheel's radial CF about the main axle can be used to accelerate the flyweight

- the resulting angular momentum of the flyweight generates precessional torque about the main axle

...which looks like a positive feedback loop.

If we directly swap out G for CF in the above demo and explanation, then the appropriate orientation for the flyweights lies in the axial plane - the same plane as the axle. In this position, the outward radial force should be translated into an angular force (torque), via precession, exactly as shown in the video.


It only occurred to me today that the flyweights in MT142 are indeed in this axial orientation...!

Taking into consideration the fact that MT142 and MT136 are on opposite sides of the same page of paper (you can see the other's ink through the paper), it seems reasonable to suppose they represent a sequence of progression, and further, that the key progression of 142 over 136 is the orientation of the flyweights from radial (136) to axial (142) - thus resulting in the manifestation of precessional torque upon the parallelogram.

So the hypothesis is that while it's certainly a system of 'weights in static equilibrium', it may not be in perfect dynamic equilibrium when the flyweights and parallelogram are animated together.

I've doubts whether the particular 'over and under' weights shown in 142 are useful, as any precessional torques generated might be equal and opposite. Rather, i'm considering cross-shaped flyweights spinning in one direction, to try and generate a consistent precessional torque CW or CCW.

Still haven't got round to simming it yet, but sooon...

[MrVibrating]

huygens coined the term in 1659

http://en.wikipedia.org/wiki/History_of ... _and_Hooke

If he was familiar with the term, as seems plausible if not likely given his friendship with Leibniz, then it's all the more conspicuous by its absence in his writings.

Perhaps it still wasn't in common parlance at the time...

OTOH, as noted, he didn't even start to play with CF until towards the end of MT. If the tome does indeed represent the development sequence, as we're led to believe, then the concept was late in his considerations, and apparently, payed fairly prompt dividends..

Speaking of MT again, the puzzlingly swastika-like MT130 and MT131 bear more than a passing resemblance to the 'trajectory deflector' concept in this video:

https://www.youtube.com/watch?v=TUgwaKebHTs

The deflector here is a notional device to try and represent the forces causing the precession... so perhaps MT130 and 131 share the same inspiration - as previously supposed per MT119, perhaps here B. is trying to highlight the relative vector orientations..? It's tentative, if not tenuous, and no doubt trivial coincidence, but a possibility, nonetheless...



Incidentally, it's occurred to me that the lower snap toy on the toys page may represent spinning characters, rather than sprung ones, as might otherwise be supposed... and its proximity to the whistling top - itself a fairly resounding and unmistakable reference to CF - might reinforce this interpretation.

In other words, and to offer a tentative answer to ruggerodk's question, perhaps B. thought of CF in terms of "spin force", or somesuch..

Whatever term he preferred, we might wander further along these lines that CF, if it was indeed responsible for the breakthrough, might've been somewhat sacred to him...

If that sounds silly, consider that it seems he may have based his entire cosmogony upon CF - it may explain the motions of the Heavens and earth, and of all heavenly bodies...

Perhaps this, too, might explain why he might've been a tad dismissive of his contemporaries' explanations of the phenomenon - sure, Leibniz and Newton et al may have thought they had it wrapped - they too, as god fearing men, incorporated their science into their own religion-centered cosmogonies - but could they build a PMM? Yet this knowledge was bestowed upon B. above all others, and it was his divine duty to bring this great revelation to the great unwashed masses, in the appropriately austere manner. To emblazon it across the pages of a book for popular general consumption would be a vulgarity against the sacrosanct, bordering outright sacrilege.

And besides, he would've forfeited his reward.


So, and this is all presuming CF's important, of course, its absence of evidence in Bessler's works might be precisely because of its central importance. It's doubly secret - both for commercial, and ecclesiastical reasons.

But why, then, is the only stark reference to it - the spinning top - presented upside-down? Is this a mechanical reference, as to inverting the vector, perhaps... or else, following the "holy spin force" hypothesis, isn't an upturned top almost as risqué as an upturned crucifix? Was he skirting with some kind of blasphemy, or simply telling us that the gyro isn't balanced against gravity, but some other force...

You decide...

[JohnF]

Hope you don't mind my pointing out that in Mt 21, Bessler references centrifugal force.

"No. 21: This figure has hanging levers A which are internally applied to the cross-poles at B and thus side C becomes lighter; if, however, the lowermost lever is not periodically raised up out of its position and into C, as has already happened at C in the illustration, it remains in its old position."

- Johann Bessler

http://besslerwheel.com/wiki/index.php?title=MT_21-40

nope, don't think I'm missing much not being in here :-)

[MrVibrating]

Final point tonight: at the end of that last (excellent) video, he explains a critical point regarding the source of the torque:

- this precessional torque is dependent upon some degree of 'nutation' (new word for me, but i like it - like 'rotation', but uh.. newer?)

http://en.wikipedia.org/wiki/Nutation

So the gyro generates the precessional torque from the G vector, but the actual displacement - actually using the torque to rotate about another axis - comes at the expense of a proportionate degree of vertical displacement. That is, gravity has to succeed in pulling the gyro downwards, if slightly, in order for that off-axis motion to be converted into precessionary motion.

The cool thing though is that the equal and opposite counter-reactions mean it doesn't have to get progressively lower in order to keep precessing - it can simply wobble up and down, and this cyclical vertical motion gets consistently translated into precessional torque in one direction.


Taking this same principle into the CF plane we find that radial excursion is translated into axial rotation, in both radial directions; inwards and outwards. Pull the gyro in towards the axle to accelerate the wheel, and let it out again, also accelerating the wheel. In other words, the suggestion is that we can convert radial nutation into consistent precessional torque..

And rather than a slight wobble, we can have arbitrarily large radial excursions. Power would depend only upon diameter...

If radial excursions likewise drive the gyros (as by screw-threaded spokes, say) then radial nutation can both accelerate the gyros, and the wheel, at the same time and in the same action. Yanking the gyros in and out pumps the angular torque on each stroke... but nothing needs to get progressively lower in the gravity field, provided the nutation is converted back to spin on the gyros, as well as angular motion of the net system... Hence the source wouldn't be GPE but simply inertia..! Given their fundamental equivalence the distinction may be ultimately superfluous; either way it'd be a classical symmetry break. But this nutation could be just the thing we need to circumvent an ever-decreasing PE well... in a similar vein to Cloud Camper's thoughts on resonance, perhaps simply nutating up and down the CF gradient is sufficiently analogous to an MC Escher staircase as to obviate the second law...

[MrVibrating]

Hope you don't mind my pointing out that in Mt 21, Bessler references centrifugal force.

"No. 21: This figure has hanging levers A which are internally applied to the cross-poles at B and thus side C becomes lighter; if, however, the lowermost lever is not periodically raised up out of its position and into C, as has already happened at C in the illustration, it remains in its old position."

- Johann Bessler

http://besslerwheel.com/wiki/index.php?title=MT_21-40

nope, don't think I'm missing much not being in here :-)

Hmm, where's the CF reference there? It looks like the weights hang down against gravity - CF would hold them all flat against the rim..?

Evidently, one of us is missing something... ;P

At any rate, i'm not discounting the possibility of earlier references. It is puzzling though that he devotes so much of MT to attempted gravitational exploits, before roundly trashing the whole notion of over-balancing in AP.

I'll never say never, but i think i've nearly exhausted my own grasp of horizontal vs vertical translations to pretty much exclude that whole class of interactions, whether springs are added or whatever. The whole gravitational system is too closed and symmetry-bound.

What i'm sure all veteran mobilists here agree is that you're left with the irksome impression that there must be something else. There just has to be some other interplay of forces into the equation, before anything interesting's gonna fall out. Else, whence the non-linearity..?

[MrVibrating]

Might the mysterious hearts in MT130 represent a driving force of a 'beating' nature...


Like nutation, for instance?



The hearts would indicate the direction of the resultant force, rather than the direction of the nutation itself. The intended hint would be simply that 'something that beats rhythmically' also applies torque...