Poss. Symmetry Break?

[MrVibrating]

What i find interesting here is that the gain appears fully autonomous. The spring applies 0.1 Newton for 0.1 seconds, just enough force to knock the weights out of their precarious balance point, and from thereon the only source of torque is MoI variation from the sliding weights, and the only linear force being applied to the sliding weights is CF / CP.

The two appear to settle into a closed-feedback loop. An MoI / CoM / CF / CP circle jerk. Gravity is disabled.

To move forward, i think it would be worth swapping out the pulleys for scissorjacks.

So i'll need some mechanism to couple opening and closing jacks, so that they work in harmony.

But in MT 39, Bessler uses pulleys for this synchronisation, whereas i want to eliminate them as a potential source of sim error.

So i'll need to come up with some kind of pin joint coupling, to get the two jacks extending and retracting in unison, without invoking the vagaries (and potential simulation pitfalls) of flexible or semi-rigid transmissions.

One suspicion i have regarding pulleys is that the sim might introduce uneven tensions on either side of a rotation, thus generating stray torque.

Of course, the possibility remains, for now, that such an unforseen consequence may be a legit gain mechanism, however it's just as likely a potential error source, so the priority is to come up with other means of applying the theory, to see if the results persist..

[MrVibrating]

Thinking about it, the solution to paired opposing jacks is an intermediary scissor link made from a pair of inverted 'V' shapes - when one end's closed, the other opens.

Bessler includes such a linkage acting between the stampers and axle in his Archimedes screw diagram.

[MrVibrating]

OK so paired opposing jacks are doable, however i also need them to be able to counter-rotate about their central axis..



Doing so without pulleys could be tricky, and complex gearing or stators will defeat the point.. need some more thought on this..

[MrVibrating]

I'm not sure you've quite grasped the concept

Assume I don't, I just cherry picked the visual: You've typed a lot of info to take in.

So here's an idea for which I'm not sure it coincides with yours (so ignore if it deviates too much), at least it fits your name :-)

When a working wheel is in continuous rotation the centrifugal/centripetal force is set and adds an acceleration gradient on top of gravity. I guess whatever mechanism passes through such summed gradient will find balance, despite being more complex than gravity alone the effect is not much different. If this is really true (as I didn't exhaustively test the math involved), the rim of a rotating disc can be replaced by solid ground: making things a bit easier.

As those weights wobble around the wheel there's a frequent vibration in MOI which reflect in frequency of the centrifugal/centripetal force. As you deduced, it can be mapped onto the wheel rotation: so we can temporarily set rotation aside.
The oscillation in wheel rotation (caused by other mechanisms) could be replaced by a spring-cushioned bar.
Is it possible for a single mechanism in focus to ride this oscillation, and make that bar resonate with a bigger amplitude compared to a passive mechanism? (and does it indeed translate to a rotation as implied?)

I've played with this concept, in various ways, previously.

The changing vector sum of CF + gravity, as experienced by a mass orbiting a vertical center of rotation, was the concept that prompted me to start this mission in earnest, IIRC 3 or 4 years ago now. The basic idea is that gravity is always pointing downwards, while CF is always vectored outwards, and so in a full vertical rotation, CF and G align additively and subtractively each in turn. When the mass is at TDC, CF and G are opposing, and at BDC they're cooperating.

Suffice to say i haven't yet found a way to harness that potential gradient. Symmetry is still enforced, because if you drop a weight when it's heavier at BDC, you then have to rotate it back round to TDC at this new, wider radius, and so re-inputting the GPE you've just harnessed.

Likewise, when raising the weight at TDC, where CF and G can, in principe, fully cancel, this cancellation robs us of the very gradient we would want to harness, defeating the object - the weight just falls back down under less gravitation than it would've if CF wasn't interfering.

So unfortunately, this same symmetry applies to a gentle wobble as much as it does to a larger radial translation... we could connect our armatures to a hub that rotates slightly off-center, introducing such a vibration due to the constantly-alternating G vector relative to the CF / CP vectors (again, CF is always vectored outwards, while once per rotation G is vectored alternately outwards then inwards), but anything we drop radially must then be re-lifted in the axial plane, by the vertical rotation, and similarly, anything we raise radially has to be dropped axially.

The amount of weight and the RPM can be tuned to 'smooth' over any resulting wobble of an orbiting mass, resulting in a stable diagonally-oriented elliptical trajectory, which looks kind of cool, but doesn't seem particularly useful.

But that's not an exhaustive treatment of course. And Bessler's one-direction wheel was described as lurching against one of its support posts. Also, the Weisenstein diagrams (with the three pendulums) are suggestive (to me at least) that an unbalanced reactionary force may be involved.

But the most salient point you raise, i think, is that an eccentric rotation, as from a slightly off-center axis, does indeed offer another means of varying the effective MoI, as the net radius varies across a full cycle. Again, this implies that epicycles are an interesting phenomenon to keep in mind..

This dynamic also seems to apply to that last sim showing anomolous gains, and while i fully expact that to be due to error, i'll certainly be investigating this angle in trying to eliminate it..

[MrVibrating]

Right, the gain in the last sim was definitely an error, however i simplified the test of the hypothesis and i'm getting what looks like a reliable positive result.

The concept is simple - when we pull an orbiting mass inwards, its orbital velocity accelerates.

If however the rotating system also contains other mass, which just keeps spinning at its fixed radius, then the acceleration torque caused by retracting the orbiting mass is divided into that additional, constant MoI.

Hence, the amount of acceleration, and thus the final energy, of the complete rotating system, is a function of how much additional, non-radially moving mass has to be accelerated.

The example i've been working with is a simple rigid pole. One end is pivoted to earth, and a linear spring extends from that pivoted end, across to the opposite, floating end, connecting to a small mass that slides up and down the pole.

Gravity is disabled, and the pole is set to rotate at a fixed RPM.

The spring is then preloaded with just enough PE to pull the orbiting weight inwards, along the pole, into the center of rotation, against centrifugal force.

Simple, right?

Except, keeping all else equal, the RKE gain from the MoI retraction is a function of the pole mass!

Increase the pole mass, keeping everything else the same, and the final energy increases..

Will come back to this tomorrow, but if it checks out, it should be possible to sink positive and negative torques from decreasing vs increasing MoI's, into different-sized masses, and thus net MoI's, for an asymmetric distribution of CW / CCW RKE..

[MrVibrating]

Quick example of a gain cycle exploiting the principle; retract an orbiting mass inwards along a heavy pole, then let it slide back out along a lighter pole - the weight itself costs the same energy to haul inwards, as it repays on its way back out. But on the way in, it adds more RKE to the net system than it takes back on the way out, so the cycle ends with everything in the same position as it began, but with a small yet significant remainder of RKE left in the net system..

There's still uncertainties to iron out - the amount of PE needed from the spring will increase as net RKE and thus velocity rises. However i don't forsee any problem with simply preloading the springs with more PE than they'll initially need at low RPM's - springs are, after all, conservative so it won't be going anywhere. Just means the max velocity will be a balance between peak CF and spring force.

More tomorrow..

[daxwc]

MrVibrating it is my opinion Bessler may have been using a spring to retract (reset) an empty scissor-jack. I have absolutely no evidence of this it is just a feeling from working with them. Often I will put an elastic around the first two center pins.

[MrVibrating]

Latest results:

A 1 kg mass slides along a rotating beam with a 2 meter radius. Gravity is disabled, the beam rotates at 10 RPM, and an actuator is used to pull the orbiting mass from the outer end, into the center.

The system's inital energy is taken as the sum of the beam and orbiting mass KE's.

The final energy is their revised sum, after the orbiting mass has been fully retracted into the center of rotation.

The experiment is ran twice, keeping all details identical except for the mass of the beam; for the first run, the beam mass is 10 kg, and for the second, it is reduced to 1 kg. Again, the dimensions, RPM and orbital mass remain unchanged between runs - only the beam mass is altered.

The following result is noted:

- retracting the mass upon a heavier beam causes a smaller change in net MoI than when replaced by a lighter beam

- it thus causes less angular acceleration, since there is more mass to be accelrated

- with less angular acceleration, comes less CF, and hence less work retracting the mass

- conversely, with a lighter beam, the net change in MoI is more significant, thus the angular acceleration is greater, and hence so is the CF, and so more work must be done retracting the weight inwards the closer - and thus faster - it gets towards the center.

So centrifugal force is decreasing as a function of radius, while at the same time increasing as a function of angular velocity, as the orbital radius narrows.

With the lighter beam, more work must be done to retract the same mass the same distance along the faster-accelerating beam against its higher resulting CF.

With the heavier beam, its higher angular inertia means it doesn't accelerate so quickly even though it is subjected to the same amount of torque from the inbound sliding mass. So with its lower rise in RPM, centrifugal force doesn't rise as far or as fast, and less work is required to pull the mass inwards.

Accordingly, the difference in net system energy after retraction is equal to the different work requirements - if the lighter system required a further 10 J of input work compared to the heavier one, then it ends up with that extra 10 J of RKE.

Likewise, if we only need to perform 10 J less work to retract the mass along a heavier beam, then its final RKE is 10 J less than the ligher one.


So the implication of all this is that we can pump a mass in and out against CF, and so applying a positive and negative torque in turn, while sinking these opposing torques into different-sized masses (more to the point, angular inertias).

If the CW MoI is different to the CCW MoI, then so is the CW vs CCW RKE (because RKE = 1/2 MoI * RPM squared).

Thus the net system has more energy (angular KE) in one direction, than the other.


If this RKE is directly traded for GPE, then it follows that we can have more positive than negative GPE - in other words, use the positive torque from retracting the sliding mass to accelerate the whole system, and then use the negative torque from extending the sliding weight to lift itself.

The positive torque is thus divided into the net system's MoI, while the negative torque is only divided into the sliding mass's own MoI.

The net system is thus accelerated a little by the inbound stroke, but not decelerated at all by the outbound stroke - when sliding back out, the weight simply decelerates its own orbital RPM, while the net system continues on, unaffected.

To close the loop and end with a net gain, requires gravity to restore the RPM of the extended weight, to bring it back up to equal speed with the net system.


That's the current overview. Will need to carefully tally the details to see if it runs up against a brick-wall symmetry, or actually breaks through..

[MrVibrating]

MrVibrating it is my opinion Bessler may have been using a spring to retract (reset) an empty scissor-jack. I have absolutely no evidence of this it is just a feeling from working with them. Often I will put an elastic around the first two center pins.

in this case it'll all come down to whether or not the proposed energy asymmetry allows us to reset the spring or relift the weight or whatever...

As ever in these early stages, your mind's explicitly geared towards looking for advantages, and so the corresponding disadvantages are initially overlooked.

So i'm most likely trying to rob Peter to pay Paul.. even if i haven't grasped why yet..

I fully expect tho that if i 'storyboard' out the concept into discrete steps, i'll end up with something 'out' that needs to be 'in', or down that needs to be up etc.. and if all the ups, downs, ins and outs tally, the net energy will be zilch.

But merrily we blunder on...

[MrVibrating]

Just wasted another hour staring at MT 41.

I'm sure it's encoding the same message as the toys page - we have scissorjacks representing inertia, two pairs of weights alternating betwen inner and outer positions, no mechanism to lift the weights against gravity or any indication of how they're activated.

Plus there's those little slits in the axle, which suggest (to my eyes) that the radial spokes the weights are attached to can rotate independently of the axle. The same slits also appear where the housing meets the axle, suggesting that rather than a cross-sectional slice through the middle of a continuous wheel, what we're seeing is two U-shaped frames, inverted, which can also rotate independently of the axle.

The scissorjacks seem to correspond to the inertial torques that would be produced by the weights moving up or down - the lower pair of jacks are open, and the two weights are in at the center, where MoI is minimal and thus RKE increases. Conversely, the upper two jacks are closed, in opposition, as if to signify that the two negative inertial torques from the outer two weights are being made to mutually cancel.

If the negative torques from the two outboud masses are self-cancelling, while the positive torques from the two inbound ones are not, then the net system gains energy every cycle; it still costs energy to move the weights in and out, but the net system is gaining energy every time the two negative torques cancel, and it's over-unity after the first full rotation.

I'm sure i'm almost there.. just one last leap of imagination / revelation / inebriation could be all it takes..

[daxwc]

One bottle of wine and staring into a black and white TV with just the static on.

[MrVibrating]

Honestly, no matter what i try and watch it might as well be static for all i can take in, just constantly mulling over this problem. Knowing that there is a solution, there's so few variables and permutations that it's hardly a needle in a haystack. More like a vortex, drawing you in, towards an inevitable conclusion.

It's something simple and obvious.

EG. pulling a mass inwards causes positive torque, feeding it back out causes negative torque, so you want something that cancels that negative torque.

So it's got to be an equal opposite torque, which can either come from an equal opposite displacement, or else gravity. There isn't anything else, as far as i can see... those are the options.

It's a simple process of elimination. All the evidence is before us. A consistent explanation can be deduced.

For instance, regarding MT 41 - if, as i suspect, the 'special' thing behind the jacks is inertia, and the opposing inertial torques from the inbound vs outbound weights is the 'lesson', then i've already established that synchronised inner/outer translations cause the minimum MoI position to lie in the radial center - where the inbound and outbound masses cross paths at equal radius. Either side of that radial center, MoI increases again. This basically halves the potential MoI delta, which is the last thing you'd wanna do if that was the prime motive force..

To put it another way, if you wanna spin up by pulling an outer mass inwards, then you wanna get the maximum amount of spin from the minimum amount of pull. Chopping out half your available effect from the outset would be a no-no.

In other words, if inertial torques are the key, then you'd definitely want to be able to seperate them from one another. If both are manifest in the same body at the same time, you wipe out half the magnitude of force change you could've had if they swung in and out indepently, without interfering with eachother.

So this simple mechanical practicality is entirely consistent with MT 41, and the interpretation of those axle slits as independent articulations.

[MrVibrating]

"..weights gravitate to center and climb back up"..

So when gravitating to the center, MoI is decreasing, causing a corresponding acceleration.

When climbing back up, MoI is increasing, causing a corresponding deceleration.

So as well as causing the MoI reduction, gravity must also restore angular acceleration to a weight trading angular momentum for height / GPE.


Again, this would seem consistent with a scheme of inputting GPE when MoI is high, and outputting it when it's low.

[AB Hammer]

MrVibrating

I have used scissors in that similar configuration but I changed my direction to another approach and will post it when it is finished. But for now I am in my armor season and can't take time for wheel work until the end of Aug.

What I found it is like balls falling and the scissors seemed to be a fancy attachment. Look for newer leverage points.

I applaud your effort. Green

[MrVibrating]

Closing in on a gain cycle, i think..


Assuming clockwise rotation, use a scissorjack to quickly retract a mass inwards at the 12 o'clock position.

A scissorjack is ideal for two reasons:

1) we want a smooth clean retraction of MoI for a swift boost in energy with a minimum of the gain wasted to friction

2) instead of simply waiting for the mass to fall down, we can retract it suddenly for a small input of energy, gaining the maximum available GPE

So, in the first phase, we have a gravity-assisted MoI retraction, gaining RKE equal to the GPE used. However, that GPE was converted to torque via the MoI retraction, not by merely over-balancing.

If, in the first phase, we needed gravity to help retract a mass radially, for the second phase the requirement is different - the mass will automatically follow a radial path back out, due to CF. However this will also cause an angular deceleration, and so this is where gravity could again be useful;
- when the jack re-extends the mass, the jack's fixture to the hub is free to rotate independently, and so the negative torque from the outbound mass only decelerates the scissorjack's descent on the descending side of the rotation, while allowing the rest of the hub to rotate onwards unaffected. Gravity then re-accelerates the momentarily-stalled scissorjack and its now fully-extended mass, and thus we've reset to a high-MoI state without incurring the corresponding deceleration.


If that pans out, it's a closed-loop gain...