An explanation for the 22,5 grades angle

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I was a little bit surprised by the fact nobody objected that in this state the above counter-reaction mechanism was good for the understanding but wrong for the motion.
Any student in mechanics shall have seen the locking state of the blue cylinder. (DrWhat is perhaps more in the arms of Morphea).

The purpose of the small gear is still to retain the main wheel when the hamster falls.
In the next drawing, this time more in accordance with the laws of the mechanics, the small gear is still here (in yellow), but sticked with another gear, the both being centered. This cog twin assembly is connected with two other gears (in yellow) linked together by a rod also centered.
This assembly allows the yellow gear connected with the blue cylinder to make it's counterclockwise job and to control the position of the blue cylinder (wich shall be at any time located at 12:00). The two yellow satellites can move up and down, depending of the unbalance of the main wheel.
Any comments are welcome.

[nicbordeaux]

Any comments are welcome

Well, for starters you are going to need an awful lot of rodents because if you build that thing, the hamster will be mangled.

[DrWhat]

pf I know it's extra work but an animation would be helpful to elicit comments perhaps.

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Dear all,
I was not very satisfied for abandoning the poor hamster running on the below part of the wheel, for the single reason that apparently there was no way to overpass the 22,5 grades barrier. So far I decided to remake my calculations, this time to be sure on the truth of this assumption.
After review of a large panel of parameters, I was obliged to recognize I was wrong: there are some values able to assume the requirements, and in particular this famous 12:5 ratio giving the path of the MT137.See here for memory:http://www.besslerwheel.com/forum/viewt ... 1201#71201

In addition there is the famous drawing 'and you still don't understand' not yet explained.
On this last subject I'm convinced since a long time this drawing has to do with the hypocycloid of ratio 12:5
You can check this motion with the Java applet here (Java plugin required):
http://www.carloslabs.com/node/21
Go to the hypergraph section, select 'hypocycloid curve' and then select the following values: 24, 10,10,5

( better: 24,10,8,5 if the size of the weights is taken in account)



What is surprising with this ratio is the position of the COG and the contact point after a 45 grades rotation of the hamster, but only for a particular design.
If we put the 5:12 sized hamster rolling inside the inner rim of the main wheel, it don't assume the requirements (angle expansion and COG position).
Like explained above (I was right at this point) any design where the hamster is rolling below will be unsuccessful.
Remembering my second observation (the weights must be outside of the rolling rim, see above) I made further studies on some designs where the rolling hamster had the weights outside of the rolling path. And therefore I came on the design where the hamster was rolling on a subset of the main wheel.

The 12:5 ratio can be obtained this time by a wheel two times smaller, giving a relative 6:5 local ratio.
This is interesting because the 'ghost' turn can be taken in account, compensating the 6th missing turn.
See here for memory: http://www.besslerwheel.com/forum/viewtopic.php?t=3611
This point confirms the use of a rolling path equal to the half of the main wheel
The final main wheel will have two parts:
- an internal mechanism creating the unbalanced state (but alone not sufficient)
- a hollow cylinder of half size and centered on the same axle (where the inner rim will be used by the hamster).
This design is shown in the drawing hereafter.

The main wheel mechanism has not been represented in this drawing (some example can be taken from the various animations above).
The main wheel is in red, centered in A (main axle) and the hollow cylinder is in rosa.
Due to the size reduction we got at this point a first lever with a 2:1 ratio.

We will use now a rolling hamster respecting this 12:5 ratio
The hamster is made of two parts also:
- an outer rim with a size of 10:12 of the main wheel (where will be linked the 'outside' unbalanced mechanism)
- a cylinder with a size of 5:6 of the main wheel internal small cylinder.
The hamster is in blue in the drawing, centered in B and it's rolling cylinder is in light blue.
The contact point C is in violet, and represented in the drawing at the exact point where the climbing of the hamster is maximum.
The mobile sliding weight (in yellow) goes from D to D' in this example.
With the selected ratio, when the main wheel rotates of 37,5 grades, the hamster has rotated of 45 grades in the same time.
The hamster is always in advance on the main wheel for the retriggering with this values and the COG is at the west side of the contact point.
The main torque is applied on the B point and depends from the global COG.
Here we retrieve the question of the ratio between the weight of the main wheel and the weight of the hamster.

As you can see the calculation of the motion is very complex, and everything must be recalculated if you change one part in the design (main wheel, main ratio, value and size of the weights, etc).
Thus an animation is difficult (I will try to).

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Dear all,
I made some new experiments with the 'hamster design', and using the 12:5 ratio as justified above.
After several trials I did not get the expected results from the building phase for this reduction mechanism: I have no lathe and it is not easy to manufacture the needed gears.
The quality level is not high enough for a reliable operation (some teeth are sometime missed and the timing will not be respected).
At this point there is only one solution: subcontract the gears manufacturing near a third party (almost professional).

But I was frustrated (not by the money for, but because to be obliged to suspend my tests until the delivery).
And I asked myself: what can be used in replacement of these gears?
I remembered my old tests made with some polygons, see here:
http://www.besslerwheel.com/forum/download.php?id=6646
http://www.besslerwheel.com/forum/download.php?id=7005
In the same thread I explained why I abandoned this idea: at that time the synchronization between the both polygons was not sufficient.
But rethinking again on this question I finally found the solution:
if we want to keep a good contact between the sides of the both polygons, an orthogonal force will do the job.
We just need to put a traction on the summits of the decagon, with ten springs all equal but not to strong (there are here just for the correct adjustment of the parts).
And by the way I found a real useful purpose for this *$#è&@ springs...
The drawing hereafter shows how to use some springs for getting a 12:5 reduction without using the gears...
The main wheel is in red, and in the middle is an dodecagon(with 12 sides) with a size one half of the outer circumference
The hamster (in black) is a decagon (with 10 sides) an rolls on the previous dodecagon
The contact is achieved by a set of 10 springs (in violet), linked with the internal wheel (in blue), wobbling free inside the main wheel.

This is a good new, and in a mechanical point of view it works well.
I'm preparing an animation describing the whole content of my new built wheel, implementing this technology.

NB: I'm not an expert of Bessler, and as explained before I do not make my studies from this source of information (only by combining the theory and the building).
Nevertheless I keep in mind all the ideas developed around this remarkable story, and when it's possible I try to make a correlation between my work and the clues (true or false) identified here in this forum.
It is just a suggestion:
in addition of explaining the purpose for the strings used above, I think have another explanation for a mystery not explained yet clearly: the famous 'jacob ladder like' item shown on the right side of the MT138. IMHO this represents a chain, made of TEN (a coincidence?) segments with some hinge, with the purpose to be the ten sides of the rolling polygon (a part of the internal 'hamster' assembly). But who knows?

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Dear all,
I'm a little surprised by the low level of feedback, the previous drawing above being intentionally wrong.
Doing so, I was hoping at minimum one single remark, anyway I want to continue my contribution to the quest...

The next drawing is much more conform with the rules of the mechanical forces.
Because the internal hamster rotates more quicker than the main wheel, it's impossible to connect the springs to the main wheel outer rim
The only solution is to use an intermediate mechanism made by the means of FIVE rollers (in rosa) running on a rim (in rosa) glued (and therefore centered) to the main wheel .
At each axle of these five rollers we can now attach the FIVE springs (in violet). The resultant force will be centered.

If we look carefully at the 'jacob ladder like' item on the right side of the MT138 drawing, we can see the position of the small points (hinges?) wich are alternatively located on the both sides of the item. IMHO this indicates that the decagon, when rebuilt, has FIVE hinges connected to the outside with the springs, and FIVE hinges connected to the center with some rigid rods (in view to keep the pentagon geometry). They are in black on the drawing.

In addition there is another question about the MT138: why the segments of the chain are doubled every two even positions?
IMHO the doubled segments are made of two parallel rods, creating an hollow grover where some big teeth shall enter (in yellow on the drawing), this mechanism allowing a good centering, and also allowing the hamster to climb more higher without slippery.
See the detail on the lower left corner.

New shots coming soon.

edited:
I said

combining the theory and the building...

Let me come back to the theory: the principle has been given June 28th 2009 here: http://www.besslerwheel.com/forum/download.php?id=6685
and is still true. The only concept wich can be reviewed is perhaps the reference to the parametric pendulum: the reality is more simple.

[wheelrite]

very interesting, keep it up. I only wish I had something useful to add .............
regards
Jon

[DrWhat]

I agree. Pf this is your baby and you have a thought process delivering results.

If I have a design I twist and turn every combination scenario etc in my mind, but it's hard to get others to do the same.

I watch and learn and please keep posting as I hope you get a truly impressive result eventually.

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Dear Wheelrite and DrWhat,
many thanks for your encouragements.

[FunWithGravity2]

Great Ideas,

I have often wondered why your hampster does not start at the wheels center and begin to climb towards 2 oclock. As the wheel rotates under his feet he would be preloading the wheel with his own energy and arrive at the perimeter at 3 oclock, now he could use his additional momentum gained from the semi inclined plane that he pushed away from himself and the energy of his position toeasily ride the wheel to 9 oclock. The problem would be that he needs to then get off the wheel and get to the center so as not to slow it down and start the process again.

I have always liked your ideas of the off balanced hamster weight that is designed to mesh correctly with the wheel. Maybe it just needs fine tuning of a simple mech as oposed to more complex mechanical arrangements.


Dave

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Dear all,
My experiments on the dodecagon have been really useful.
Not only for discovering an efficient alternative for the replacement of the gears, but also in the understanding of the way this kind of mechanism can be used.
As you can see in the picture below, these squared teeth are present in the doorsign of karlshafen (may be a simple coincidence?).
I can say now how the flowerbowl was working.
Hereafter is an important animation showing how the chain is obliged to follow the inner rim of the hollow cylinder.
The chain links are in blue (light for the single, dark for the double). The springs are in violet and used in traction mode.
Thanks to FunwithGravity2 wich seems to be the single person understanding the full consequences of this bold above remark.
I know they are on this forum a lot of clever people, wich will immediately pass trough the next step.
Remember this previous drawing here:http://www.besslerwheel.com/forum/download.php?id=7486 and I'm pretty sure you will discover by yourself what will be shown in my next animation, wich is a logical deduction.

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The next step is obvious: we can suppress the internal hollow cylinder with the squared teeth
In the animation below:
-1- the segments in violet are the springs (variable), but all equal and acting in traction mode.
-2- the chain links are in blue light and dark (both are rigid)
-3- the segments in grey-blue are the spokes of the dodecagon (rigid).
. They do have all the same length with two possibilities:
. - six radius rotating on the main axle
. - three diameters rotating on the main axle
but with the same mechanical structuration effect. So far we have the choice.

If all the springs do have the same force, the dodecagon keeps it's perfect polygonal geometry, and the main axle is centered.
In that case everything is balanced.
Otherwise the main axle can be excentered for specific purposes.
We must now attach the hamster to the chain at 3:00.

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One possible use of this mechanism is conform with the MT135 drawing.
If you look at this drawing you will observe the position of the spokes: it's exactly the geometry you can obtain with the previous mechanism.
The drawing bellow shows how the chain links are now shifted depending from the moving side of the wheel.
This time the three grey-blue spokes are sliding across the main axle.
Because their length is no more equal to the diameter, two pairs of opposite chain links are in a different position versus the center.
The MT135 drawing shows when the commutation shall occur: at 12:00 and 6:00.
But they are several ways to implement this principle.

edited: drawing updated

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The corresponding animation (without any primemover)