Maths and Reality

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JGarriga
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Maths and Reality

Post by JGarriga »

Hi All

I will share with you a design that would be a runner from a mathematical point of view.
But probably almost impossible to build with the required accuracy and tolerances. Maybe some improvements can be done.

As its operation is not easy to understand at first sight first there is an uploaded image.

[/url]https://ibb.co/ihVuLx[url]
The real problem is not believing it to be possible
Georg Künstler
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re: Maths and Reality

Post by Georg Künstler »

Hi JGarriga,

maybe you can post an other picture where we can see an other position of your swinging pieces. It will make the movement which you are expecting clearer for us.

Where is the rope fastened ?
Best regards

Georg
JGarriga
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re: Maths and Reality

Post by JGarriga »

If You can see the image let's see what's there

1.- A Wheel able to rotate around a shaft not seen in the image.
Let's call it the rotational inertial reference.
Note that he small circle in the center is not a shaft

2.- A small circle in the center. It is an independent stationary part with round shape. Let's call it the stationary inertial reference. It is bonded to the Earth.

3.- To swinging beams attached to the wheel that can rotate each around his own swinging centers and with the wheel itself.
The swing amplitude is limited in two ways.
First by their contact at some moment with the central circle
and second by a rope.
They act as special levers connecting the stationary and the rotating inertial references in order to achieve that the component of the reaction in the rotating inertial reference is not crossing the center of rotation and producing torque on the wheel

As you can understand the gravity plays just the rule of an actuator and a switch but it is is not the real reason of the torque.
When the assembly is in movement what is increased by the levers is the rotational kinetic rotational energy itself.

Also the center of gravity of the assembly is always almost in the center.

As I said it is not easy to understand how it runs at first sight. I will try to upload an avi file iwith enough quality to clarify it.

That's all
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JGarriga
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re: Maths and Reality

Post by JGarriga »

There is another image to clarify focused on whats is happening in the center at a given time.

Due to gravity the lower beam has rotated reaching contact with the stationary circle.

The upper beam can not contact the stationary circle because his rope avoid it.

The contact between the lower beam and the stationary circle works like a cradle. In the triangle of forces exerted by this contact there is one component pointing to the center of the stationary circle ( the Earth will take account for the reaction) and another component point to center of rotation of the beam ( the wheel will take account for the reaction which is not pointing to the center of the wheel ==> torque )

Note that the wheel is intended to turn counterclockwise
https://ibb.co/h6iLAx
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Re: re: Maths and Reality

Post by JGarriga »

Georg Künstler wrote:Hi JGarriga,

maybe you can post an other picture where we can see an other position of your swinging pieces. It will make the movement which you are expecting clearer for us.

Where is the rope fastened ?
Hi Georg

One end is fastened to the beam and the other to the wheel.
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re: Maths and Reality

Post by JGarriga »

Just another image to clarify it

https://ibb.co/iA7xsc
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Art
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re: Maths and Reality

Post by Art »

Welcome JGarriga ,

That's an interesting concept and application .


With regards to your quote - "Note that the small circle in the center is not a shaft - -- 2.- A small circle in the center. It is an independent stationary part with round shape. Let's call it the stationary inertial reference. It is bonded to the Earth. " --

I think you could still think of it as the shaft as long as the shaft is fixed and not rotating in its support .

An interesting hand held demonstration of the principle can be had by perforating a disk of about 200 mm diameter and inserting a "shaft " of a smaller diameter so that there is a bit of "looseness" in the fit .

By holding both ends of the shaft to prevent rotation but at the same time "pedalling" the ends of the shaft the disk rotation will accelerate quite dramatically .

A paint can lid as the disk and a wooden dowel as the shaft works quite well .

I imagine from your posts you are probably familiar with this device already but for others who may be having trouble with the concept it might help to clarify things .

Sort of feeling is believing :)
Have had the solution to Bessler's Wheel approximately monthly for over 30 years ! But next month is "The One" !
JGarriga
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re: Maths and Reality

Post by JGarriga »

Hi Art

Thanks for your remarks

In fact I'm trying to build a prototype with bike wheels in order that the shaft remains stationary.

Actually you can replace the fixed round shaped part with a high mass cylinder hanging from the shaft ( a kind of windmill stone) and in that case the shaft can rotate attached to the wheel. But this would increase the weight of the assembly.

Even if from geometrical point of view it would run there are some issues.

.- The bearings of the wheel and the beams would be almost dimensionless
and the gap between inner and outer ring of the bearings almost nil.
Maybe a kind of magnetic bearing would be better.

.- Elasticity between beam an small circular part to be carefully analyzed.


.- A bigger central circular part and more than two beams would probably run better.

Prototype will explain...I hope.
The real problem is not believing it to be possible
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