1) It is possible to cut out a triangle by way of a turning axle.
2) Also...to turn a mass in reverse to the turn of its own CofG.
These facts are there to be seen.
1) https://www.youtube.com/shorts/Qm64fTtSLcw
2) https://www.youtube.com/watch?v=b133HC8ydGo
These two facts, most remarkable in themselves, lead I believe to something even more remarkable...Bessler's Wheel itself.
A further fact, an obvious, is that there is of course a geometry at play in order to effect facts 1/2.
There is only one Geometry of course & it don't lie...but it never tells its whole truth. For our human minds it's a puzzle to be continually explored/pieced together.
The above is the perfect example of this...someone has put compass to paper, so to speak & discovered that it's geometrically possible to make two, quite absurd on the face of it, impossibilities, possible.
The two above facts are co-dependant....fact 1 is made geometrically possible by the geometric effect/implications of fact 2.
Enough said re facts, onto applying them to Bessler's Wheel.
Take an equilateral triangle & draw a line parallel with one of its sides.This line must touch the other two sides exactly one-seventh of the way along their total lengths...making the line itself one-seventh short of the length of the triangle's sides.
This action is the very essence of this new appreciation/observation of Geometry, cleverly implemented by that someone.
It isn't actually new, it's as old as old can be...Sacred Geometry is the finest example of it's use. It would be fair, or at least easiest, to define this branch of Geometry as One-Seventh Geometry....one-seventh is the base, the essential start point from which all develops.
The links above employ this geometry & here are a couple of animations, not great I admit, created by extending that geometry to create two separate bars operating in two separate triangles...a Star of David...but connected.
A Bessler Toy D is clearly present & it is behaving exactly as toys C/D suggest...it even appears to imitate a twist, as toy D hints at.
This rectangle is of unique proportion....it has been created/defined by one-seventh geometry.
Please now ponder this further one-seventh development upon this one-seventh rectangle.
The rectangle is defined by the triangle that spawned it, as is the orange circle that contains said triangle.
The rectangle defines the size & number of smaller circles around, which number 7.
I'd beg you's to do the sums for yourselves...to confirm the fact but it ain't half as easy as it first appears. I certainly couldn't do it but I have the Head of Engineering at Bristol Uni as my neighbour, so....
If we divide the diameter of that larger defined orange circle by the diameter of any one of the seven defined circles around, it equals 1.717.
Or, as his iPad displayed after a lengthy process & to my great shock, 1.7170000000 to be absolutely precise!
I'm left pondering...maybe it's 1717 Geometry & 7's just naturally/frequently occur from it?
Whatever....on to the main event.
Here is the resultant disc & rectangle formed from this Geometry..and it has but one name, I suspect..Bessler's Wheel?
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Firstly...the geometry that created this has now been removed...but it hasn't disappeared. The rectangle here is going to move exactly as previously shown...as if it were still performing around the two triangles of a Star of David. And indeed, Bessler's wheel probably was more Star of David in its design/appearance.
The disc you see numbers three, the shape hollowed from within & they are each of a thickness that would allow for `stuff` to run around inside this cutout. These three are sandwiched together, loosely. The central disc is fixed...to an axle stand let's say. The outer two are free & independent to turn, also on their own independent stands & bearings.
Toy D sits within & it is the weight/s performing to a PM Principle here.
The toy is designed three-layered also, as per the discs....so, weight A/C is to the fore as you look let's say, B/D is to the rear & the two connecting weights A/B & C/D are centrally between.
Thus, when positioned into the three discs Toy C alignes accordingly.
A/C & B/D drive this `wheel`...A/C drives one outer disc, B/D the other.
In sequence...point A of weight A/C drives its disc, then point B of weight B/D drives the other disc. Then point C again drives A/C's disc & finally, point D drives B/D's disc.
Weights A/B & C/D, sat centrally, run around their centrally fixed disc as this driving of the two outer discs is performed.
So...The greens are the central runners, the reds the outer drivers here.
Back to the diagram... A/B it's being held in place by a centrally positioned lobe on the centrally positioned fixed disc that it runs in.
My, as ever, useless graphic skills don't accurately show it but points C/D are both pushing down centrally onto their respective lobes. As in, straight lines from the axle through points C/D will cut their lobes into half.
The weight of the whole rectangle is therefore balanced across point C, in one free to turn disc & point D in the other...& this balance is keen to unbalance.
Sticking with the direction of flow previously adopted...and of course the same action/motion, then this rectangle is about to collapse, drawing points A/D inward, pushing B/C outward to touch the rim.
In collapsing, point C is to turn, as per the animations, clockwise to end up in dip 1, in its disc...and point B likewise into dip 4 of its disc.
This appears impossible under normal rules of Geometry...it can't be the case whereby C clearly needs to turn about the axle to reach the rim at dip 1, yet point B doesn't need to turn to drop into dip 4 barely at all...if fact it does appear to need a wee turn but it's anti-clockwise if anything at all.
This IS the paramount thing for you's to appreciate... C WILL indeed turn into dip1, B into dip 4...because of the both clockwise & anti-clockwise around the central axle aspect being employed.
To repeat...this rectangle, Bessler's Toy D, is performing as per the animations, as per the looped slo-mo. If suitably applied it could cut a triangular hole...but here it's being applied otherwise.
Disturbing the mentioned balance, then A/C pushes down centrally on its lobe at point C, pushing it aside anti-clockwise as the rectangle collapses. C is the only driver driving, driving its wheel alone. The other disc is not being driven by B/D....D is busy swinging upwards/across around point C, B is busy entering dip 4 as it swings around point A.
Moving on...the rectangle has now collapsed/spread flat into dips 1/4 so now it begins to expand again.
Again fully expanded, A/C & B/D have now exchanged positions.
A continues to swing around B now, D around C...until the central runner A/B now sits centrally on its next lobe around clockwise, only now it is B/A...and the runner C/D, originally across dip 7, now sits across dip 1, 60 around....so, back to our start point, just 60 degree around clockwise.
But....as A/B ran around to become B/A so C/D has now run around to become D/C.
We can look at the diagram, reverse 60 degree & see that this new arrangement, exactly as the previous, would have B/D now driving at point D....and B/D is driving only its disc...catching it up with the first that is not being driven at this point..
This process continues on & on & points A & B will take their cue as drivers...but just to reconfirm, Toy D is moving clockwise, the discs are moving anti-clockwise...crab style, in unison.
Ok....facts. Just geometry that anyone can easily verify, leading to an action already verified, leading to Bessler's Wheel tho?
Well, the only real argument/question is, will it balance/come to rest? I think not.
Basically we have a weight/rectangle...a very floppy/unstable weight/rectangle, sat balanced atop two points that will turn under that weight at the slightest provocation. Once in motion then that balance cannot be reclaimed. & so it turns, only to reach the same scenario over & over.
It is always too tempting to wear the old head...t'would be easy to mistakenly address this thing by looking for imbalance, a permanent imbalance directly around the central axle.
But please...it never was about that. Bessler never once spoke of any such a mundane application being employed to create his `Wondrous Wheel`. And no wonder, the very notion is preposterous in the extreme.
No...Bessler spoke exclusively of something like the thing before you...of a floppy toy with a twist, of weights moving in pairs never able to reach the CofG they must constantly seek. He spoke of drivers that drive, runners that run, unusual rims, anvils (dips/rim here) receiving many blows, of wagging tails, of creeping around, heavy clubs...of crabs. I could go on...and I will.
Of 1717...a new and exciting take on our old & reliable friend.
Geometry.
Ok...let's have words.
Over 20+ years I've grown accustomed to being largely ignored & I could hardly complain. I don't recall ever once replying to another's thread, other than a handful of sarcastic quips perhaps.
And in hindsight you were all kinda right to ignore because each individual offering truly didn't assist your own personal inquiry in any way/shape/form.
But...each individual offering was for me a part of an ongoing path/journey. That path has led me to here & I'm not now, in this instance, offering anything to assist further in our Quest...I'm offering the possible completion of the Quest.
If, as wouldn't surprise me in the least, any one of you's, professing to be a seeker of PM/Bessler's Wheel, still sees fit to pass this by then, with the utmost of respect, you aren't seeing fit at all.
Confused perhaps by my presentation quite possibly...but even then, captured enough to desperately seek clarification surely?
I will attempt to build this, it's simple enough...but being 90% bedridden & having less skills at building stuff than I have at graphic artistry....God would need to be firmly onside to achieve a successful outcome me thinks.
There are those of you well capable of building this & from my standpoint at least, you should be excited to crack on & do so.
It's a piss easy, potentially enjoyable, project for someone here I'm sure, rewarding on a whole other level if successful and costs relatively little I imagine. Even old me on a State pension could probably stretch to it & I'd gladly pay the cost of materials to any would be builder, as far as I'm able to.
Just one final addition, for accuracy sake...
The action/cycle here is best considered as from fully collapsed rectangle to full collapsed again... The above shows the half cycle position. Able to look along the axle & through to the rear disc then there is a motion/pattern created by the lobes of both discs as they crab their way around. When as shown, at the halfway point, you'd be seeing 14 lobes each intersecting the other by 50%.
You will see just seven lobes in the fully collapsed position, where the 14 lobes align 7/7.
I mention this although I see no reason to expand upon it other than to add that it's destined to be a quite mesmerizing effect in motion.
How precisely is it perpetuating?
Well, Bessler said by some Principle of excess weight & that would have to be a different principle of excess weight than the one we all know & struggle with to the point of loathing. As of now I'm not seeing any Principle worthy of that terminology. I'm seeing a rectangle that's operating three around...30/60/120's around. And it's doing this in a seven around. Thus the seven around must shift around to accommodate this...& it does. The axle is indeed, in its turn, also moving ,as the rectangle creeps slowly backwards as it turns forward.
Bless/Gill