An explanation for the 22,5 grades angle

[DrWhat]

The comments that Bessler's wheel seemed empty could point to just such a design (but what is the solution?)

Usually the issue with a 'wheel inside a wheel' is that whatever the small wheel does inside the big wheel, then the small wheel should NOT also do when placed on the ground by itself. The dynamics need to involve the bigger wheel in a different way.

So whatever you design, take out the small wheel and ask yourself "did I really need the big wheel in the first place?" And this helps rethink the design.

D

[path_finder]

Dear ABhammer, not_me and DrWhat, many thanks for your comments.

@ABhammer,
Just one small suggestion:
if the hamster cannot climb high enough, why do not push it by another mean at the right moment, giving to him the small missing encouragement?
A such way in particular could be a second hamster, rolling on the descending side of the wheel (between 9:00 and 6:00) and linked with the first one.

@not_me,
The big question is not to know if the hamster shall be inside or outside the rim of the wheel, but how to lift-up the hamster at the top of the wheel whatever the used path.

@DrWhat,
When you say: "did I really need the big wheel in the first place?" are you referring to this concept
http://www.besslerwheel.com/forum/download.php?id=6504
where the function of the axles are inverted (power,control)?
Or do you have another idea in mind?

[path_finder]

Let's continue the examination of the conditions needed for the highest climb of the cylinder (hamster).

During the climbing the hamster COG must be always at the east side of the vertical line passing through the contact point (assuming a clockwise rotation of the main wheel).
The dimension of the cylinder has been chosen half of the main wheel.
This particular ratio allows us the benefice of a rotation speed for the cylinder doubled versus the speed of the main wheel.
Now, on the next drawing we suppose the main wheel locked (no rotation authorized).
The rolling cylinder (hamster) starts from the 6:00 keeling position (points A and B)
We suppose the internal unbalance allows it to climb until the points A' and B', corresponding with a rotation of 45 grades on itself.
The hamster COG on this drawing is the red circle, and if located at the middle of a radius (like in the drawing), we can see that at the arriving position this COG is at the west side of the vertical line passing through the contact point B'. So far this is not correct.

If we want to have the COG always at the east side of the vertical line passing through the contact point, the only solution is to locate the COG at the point B (and finally at the B' position). This means that the COG must be located at the extremity of the diameter and at 3:00 of the cylinder (when at the keeling position). Here again we retrieve the hypocycloidal motion along a radius.

The above defined position is a minimum, and may be not sufficient with the friction.
There is another way to solve this question: make the COG more external, in view to be whatever sure that the COG is more east. In that case the curve followed by the COG will be a more complex cycloid (like the writing ornaments of Bessler?). I will try to make soon the corresponding animation.

Anyway the drawing below was supposing the main wheel locked.
But now what happens if the main wheel is left free? It's obvious that everything depends from the mutual interaction of the masses.
- If the main wheel is really heavy and the cylinder too much light, the hamster will have a small effect on the main wheel rotation, but instead will have no particular effort for climbing more higher.
- If the main wheel is really light (made in balsa wood) and the cylinder is very heavy, the hamster will drive very soon the main wheel and thanks a very low torque.
So far the question now is: what shall be the values of the both masses?

[path_finder]

edited (published twice by mistake)

the post continues here:

the secret could be in the ratio between the weight of the main wheel frame and the weight of the hamster...


Just a suggestion how to implement easily a ratchet, locking backward the hamster:
The simplest way: just a rod (in violet) jumping from tooth to tooth (the 'small curved planks' discussed in another thread)
A more cleaver way: a very light cylinder, sticked always with the hamster thanks an helicoidal spring.
See the drawing below.

[path_finder]

Dear all,
I made some complementary calculations, in particular to detect what kind of assembly can overpass the 45 grades position.
Why 45 grades? it's because if the hamster is able to climb until the main wheel diagonal, then the clutch (ratchet) will restore it after a 45 grades backward travel of the main wheel.
In fact there is a big unknown parameter: the rotation speed of the main wheel.
Everything is depending from this rotation speed.
If this rotation speed is fast, the cylinder (hamster) will reach the 45 grades position very easily.
But this rotation speed is depending from the torque, therefore from the position of the cylinder versus the keeling position.
This is a dynamic assembly very complex.

In the following drawing we can see a primover based on two blue weights sliding on two orthogonal rods (therefore retrigered every 90 grades).
The relative motion between the main wheel and the rolling cylinder (hamster) has been respected (when the main wheel rotates of N grades, the cylinder rotates of 2xN grades).
But this is not sufficient, because if the main wheel rotates more quickly, the cylinder we be sometime positioned at the west part of the keeling position (in this next drawing the rotation has been repartited equally between the both parts).
The drawing shows the mutual positions when the main wheel was rotated of 0 - 7,5 - 15 - 22,5 grades.
The contact point is the violet cross.
The COG is the blue cross.
With this design (and with this rule for the main wheel rotation speed) we can see that the COG passes on the West between 15 and 22,5 grades, a poor result in fact.

As explained above the masses of the moving parts do have a big importance.
This is the reason why, at this step of the reflexion, only the practical experiment can tell us what's really happens.
I built a such as assembly, and will give you soon the shots and the results of the experiments.
But now some reactions indicate to me that the end of the road is here.

[path_finder]

In a previous post I suggested to give a small encouragement to this poor hamster, allowing it to reach the 45 grades angle.
Here is a way for.
In this animation below is the combination of two important concepts shown above.
Now the backward locking rod is not independent, but it's the weight itself during the return path.
This new concept has three enormous advantages:
- the weight is attached with the outer rim of the main wheel (not contributing anymore with the hamster COG).
- the COG of the hamster pushes on a better way (this time at the back side and not only by its weight).
- the weight on the left side can be repositioned at the reset point (9:00) by the main wheel (acting like a flywheel).
I'm asking me what could be the own mass of the hamster (apart the sliding weights) versus the mass of the main wheel frame.
The unit I'm building will give me the answer.

[DrWhat]

pathfinder,

this has already been built! Cheers.

Sliders on other side (unseen) of small wheel are 90 degrees out of phase.

[path_finder]

Dear DrWhat,
Many thanks for sharing your data.
Even if the shot is explicit, there are apparently some small differences with the above animation.
First the size of the hamster seems to be much more close from 5/12 instead 1:2 used in my animation.
The sliding weights are not exactly the same, in your wheel they travel on the diameter of the small wheel, instead in my design they are outside of the hamster.
At least I cannot see the clutch (ratchet) mechanism, needed for locking the climbing hamster at the highest point.
Can you precise the results of your experiments, and if it works in this state what can be the mutual ratio of the masses between the main wheel and the roller (hamster).
Did you made some modifications after this step?

edited:
I found again your previous post, where this wheel has been shown yet.
It seems to be much more close from this (as explained at that time):
http://www.besslerwheel.com/forum/download.php?id=6968
But IMHO this last concept is not sufficient. The weights must go outside.
Another alternative is perhaps in the exchange of the axles, like here:
http://www.besslerwheel.com/forum/download.php?id=6504

[DrWhat]

pf, I gave up on this idea shortly after building this. Realizing as such it would not work. The rod weights sliding ended up smashing various parts, even though I had springs to soften the impacts at the ends of the tubes.

I don't have exact dimensions any longer.

I then moved house and like Bessler had sadness but also great joy at smashing up the wheel. Needed two skip bins to get rid of all my perpetual headaches.

[path_finder]

All experiments I made changing the parameters (ratio, lengths, location, etc) conducted me to the big following conclusion:
if the hamster runs at the bottom of the wheel, the excentricity of the COG will never be sufficient for reaching the 22,5 grades position.
It's some wasted time, but perhaps not completely loosen, because now I know why all 'Somerset like' wheel have been misused until now.

Many thanks to DrWhat. He said somewhere the axles shall be exchanged.
Thinking about this pertinent comment, I remember a reflexion of Bessler: somewhere he suggested to invert everything.
Very confident in my 'hamster' concept, I reconsidered the position of this poor running pet: why not on the roof, outside, like tested, but not below.
Basically there is no particular prohibition to put the hamster at 12:00 and to leave him free.
This position is particular, and if perfectly standing at 12:00 this hamster will be in a metastable equilibrium, keeping it's position only by the mean of the friction on the main axle.
Then if rotating clockwise the hamster shall be reversed and climb in the direction of 12:00 (the contrary if counterclockwise).
The mechanism able to do a such as counter-reaction is very complex.
So far I decided to exchange the axles.

Instead to refer always with a central axle, I made some investigations on the way to dispose the main axle of the wheel with a different way.
One particular assembly seemed to be interesting: imagine an hula-hoop hung on a rotating cylinder (only the axle of the cylinder is fixed to the ground).
The hula-hoop can not only be a pendulum but also rotate on itself.
Because the friction any rotation of the hula-hoop drives the internal cylinder with a kicker rotation but in the same direction.
The motion of the hula-hoop can be also the behavior of a pendulum.
By combining the both motions (rotation and pendulum) we can obtain an efficient counter-reaction

Applying this concept, the main wheel will be an hollow cylinder, supported by an internal rotating cylinder, with the contact on the inner rim of the main wheel.
The animation below shows the concept.
The main wheel (in red) is unbalanced, retriggered every 45 grades by the sliding balls (the hamster). It's axle is free.
The behavior of this wheel is basically a pendulum, but this wheel can also rotate around the internal cylinder (in blue).
This rotating cylinder has an axle fixed to the ground, and therefore supports the whole assembly.
Because its size has been selected half of the size of the main wheel, it rotates two times kicker than the main wheel in any conditions (permanent or stepped).
This ratio allows the right timing for the retriggering.

As explained before, the purpose of the animations is only to show the wished goal (not always the reality): then it is your job to find the way for.
But caution! in that state (no pendulum motion taken in account, only a regular rotation) it will not work, some important improvements are needed (coming soon).

[Trevor Lyn Whatford]

Hi Path-finder,

I have done a lot of work on the hamster wheel! they look cute but the hamster will bite you!

The force of the hamster is normally from the axle to the rim thus lock up!

the force need to a downwards force! by placing your foot on a bicycles front wheel at 5 o,clock will move the whole bike, then you are sucked in and the hamster bites you!

I saw a possible hamster wheel in Jims reservoir compression system, wherein the hamster was fluid weight chased by a compression roller, the fluid weight is a downward force and thats why I got excited! I will try and bring it here.

Regards Trevor

Edit,I tried but it did not work!

[path_finder]

Dear Travor Lyn Whatford,
Many thanks for your comments. I agree totally with you: in that state it don't work.
Put your pedals at 12:00 and 6:00 and push on vertically: nothing happens.
But suppose than meanwhile the axle of your pedals goes backward: your COG will apply a torque, wich is independant from the pedals. The key is into the combination of the pendulum and the rotation.

edited:
Just a small improvement.
In view to show that the 'Somerset like' wheel is not totally stupid... It depends from the way you use it: for sure, rotating on a central axle it will never work.
But in combination with an pendular axle (with a correct timing)?
NB: no clutch are included yet in this animation. so far the red axle seems to be standing at it's keeling position, instead in presence of some clutch it will oscillate a little bit.

[path_finder]

Next improvement:
Let's suppose now that the axle of the blue cylinder is free (not fixed to the ground like above before).
The cylinder is now supported by a plane, acting like an arm of Roberval balance.
The motion of this plane is coordinated with the displacement of the both wheels and with the clutch inside the blue cylinder axle.
Hereafter a drawing showing the concept.

edited:
some aspects of this design have perhaps a connection with the structure used by Mr Hamel. See here:
http://jnaudin.free.fr/html/hamelfs.htm and the animation:http://jnaudin.free.fr/images/h45banm.gif
and perhaps with the principle used by the Gurbakhsh Singh Mann gravity machine:
http://gurbakhshsinghmannglobalenergy.com/biz/index.htm

[Trevor Lyn Whatford]

Hi Path_finder,

I believe that the answer to the hamster wheel is fluid displacement as just like a hamster you need some thing that runs!

When I get some time I will draw what I have in mind! at the minute I have to many Ideas floating around in my head that need to be worked out first!

Regards Trevor

[path_finder]

The most important improvement: the counter-reaction mechanism.
As suggested above we can let shift the axle of the blue roller on the both sides of the metastable position.
The use of a plane is possible, like the well known exercise, see here: http://www.youtube.com/watch?v=tiICyn_OgRw
But it's not sufficient: when the hamster falls at 1:00, she must climb back to 12:00.
There is another way much more clever: instead to move up the hamster, turn back the main wheel
This can be done very easily with a gear mechanism, where the extra gear let reverse the main wheel
This principle is shown in the drawing below.
(in addition there is the path of the weights)

In this drawing the ratios are: 180-150-30 (either 6-5-1). Several ratios are possible, but in the case of Bessler Gera wheel the number of teeth will be: 120-100-20.
When the main wheel rotates clockwise, the small red gear (a real part of the main wheel) applies a counterclockwise torque six times stronger, but meanwhile the blue roller has rotated. A full animation showing the whole operation will come soon.