Toad Elevating Moment

[MrVibrating]

lol the Merseburg plates show three "perpendiculi" - geddit? Yeah they "regulate the motion" alright...


There's right-angled weights under the right-angled perpendiculi, and a circular one at the bottom. Circles'n'squares, again, per MT138-141.

All three perpendiculi are in direct-drive with the axle.

Like Johann said, the clues only make sense once you already know what he's talking about...

Those Merseburg perpendiculi, riding their axles off-center, were a big clue for me. I simmed them as shown, which was where i first picked up the idea of 'tracking' around the axle, rather than smooth rotation. I tried it on various potential interpretations of MT137 last week, for instance (see attached). Hence once i'd sussed the 137=APW link, sticking it on a rolling pivot wasn't quite the ingenious flash of inspiration it might otherwise seem - it was the first thing i tried, as a jack stuck to a fixed rotor can't move so well (as demonstrated earlier).

Sorry to gas on - just laying out how the design developed, for whatever pity or posterity...

[Fletcher]

Surely this can't be violating anything? It satisfies everyone from Lorentz to Noether and Joule, Newton and Einstein. It's hard to even say exactly where the symmetry break lies... (?)



The only question is, where does WM2D get it's energy from?

It gets it's energy for rotation from the PE it had when you began to run the sim - the PE is converted to KE after some losses to parts elasticity [being less than perfectly elastic at '1.0' which would be a perfect spring] - losses to elasticity are deformation resilience losses of contacts.

It continues to rotate because there are no system losses i.e. no loads of any sort which would diminish the KE quotient remaining e.g. frictions including air drag etc.

Suggestion:

Pin the flywheel so it can't rotate & run the sim - leave it for a while until all the parts settle at their combined position of least PE i.e. lowest system CoM - go to menu WORLD>START HERE - check that initial velocities of parts are zeroed out & run the sim again.

N.B. a true PMM should, after an impressed start from gravity OOB or a push in one direction, show ACCELERATION until lag [ability for parts to move internally into position quickly enough] causes the law of diminishing returns to take effect & it settles to a constant rpm.

Just My Opinions.

[erick]

Hello Fellow Nerds,

Quite and interesting and stimulating discussion going on here. Very refreshing after recent events/discussions! To be honest, many of the more granular, mathematical based conversation is way over my head but the results sure are interesting! I've always been more of a "throwing spaghetti against the wall and seeing what sticks" type of designer :-)

Many thanks to MrVibrating for starting and continuing this great dialogue!

In terms of the design itself: Definitely not anything that I would have ever considered but as mentioned above the results can't be argued with. The similarities to MT137 can't be denied which in it of itself seems promising.

Some things that I notice:

-While the design is definitely similar to MT 137 it differs insofar as the outermost ends of your bars, arms, whatever do not connect with one another as they seem to do in the illustration of MT137. I expect this might come about as you add more mechanisms to the system. I will be interesting to see how this affects the designs rotation.

-I notice that in your model (posted on page 5 of the thread) that the design does not have air resistance enabled. Once enabled it does not perform nearly as impressively as it does without air resistance. Maybe it's been discussed earlier in the thread and has been purposely disabled at this stage of the design process. In my experience, it's not hard to create false positives in WM2D when air resistance isn't on. Just my 2C.

Reproducibility of results has always been a crucial "step 2" in my design process when I've found something that I believe might work due to a successful WM2D experiment. I basically try to recreate the same assembly from scratch and see if it behaves as expected. Most times my designs do not make it past this second step. To that end I will try to recreate what you have here and report back to the group.

Thanks again to MrVibrating for getting this very inspiring conversation going!

E

[Tarsier79]

As Fletcher suggested, turning the accuracy right up ensures the design does not pass 120 degrees. I guess this means it is running due to collision errors with the circle in the programming.

[MrVibrating]

Back from work, but was thinking earlier - the Merseburg illustrations also depict the torque sequence: note that the first 'perpendiculi' rides the axle, the second rotates with it, the third rides it again... and so on.

@Fletch - yes there IS input PE in current versions, and the reason why is that to align the jack centrally i first set the axle to maximum width (because it's easy to align the axle to the wheel), and then align the jack to this enlarged axle (so about .145 in the current model). But the axle needs to be as small as possible to increase the gain, so when i then reduce it in size there's a gap left.

Also the springs make it defficult to minimise input PE.

However i've played enough with the un-sprung original version to see that it's impossible not to have some input PE - the only issue then is whether it's enough to sustain motion in one direction, or whether it will just oscillate and keel.

This, it turns out, depends on the precise torque phase upon which it starts. Aligned centrally (as described above), the torque sequence is as follows:

1) short track from just after the apex of the previous 45° bump, up to the first 90° bump. This phase torques the axle, and this energy is stored in the wheel's momentum.

2) the 90° bump then pinches the axle, gripping it. The wheel's stored momentum from the tracking torque is now transferred to the jack, rotating it.

3) in addition to this input from the wheel to the jack, and in direct response to it, the jack linkages shift relative to eachother, moving the jack's CoM from the upwards side, to the downwards side. Thus there follows an output of torque from the jack back into the wheel, from this over-balancing moment.

4) there then follows a longer track up to and over the next 45° bump, looping the sequence.


So, as you can probably imagine, with multiple jacks on the axle, (or at least, four), one will always be at the top of its hill, so to speak.

But with just one jack on the axle, it has to start from the beginning of the sequence, at point 1. If we move it to just behind point 1, we're in a 45° rut. If we move to the opposite side of the rut and try from there, we find that we've shifted the jack's CoM to the wrong side of the axle and it then counter-rotates, it's success in that direction again dependent upon how the torque sequence unfolds relative to its starting position. If we move it slightly forward of point 1 instead, then we've reduced the 'run up' to the 90° bump, and thus won't have enough KE invested in the wheel to enable it to rotate the jack through 90°.

So this 90° point is a kind of 'sticky spot', where the workload changes direction, and the wheel puts work back into the jack. If it doesn't have enough, it won't pass go...

To make sure it has enough, we want a heavy jack, with a small axle. This is hard to do in WM2D for now because the current config loses traction as the axle gets thinner. Hence we can put more KE into the wheel from the jack, but then that energy can't transfer back to the jack from the wheel when we hit that 90° hurdle, and instead the jack just slips uselessly on the axle.

So i'm currently mitigating this by having a larger axle, and lighter jack, so that the jack can get better purchase on the axle during this critical rotation phase. However the tradeoff is that we thus get a shortened run-up and less KE input from the jack to the wheel.

So yes, in the current, single jack application, it's possible to start the system from the 'wrong' position in the torque sequence, and it will thus keel.

Fixing the traction problem will be the principal solution to this, followed by multiplying the number of jacks.

Also, the over-balancing moment is currently miniscule, so this needs optimising - i've yet to address this aspect fully. The weekend's looming, should find the time then.

In the meantime, consider the torque sequence, and you'll see it's intrinsically over-unity on this basis alone. I've attached a minimal-PE config as you suggested, but obviously, it's still 'primed' somewhat insofar as it's poised at the optimal point in its torque sequence. At first it is totally motionless.. then a microjoule appears, and then another...

With four such mechanisms in place, it will be similarly 'primed' from any starting angle...!

Finally, it should be possible to plot the force/distance integrals from first principles, just from assumed masses and dimensions. Yes the sim has limitations, however it's done its job in allowing us to peer beneath the real-world losses to see the underlying thermodynamics, and this is what really matters. The back-of-envelope calcs should confirm this point (likewise ignoring entropic losses). But also, the sim allows us to hone the design to something build-worthy - obviously in its current state, it'd be a waste of Mecanno...

I do hope i can start a build by the w/e though...!

[MrVibrating]

As Fletcher suggested, turning the accuracy right up ensures the design does not pass 120 degrees. I guess this means it is running due to collision errors with the circle in the programming.

I'm unable to replicate that - i get auto-rotation at any accuracy.

The highest i can set it, and still see sufficient gain, is 512 - for that i get about 50° of rotation and about 112 millijoules before it bugs out with "an internal limit" reached.

Anyone know what this limit is, or how to raise it? Is it 'cause it's logging stuff - if so can i disable logging? I'm on XP with 3.5gb, would've thought it could handle more than this....

Again, this is only a sim, but we can verify its maths independently..

The form of the symmetry break is that the 'tracking' torque (where it's riding the axle) is a function of the jack's weight, versus the axle-to-inner-jack circumference ratio, whereas the rotational torque is a function of the jack's mass and the OB moment.

Obviously, these two values can be varied independently of each other - they're 'thermodynamically decoupled' properties, being functions of different geometric values. This is what allows the disunity between input and output force/distance integrals.

I've just manged to squeeze a couple of cycles out of 128 accuracy on the last-posted sim above, ending with 429mj on the wheel by the time it runs out of memory - having started with zero. This isn't an accumulated rounding error (at least not in the conventional sense!).

This isn't an artifact, it's an inevitable input/output work asymmetry arising from the alternating transmission system..! The trick now is to widen it as far as possible, and then start multiplying it along an axle...

[MrVibrating]

Hello Fellow Nerds,

Quite and interesting and stimulating discussion going on here. Very refreshing after recent events/discussions! To be honest, many of the more granular, mathematical based conversation is way over my head but the results sure are interesting! I've always been more of a "throwing spaghetti against the wall and seeing what sticks" type of designer :-)

Many thanks to MrVibrating for starting and continuing this great dialogue!

In terms of the design itself: Definitely not anything that I would have ever considered but as mentioned above the results can't be argued with. The similarities to MT137 can't be denied which in it of itself seems promising.

Some things that I notice:

-While the design is definitely similar to MT 137 it differs insofar as the outermost ends of your bars, arms, whatever do not connect with one another as they seem to do in the illustration of MT137. I expect this might come about as you add more mechanisms to the system. I will be interesting to see how this affects the designs rotation.

-I notice that in your model (posted on page 5 of the thread) that the design does not have air resistance enabled. Once enabled it does not perform nearly as impressively as it does without air resistance. Maybe it's been discussed earlier in the thread and has been purposely disabled at this stage of the design process. In my experience, it's not hard to create false positives in WM2D when air resistance isn't on. Just my 2C.

Reproducibility of results has always been a crucial "step 2" in my design process when I've found something that I believe might work due to a successful WM2D experiment. I basically try to recreate the same assembly from scratch and see if it behaves as expected. Most times my designs do not make it past this second step. To that end I will try to recreate what you have here and report back to the group.

Thanks again to MrVibrating for getting this very inspiring conversation going!

E

Cheers mate, and good points. On the first, i'm still far from happy with the jack mechanism, specifically how it's connected, and designed in the finer details. The over-balancing action needs amplifying, somehow. So it's yet to become clear how the arms should connect - do they need to be so long, should they be sprung, or using linear bearings, etc... all these issues will be worked through. I suspect, though, for now, that the poles can be arranged to under-extend on one side while over-extending on the other, as it currently does, but moreso. Precisely how to exaggerate this action is a key question, and will probably decide the answer to your question.. as you say, a "suck it and see" approach should quickly reveal any interesting trends...

On your second point, they're valid concerns however there's nothing to worry about. I don't want to labour this point too far, but as you'll no doubt be aware, when we're addressing the efficiency of a particular interaction, we ignore entropic losses because they're a tertiary concern to the matter of interest; which is the thermodynamic efficiency of the particular interaction in question.

Obviously, in a real-world application, losses apply, but what we want to know first is how much such 'dissipative' loss we can afford to tolerate. Provided it's a fraction of the gain, and not all of it, we're laughing.

Or at least, we'd see some visual evidence of excess energy. However, even if ALL of the gain gets immediately sunk into waste heat, showing zero energy in the intended output field, the system is still overunity, and calorimetry would confirm this. So i'm not being facetious when i give the SI system as an example of this kind of empiricism - one Watt equals one Joule per second, and not "1 J/s after losses". Likewise, we want to know output vs input efficiency of a putative symmetry break, and hence losses are a distraction to that key question.

However if you want a flavour of the energy density available here, use any of the above configs and maximise the jack's weight - so taking the last-posted config, i've just made all weight poles 20kg.

Now set the axle as small as you like - i've gone for 50mm (obviously, its the inner/outer ratio that matters, not the absolute size of either).

Now, we know already it takes some energy to rotate the jack through its 'sticky' spot, the 90° rotation, however we also know that if the axle's too small, it won't be able to ride out the 90° bumps, and will instead will nestle up to them and slowly grind itself to sleep against it. But this is a design issue, not a physics issue.

Also, this input energy from the wheel to the jack, is immediately reciprocated by a return of OB energy from the jack back into the wheel - in other words, the 90° bump is fully conservative - we get back, going downhill, what we lost going uphill.

What matters, physically, is that using the above values, when it hits that wall the wheel has over 20J of energy. If only it could grip the jack with the teeny axle, it has many times more energy than it needs to rotate it.

Yet it can't, because it's slipping.

Not because there's insufficient energy available!

And this is with air resistance set to HIGH!

It's way, waaay over unity. Over the hills and far away, way. Forget 4x OU, we're talking, potentially, much more output energy from the jack 'tracking', than input energy required to rotate it.... it's just a matter of dotting the t's and crossing the i's.... ;)


And finally, good luck with the replication, though i suspect you won't need much... just make the axle as small as possible, and see what you can do to minimise slippage..


Also, are there any other sims worth checking this on, just for further independent validity...?

[ruggerodk]

MrVibrating:
This all sounds very, very exciting - and I'm sure alot is trying to follow you description of the sequences ;-)

Could you help all of us without wm2d, and provide an animation (video) of the motion? Or a screenshot of each sequence mentioned?

I - for one - would really appreciate it.

keep up the good job!

EDIT - NB: uploaded a crop-shot of the 3 Merseburg pendulum's attachment points (or sliding pivot)

ruggero ;-)

[erick]

Hello All,

Attached is an attempt I made to create a similar arrangement, heavily influenced by MT137. For this simulation I used a series of rods and circles in order to be able to precisely control lengths and distances between the connecting "nodes" (the circles) which I had previously laid out in Adobe Illustrator. There are no rigid joints in this assembly. All of the rods could swivel were they not held in place by the other right angle assemblies (per MrVibrating's initial design). This method of creation has the added benefit of creating a sort of roller bearing effect around the axle.

Speaking of the axle: I have toleranced the axle to be .001" smaller than the required radius (to make the inner "bearing wheels" rest continually on the axle).

It doesn't revolve perpetually but it does self start and gain momentum...

Anyway, take a look, play around etc.

E

[MrVibrating]

MrVibrating:
This all sounds very, very exciting - and I'm sure alot is trying to follow you description of the sequences ;-)

Could you help all of us without wm2d, and provide an animation (video) of the motion? Or a screenshot of each sequence mentioned?

I - for one - would really appreciate it.

keep up the good job!

EDIT - NB: uploaded a crop-shot of the 3 Merseburg pendulum's attachment points (or sliding pivot)

ruggero ;-)

Cheers mate, and yes a slo-mo vid of the axle action would be cool, however i'm not setup for grabbing video right now, i'll look into it. If anyone else is able to though i'd appreciate it too... i have to work during the day so on a time budget here...

But yep the toque sequence is basically as illustrated, the jack hangs off the axle, and alternately rides across it a little way, then 'latches' onto it, rotating with it through the 90° sections, before then coasting again over the intervening 45° bumps, and each time it gains more energy from rolling the axle, than is required to rotate the jack at the subsequent 90° section.

It's like an MC Escher staircase of ever-rising PE... but that's illusory - really, it's an input force-distance integral, and an output one. The system has two, different and mutually independent PE's, for each of the two types of traction/transmission involved, and the difference between these is thermodynamically free, whether loss or gain.

And once again i'll repeat that there's nothing special about gravity here, but for its relative ubiquity and ease of access to our current means.

Shrink the scale to millimeters, and swap out gravity for EM, and our energy density increases ten billion fold.

It's the mechanism that's over unity, nothing more. It's currently an asymmetric gravitational interaction. But force is force, and any applied force will produce the same results, according to its magnitude.

I'll be sticking with gravity for now, but this is just kindergarten, compared to what we should be considering...

[MrVibrating]

Hello All,

Attached is an attempt I made to create a similar arrangement, heavily influenced by MT137. For this simulation I used a series of rods and circles in order to be able to precisely control lengths and distances between the connecting "nodes" (the circles) which I had previously laid out in Adobe Illustrator. There are no rigid joints in this assembly. All of the rods could swivel were they not held in place by the other right angle assemblies (per MrVibrating's initial design). This method of creation has the added benefit of creating a sort of roller bearing effect around the axle.

Speaking of the axle: I have toleranced the axle to be .001" smaller than the required radius (to make the inner "bearing wheels" rest continually on the axle).

It doesn't revolve perpetually but it does self start and gain momentum...

Anyway, take a look, play around etc.

E

LOL wow that IS fascinating.. where's the energy coming from there, then? Yeah it runs down but looks like you got some kind of macro-scale brownian noise there, or something... could be a rounding error causing a chaotic 'many body' reverberation.. type stuff? Either way, could it be rectified, say, with a ratchet and pawl, or something? It is surprisingly busy for the apparent input PE.. interesting, cheers for sharing.. :)

[MrVibrating]

Well, i tried adding roughly-improvised gear teeth and the sim just can't handle that much complexity, aparrently... just kept becoming unstable and throwing errors...

What it really needs is a gear wheel for the axis, and a corresponding rack (a flat gear strip) around the jack's inner circumference. I don't think WM2D can do this, but i know my Mecanno set does...

[erick]

At some point someone had posted a gear creation script for WM2D. I'm not sure where but somewhere. I have used it in the past and it's quite easy. I have since lost it though...

E

[Fletcher]

IIRC it was jim_mich. ETA: http://www.besslerwheel.com/forum/viewt ... 3254#13254

In the mean time, short of a rack & pinion appearing, which btw is really hard to build in WM [well, I couldn't do it anyway, using gears function], try selecting each element > Properties & increasing static friction & dynamic friction from 0.3 to 1.0 - see if this helps.

ETA: direction rectifier / ratchet in attachment.

[MrVibrating]

Whose bitch are the laws of physics..?





:)