The Trick?

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Gill Simo
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The Trick?

Post by Gill Simo »

Please look, perhaps again, at this looping animation and reaffirm that the almond shape is turning clockwise, its centre of gravity turning anti-clockwise...making it possible for the two tips of said almond to scribe a perfect equilateral triangle.

https://youtu.be/b133HC8ydGo

The triangle is of course stationary here but having familiarized yourself with the action within it, then lets now turn the triangle to facilitate this action.
FIG 1.jpg
To the left, the almond (now replaced by a single straight bar of weight) is balanced horizontally, parallel with triangle side/base C/D.
The faint black lines show the projected movement this bar will make as the disc/triangle turns clockwise

After a turn of 60 degree we reach the middle diagram....again the faint lines show the projected movement of the bar as the disc/triangle moves on clockwise. This results in the diagram to the right.

So...a turn of the disc/triangle through 120 degree results in the bar returned to its starting point although one can see that its now parallel with a different triangle side/base (B/A) & the bar has itself turned through 180 degree.
A further 120 will be likewise ,though the bar will then be parallel with the 3rd side/base upon completion. Another 120 will return us to the left diagram.

Thus, in this way, in one 360 degree revolution of the disc/triangle the bar will have not only been parallel with the three sides/bases of the triangle...it would have used all three points A/B/C of the triangle as a pivot to swing the bar across all three sides.

The sequence of point/side selection is anti-clockwise...first base C/D, then anti clockwise onto base B/A...onto base A/C, likewise points C to B to A.

Just in order to be entirely factual...one complete revolution does not actually return back to the left diagram. The bar will have turned through 180 three times so it's reversed & it'll take another complete revolution to fully return/mirror the left diagram....of no significance but a fact.

Of great significance however is the swing of this bar...you'll see that it is always a swing across the horizontal side uppermost, pivoting from a point lower most.
If set as shown in the middle diagram, then any slight movement of the disc/triangle around, in either direction, will immediately see the bar swing across in accordance. The point being...this central point is finely balanced and if the disc/triangle were turning constantly then the swing of the bar will be from fully left to right (or visa-versa) with no possibility for it to come to rest at this fine centre/balanced point.

Now we simply have to take a second disc/triangle & fix it at 180 degree to the first, forming a fixed Star of David seen along the axle line.
FIG 2.jpg
This also has a bar & it can easily be seen that when the bar in disc/triangle one is horizontal/parallel with its triangle side/base, then the bar in disc/triangle two must be vertical, halfway through its swing across its triangle's uppermost side.

In this fashion we always, as the discs/triangles turn, have a bar/weight uppermost, above the axle, swinging across & straight through its vertical point of balance...causing a turn through 120 degree having done so to only ever reach the same situation.

It is entirely due to the reverse directions of turn inherent in the almond/bar & its centre of gravity, that makes the geometry here possible (the ability to scribe a perfect equilateral triangle from a point) & in the process, effect this quite simple trick of flailing, in essence.

A bar sat horizontal/parallel is pulled away/back from its own end's swing across...as its opposite end is dragged/pulled back into a pivot point for that swing to occur. This `pulling back` is provided by the bar's CofG turning in reverse to the bar itself.

A flailing action no different than swinging a weight on a string as such, although this flailing occurs at a single point 120 degree around from top/centre, either side dependent on direction of turn & it is applied six times per revolution at this point.

I haven't shown the centre point of the bar/s but rest assured, they turn anti-clockwise as per the looping animation.

The bars remain at 90 degree to each other throughout by the way & the point where they cross each other also turns anti-clockwise around the central axle.

I attempted to build this thing & by my standards it was a lifetime best build attempt but alas, my standards are so pitifully low that my best still fell well short of the standard required here. But I learned & now await delivery of more `stuff` to hopefully go on & out best that lifetime best.

'Tis a hindrance in this PM pursuit for any 70yr old to have less aptitude than a 7yr old at constructing stuff :(

Bless/Gill
"Everything you know will always equal the sum of your ignorance"
Gill Simo
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Re: The Trick?

Post by Gill Simo »

I trust this is being clearly understood but dismissed hitherto as not worthy of reply/question and not simple confusion at play?
Perhaps I can encourage by progressively questioning you's instead?
Starting with...

Turn anything around a fixed point & around is precisely the resultant motion...a constant arc, 360 around, a circle.
So...how is the almond in the looping animation managing to swing one tip around its fixed point other tip, yet manage to scribe not an arc but a straight line, if not by way of the explanation already offered please?

And, if I may...how is it possible for any ardent PM enthusiast to not immediately recognize that a mass moving around in one direction whilst it (it's centre point) also moves around in the opposite direction serves them up a true & very necessary inventive step towards possible PM success. If you conclude this inventive step an irrelevance not worth the bother then please be kind enough to explain to me why?

Thanks/Gill
"Everything you know will always equal the sum of your ignorance"
SHADOW
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Re: The Trick?

Post by SHADOW »

Bonjour Gill,
Nous n'avons pas tous votre capacité à appréhender les concepts virtuels et les trajectoires de points, pour ma part je suis limité dans ma compréhention de cela!
Dans le systhème mécanique de référence il y a une manivelle que vous ne représentez pas donc j'ai du mal à vous suivre dans votre démarche!
Je ne vois pas le centre de gravité de la barre tourner en sens inverse.

Hello Gill,
We do not all have your ability to grasp the virtual concepts and the trajectories of points, for my part I am limited in my understanding of this!
In the reference mechanical system there is a crank that you do not represent so I have trouble following you in your step!
I do not see the centre of gravity of the bar turning in reverse.
Last edited by SHADOW on Sat Sep 28, 2024 6:32 am, edited 1 time in total.
La propriété, c'est le vol!
P.J. PROUDHON
SHADOW
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Location: France

Re: The Trick?

Post by SHADOW »

Gill,
j'ai pris le temps de faire un test sous Algodoo, je confirme que le centre de gravité de la barrze tourne en sens oposé de la rotation de cette barre!
De la position Horizontale de la barre, un des coté rejoint l'angle supérieur, l'autre coté descend vers le milieu du coté du triangle.
La longueur de la barre est égal à la hauteur du triangle.
Pour le test j'ai ajouté deux rouleaux.

Gill,
I took the time to do a test under Algodoo, I confirm that the center of gravity of the barze turns in the opposite direction of the rotation of this bar!
From the horizontal position of the bar, one side joins the upper angle, the other side goes down towards the middle of the triangle.
The length of the bar is equal to the height of the triangle.
For the test I added two rolls.
Attachments
Test Gill Simo.png
Capture d’écran 2024-09-28 134313.png
Last edited by SHADOW on Sat Sep 28, 2024 11:44 am, edited 3 times in total.
La propriété, c'est le vol!
P.J. PROUDHON
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