Toad Elevating Moment

[MrVibrating]

This is all a terrible distraction, i'm sure, but for the hell of it i just made another one.

http://www71.zippyshare.com/v/91558210/file.html

This time it rotates in the opposite direction, and the larger weight 'lifts' the lighter one.

One jack, 72° rotation, can't get WM to plot integrals but looks like a good few J under the curve - and that's from less than a quadrant of torque.

Total system mass is about 30kg, 19 meter jack at full extension.. so not entirely practical but certainly doable.

Net change in height for that output of a few Joules is zero.. That jack doesn't lift jack.

How is this possible? Where's the energy come from if no mass has changed height? Nothing has moved lower in the gravity field, yet there's a GPE output.

GPE = GMH - gravity times mass times height. Yet here, no mass changes any height.

Not even a teeny weeny little ickle bitsy witsy.

There just SO isn't.

And it can't be a simulation error because i logically predicted (see above) the same result - and while i'm certainly fallible, the simulation shouldn't confirm my delusions, surely? Maybe the sim's a figment of my psychosis!?

What else are we to conclude - that the masses DO change height, but they're equal and opposite motions and so cancel? I mean that was basically my rationale, but c'mon - nothing's actually moved vertically! The logic's akin to trying to lift yourself by your bootstraps, failing, but then accelerating the earth instead!

If we drop the weights once the jack's fully retracted, capture the GPE from that fall, reset the now-empty (and potentially counter-balanced) jack for peanuts, then re-lift the weights back onto the jack using their previously-harvested GPE, we can repeat the cycle; fall inwards, then downwards, then reset and re-lift... each cycle we gain a few Joules of free RKE from 72° of free torque, from a free "horizontal fall". Of course, re-positioning the detached, fallen weights horizontally prior to re-lifting is a zero-sum deal 'cos it's conserved and reversible inertial work (it costs to accelerate the masses horizontally, but they pay out an equal amount upon stopping). Pretty much the same as the drop and re-lift...

Ergo, provided the free energy exceeds the frictional losses (though strictly speaking, even if it doesn't), we're over-unity.

Which is nice. :)

[MrVibrating]

Vibrator .. I had a play with your sims - I centered them on the page & turned up the accuracy & turned on View > 'System Center of Mass', & zoomed in close.

Take a look - you'll see that there is a drop in CoM i.e. loss of PE & this leads to the torque IMO.

The question is has there been an increase in system KE greater than PE gravity lost ? - What do you think ?

Interesting and thanks for taking a look - however i can't see it myself... of the two versions you've linked, the first (1-down 6-up) wasn't intended to show the effect (since the masses change height) - it was just to show how my reasoning progressed (it merely demonstrates that radial and axial speeds can be synced to offset the axial speed of the jack, ie. near-perfect linear-to-rotary translation).

The second one was intended to harness that coordination to show an output of GPE with no corresponding change in height - however the file you've linked no longer does this - something's thrown it out of kilter.

Also when you say "Zoom in" - you mean increase the data resolution? How do i do that (sorry still learning here).

The most recent one i've posted above might be easier to analyse (i've made the weights easily visible again, and spent more time optimising the balances).

I've zoomed in on the image (i have a 6-screen spanned monitor) and the transit is as horizontal as i can get it, so far. There's a certain tricky constraint in that the acceleration curve of the jack peaks around the 45° point, then drops again, while on the other hand, the rotational inertia of the wheel drops as it reaches max speed - hence we're trying to offset a parabola with a half-parabola. I managed to get a reasonable compromise by tweaking the rotor's radius and mass, erring on the side of a very shallow rise and fall - however being careful to ensure the weights begin and end their radial excursion at the same height.

Obviously, whatever happens once they collide and bounce off each other can be disregarded for now, it's incidental to the fact that the weights begin and end their horizontal transit at the same height, yet considerable work has been done on the system, ostensibly at the expense of the weight's horizontal displacement.

IOW i don't believe the output energy is equal to the GPE of the system, which should by all conventional reckoning be negligible. Remember, 1J = 1kg / 1m/s^2... It just doesn't add up.

Bashically, Y translations have a positive or negative value, and X translations usually have zero value (thanks to inertial symmetry), hence a trajectory traveling an equal distance up, down and sideways yields zero work.

Here however, an X translation yields non-zero work. But the subsequent, 'reset' X-translation is perfectly conventional, symmetrical and thus zero cost. Finally, the up and down Y translations again sum to zero, leaving the free positive X translation in remainder, hence we have a closed loop gain, a path-dependent interaction which creates energy in one direction of travel, and destroys an equal amount in reverse..

And five of 'em add up to 360° of free "horizontal fall" torque.

[MrVibrating]

ETA: I've double-checked the most recent config and you can tweak the flatness by adding or subtracting a few milligrams to either mass. But any remaining variation is in the order of milligrams over millimeters, ie. microjoules.

Thus only the horizontal displacement of the weights could account for the gain. They really ARE falling inwards, instead of downwards.

:)

[MrVibrating]

I am not a WM2D user, but for the sake of helping others I do have the capabilities and knowledge to download and run a simulation.

The first above, I was told has inconsistent restraints and was asked if I wish to continue.

As for the second, it is with my hands on experience that tells me you cannot gain anything from scissors if allowed to open to the acute angle shown. It will require more force/mass to open and close than will ever be gained.

Ralph

Cheers, the second one, and the last, most recent one demonstrate two masses causing a jack to retract, and so torquing a wheel, without changing height.

Only the initial linear-to-radial translation is of interest, whatever happens in the sim afterwards is besides the point. What's important is that we have an output of torque from a horizontal 'fall'.

So yes, you're correct that it'll cost energy to re-extend the jacks, and likewise it'll cost more energy to re-lift the weights after they fall from the retracted jack (not yet simulated). However these are regular, symmetrical energy exchanges, and there's no causal relationship between frictional losses (which are a function of design choices like bearings etc.) and gain (which is a function of mass and, somewhat sensationally, if not controversially, free horizontal displacement).

In a nutshell, we gain because we don't have to reciprocate the jack's largesse by pulling the retracted weights back out again.. we can knock that bill by simply dropping the weights, resetting the unloaded-but-perfectly-balanced empty jack, then re-positioning the weights horizontally against nothing more than inertia, then re-lifting them - all of these actions are symmetrically conservative, hence only frictional losses apply.

Each time we repeat the cycle we get torque on tick, then wipe the slate and start over. Everything else in between is just the set-up and sting.

[Fletcher]

Here is your latest sim tweaked again.

I had to look at the 'properties' of every object on screen & ZERO OUT the residual Vx; Vy; & Vo [3rd to 6th inputs down in properties] - see pic below.

What this means is that you've been building new sims from old ones & dragging parts around - this sometimes carries over residual quantities in the above inputs - they need to be zeroed out so they have no motion at all from sim RUN START, else they effect the result.

It is something we users just get used to checking if a result looks a little anomalous - it will also definitely happen if you use the 'start from here' when a sim was already underway.

I have also added OUTPUTS for just the balance weights as KE translational & I've netted out the PEG so you can at a glance see what happens i.e. is the PE decline [& there is one] less than the KE gain.

N.B. I have not at this stage looked at the scissors themselves to either take them back to 0.001kg mass [low effect] or to add in their individual KE's etc.

What happens now ?

P.S. the zoom is a little icon of a magnifying glass top of page.

[Fletcher]

In a nutshell, we gain because we don't have to reciprocate the jack's largesse by pulling the retracted weights back out again.. we can knock that bill by simply dropping the weights, resetting the unloaded-but-perfectly-balanced empty jack, then re-positioning the weights horizontally against nothing more than inertia, then re-lifting them - all of these actions are symmetrically conservative, hence only frictional losses apply.

Each time we repeat the cycle we get torque on tick, then wipe the slate and start over. Everything else in between is just the set-up and sting.

Firstly, I would love for a anomaly to be found.

Secondly, does a sim pass the logic test where there appears an anomaly.

My logic/intuition tells me that if you have a flywheel & attached to it horizontally is a scissor jack with unequal masses at its ends at different distances & it balances then it has zero PE.

f1 x d2 = f2 x d1 = leverage law

It also has no torque because it is balanced each side of the pivot/axle.

If the sim rotates [has torque] it is because it is not balanced & it will loose PEG.

The reason is that gravity acceleration acts vertically, it has no horizontal component, or no shearing stress [as currently understood].

[MrVibrating]

Aha! You're absolutely right, i hadn't noticed that at all, doh!.

I likewise zeroed all the motion fields and it does substantially reduce the anomaly doesn't it..?

In fact, it goes down to millijoules.. presumably within the range of residual Y motion.

Ah well, least that was cleared up quickly, ta very much!

However there may yet be one redeeming property here insofar as it seems the system has no balance point - it's inherently unstable. I couldn't find any blend of variables that would sit still horizontally and NOT cause the weights to gravitate to the center.. so while it now seems fairly evident the resulting torque is never going to raise a 70lb box of bricks, it's still a little bit interesting, maybe..

I mean, notwithstanding the fact that it cannot possibly perform useful work, obviously.

Still, if nothing else, we have a system in which a pair of weights, set one against another, can never obtain equilibrium... at least for a while.. and maybe there's still merit in using the jacks as a direct-drive mechanism, albeit without counter-weighting them in quite this way.. the jack certainly does work as a means of translating linear motion to torque, so i've not exhausted all options, yet...

(and with that bubble burst at least i'll get a decent night's kip eh) ;)

[Fletcher]

A bit of red eye would be worth it once in a while but the ticker might not like the excitement.

[MrVibrating]

Firstly, I would love for a anomaly to be found.

Secondly, does a sim pass the logic test where there appears an anomaly.

My logic/intuition tells me that if you have a flywheel & attached to it horizontally is a scissor jack with unequal masses at its ends at different distances & it balances then it has zero PE.

f1 x d2 = f2 x d1 = leverage law

It also has no torque because it is balanced each side of the pivot/axle.

If the sim rotates [has torque] it is because it is not balanced & it will loose PEG.

The reason is that gravity acceleration acts vertically, it has no horizontal component, or no shearing stress [as currently understood].

Total agreement, however what i was looking at was persistent torque, disproportionate to vertical displacement. It was the net effect of the accumulated junk motion you pointed out. I'd hypothesised, incorrectly, that the linear-to-radial translation in the first sim might still work if balanced to the horizontal, and the 2nd sim seemed to confirm that unlikely conclusion... ditto the the 3rd..


Still, as a drive mechanism - in the vertical plane at least - it has certain properties consistent with various clues... i still think there's a literal interpretation of the Toys page, and its consistencies with MT41 etc. This was just a brief divergence...

Thanks again..!

[scott]

Excellence all around! Anarchic principles at their best. Kudos to all involved.

[AB Hammer]

MrVibrating and Fletcher

I suggest that each of you should build (if you don't have a set already) a set of stork's-bills and a standard set of scissor jacks and get a feel for what they do to go along with your simulations. Sometimes having a physical visual aid helps.

[MrVibrating]

Definitely, tho i'd actually done things the other way 'round - built every type of storks bill i could imagine, even rotary ones. In the end though it seems this is one mechanism better simulated than built, as a real rig has compounding issues of increasing friction and slack in the transmission, the more sections one adds, and this makes precise measurements impractical. Being able to zero friction, free play, and the jack's own mass was the main reason i started simming 'em.

Again though, having played with real 'uns, their acceleration curves as a function of no. of linkages are certainly a cool property. Could easily have someone's eye out in a blink...


Today however i've mostly been staring at MT137. I worked through all possible combinations and weighed up each one's potential relevance. The most consistent is this recurrent clover emblem, as per the AP wheel:


(click to enlarge)

To quote AP:

"Are you, my friend, a man of patience, piety, chastity, honour,
purity, truthfulness, diligence and reserve? A man for whom a
mere clover-leaf could be reward enough?"

Taking the above in conjunction with AP's description of the mechanism (paraphrasing from memory) "two pairs of weights, one takes up an outer position whilst the other occupies an inner position..[..]...Later they swap places" we might also suppose this clover motif may be a plan view of MT41's arrangement of weights, where upper and lower pairs are labelled as distinct couples A and B.


This, then, seems to culminate in a further conundrum: how do 3 intersecting square sections like this integrate 4 weights in two pairs? What's this got to do with their cylindrical shape? This geometry looks suited to things that happen in threes or sixes, perhaps, but two-by-two?

Maybe the magical action has a 3:1 ratio instead. Or maybe the wankel shape at the intersection of the three squares controls four strokes, per its namesake internal combustion motor. (Totally blue-skying this here, bear with me...) The squares terminate on the opposite side of the axle, and as noted previously a weight borne on the 'wrong' side of a wheel would lift itself, were such a thing possible...

There's three inner 'points' at the 90° apexes, and three outer points at the intersections of the three quadrants. We've got three quadrants arranged into a circle, ie. a circle missing one quadrant, or two 'circles' 90° out of phase (one 'true' circle, the wheel itself, overlaid with a very fat, rounded Reuleaux triangle).

The notion that the AP wheel may have anything to do with MT41 may seem less strikingly discordant when one notices the similarities between the axles - specifically the gaps between the axle and the radial (well, off-radial anyway) beams.

These off-radial lines may also be a lead - a true radial line traces a shortest path from center to edge, but here our lines are longer. Besides the 90° angles there's 60 and 120° increments between them. Perhaps these angles are critical?

Obviously, the axle is much larger in MT137 - does this increased thickness, relative to the AP diagram, suggest the axle thickness must increase in order to facilitate more mechanisms in similar sets of three? If so then this would imply a cut-off point in how wide an incarnation of the machine may be - with diminishing returns as more mechanisms add more axle girth, limiting the available radial travel... perhaps this is why Bessler talked of increasing the radius, rather than the width (he may have mentioned adding machines in parallel, but didn't to my knowledge speak of simply widening the drums to arbitrary thickness)?

The suggestion of a co-axial (or even tri-axial) shaft in the AP wheel might also be consistent with the Wankel / Reuleaux figure.

And this whole thing about squaring the circle - perhaps that wasn't so much a diversion as it at first seemed... all we have here is squares'n'circles.

Look at the snap toys on the Toys page - a big circular anvil with a short displacement, vs a smaller square anvil with a larger displacement.

4 sets of 3. We need a 4:1 energy gain (according to AP). There's 5 positions on the Toy's page shaft - 1 input and 4 outputs? Could this wankle geometry point to a solution to Bessler's '1 down 4 up' riddle?

As ever, the only thing spinning here right now is my head..Somehow, though, there must be a way to reconcile these seemingly disparate things... to square this circle, if you'll pardon the pun.

But yep, full frontal nudity. That's what we're dealing with here. The AP wheel and MT137 are side views of the machine in the nod; the former's an extreme close-up, the latter, an all-out orgy, as it were.

(NB and when i say i worked through all possible interpretations of MT137, i mean i went through every possible H-V translation, simmed the thing in various sections and as a complete mechanism, tried adding weights in various places, connecting different sections to different axles.. i spent all week on it, and this was the most consistent thread, as perplexing as it may be for now)

[MrVibrating]

lol, one, obvious solution to the paradox would be that there's at least one, other, weight in addition to each set of 4, stashed inside the axle...

If the above speculation that the axle thickness has to increase as more mechanisms are added is valid, then these stowed weights cannot be aligned perfectly axial / side-by-side, for some reason, but must instead crowd around the axle.

Perhaps this is because they're two in number, for a total of six per set, hence as more mechanisms are added, these pairs at dead-center mean they get increasingly separated?

Do they move out, or just sit there as 'hidden' counter-balances (active only upon their companions' center of gravity, rather than the wheel's)?

Presumably they assist the inner and outer weights with trading places... Perhaps there's three positions in their cycle, then, rather than just 'inner' and 'outer'? In other words do they take it in turns to stow away?

Again, the only difference between the AP wheel and MT 137 is the number of 'clover leaf' sets, and an apparently corresponding increase in axle width. This leaves a numerical base 3 / base 4 mismatch, and wildly varying axle width, and both would most simply be resolved by extra weights hidden inside the axle...

It's an argument. I'm not saying it's a GOOD argument, but it's all i've got going on for now....

[MrVibrating]

It's reminiscent of the prominent 'angle hook' of MT53 / 54 and elsewhere, and also perhaps MT25 - maybe weight-poles extend outwards from the apexes of the squares?

MT64 / 65 also seem to be strongly hinting that right-angles are key.

MT135 can also be deconstructed into right-angled sections... 136 is also just circles and squares. 134 may also be relevant, perhaps describing one way to actuate the square sections.

Perhaps this also explains the scissorjack - perhaps the way these squares link forms a novel type of jack..?

Maybe this config has a resting state whereby there's two weights forced upwards by a single weight hanging directly downwards - all three balancing, but with the system's center of mass raised above the axle...? Wrong number of weights, i know, but something to investigate later perhaps...

[MrVibrating]

Well i built one in WM2D.

The very first one auto-rotated.

I tweaked it slightly to perfect the angles and align the linkages as centrally as possible, and here's the result:

http://www41.zippyshare.com/v/98417076/file.html

It ain't fast, so be patient - it's almost as if it can barely rotate at all, just as the Man said. For now, it starts with a partial oscillation as momentum builds, then just keeps rolling clockwise. Presumably this principle's bi-directional though...

Note especially that currently there are no weights attached. Yes, you read that correctly. It self-starts and accelerates up to steady speed automatically, using only the jack's own mass.

Mass densities, friction etc. are all normal. Input PE is zero.

This thing's raring to go - tomorrow i'll start adding weight loads (tho feel free to try whatever you like in the meantime eh) - but even in this nascent state, it's a self-starting runner right off the drawing board!

It's been staring us in the face all this time - it's simply the Apologia wheel! MT137 is four of them, just as i deduced...

Funnily enough, right-angled brackets were the very first thing i thought of when i started this mission back in April. I didn't get further than Paint sketches then before sticking it on the back burner, but i've had a persistent itch about them ever since.... admittedly i imagined a somewhat more tumbling action, but all the same, can't help thinking that with a little more focus i could've had this months ago..

Went to work today with 2 hours sleep, but it was totally worth it.. :)

Yo Fletch, shoot me down bro..!