A double parametric pendulum, linked to a seesaw axle, could be the solution...

[path_finder]

For those new guests in this forum not familiar with the parametric pendulum, the Botafumeiro can be seen here (again):
http://www.youtube.com/watch?v=hBJsaxWiCL8
The principle is explained here and you can test it manually yourself:
http://www.sciences.univ-nantes.fr/phys ... meiro.html

As you can see the rotation is perfect when the length of the pendulum
- is reduced at 6:00 (when you pull the rope)
- and extended at 12:00(when you loose the rope).
Now imagine a vertical plate with an horizontal axle in the middle.
On each side of the plate is a pendulum rotating on this axis.
The pendula are fixed at the same axle but in opposite direction (when the side A pendulum is at 4:00, the side B is at 10:00).
In that configuration this assembly is perfectly balanced and shall find its equilibrium somewhere (depending of the residues of friction).
If you move one pendulum, the full assembly rotates on the both sides of the plate, and if there was not friction at all, would rotate indefinitely.

Now look at the double 'botafumeiro' modification:
Imagine that the previous axle is not a simple horizontal rod rotating inside a bearing, but a small seesaw (teeter-totter), like shown in the picture below.
(I will later try to make an gif animation).
When the side A pendulum at 12:00 falls, the side B pendulum at 6:00 lifts up
When the side A pendulum at 6:00 lifts up, the side B pendulum at 12:00 falls
The rest of the time the both pendula still keep the middle range circle position.
All over the time this assembly is remaining balanced (on a strict gravitational point of view).
But the two parametric pendula meanwhile reached a more and more greater rotation speed.

This is the working principle of this double parametric pendulum.
Now the question is: what should be the mechanism able to animate the seesaw at the center of the plate?
The MT138 workers can be useful in this case to do the job...
Please note that for starting a gentle push is needed.

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I want to apologize for the error made in the last drawing: the in air floating red path was wrong.
I'm surprised nobody mentioned that point to me. Perhaps this topic did not interested anyone. But anyway.
This does not change anything on the suggested concept.
The correct path is shown this time in the first drawing below.

The purpose of the second drawing is to give more details on the way this assembly is working.
First, although the previous drawing just showed the both pendula in a theoretical attitude, the next one solves the mechanical constraints in view to obtain not only a rigid pendulum, but also it's path wich must be parallel to the plate. For this goal each twin yellow weight is fixed to a frame made of a two parallelograms linked with some rods.
So far the animation shows only a side of the plate (the other side can be completed with the same structure, but with a 'point symmetry' across the center of the plate.

The light green crown rotates around the center of the plate thanks to the small white rollers (their flanges and bearings are not represented).
The frame's main axle is a diameter of the internal hole of this green crown.
This axle is the support of the first corner of the parallelogram frame.
The second corner of this frame rotates around the axle passing through the two other points located on the green crown.
The right part of the drawing shows the two positions (red and blue) taken by the pendulum frame (the weights are in yellow).

The light green crown (supporting the both pendula) rotates with a direction coming from the starting gentle push, but in the clockwise direction if the first drawing above is respected.
The animation shows the path of the weights, surimposed to the conceptual drawing.
There is a possibility to include a second frame inside the first, a little bit smaller (to avoid the mutual collisions) and dephased of 90 grades from the first frame (the axis will be crossed with the first red-blue main axle)

The remaining question is: what mechanism will be able to invert the seesaw two times per turn almost at the vertical position of the pendula

[Bill_Mothershead]

Perhaps this topic did not interested anyone.

VERY interesting but....

1) people (expecially us Americans) are likely intimitated by
the first site being unreadable (not even educated enough to
know what languge it is in).

2) jumped into the video expecting it to be a science experiment
perhaps in a barren lab or classroom but got some kind of
religous ritual in an old cathederial. Not expected.

I kinda, sorta, see just a glimps of something like a caos
pendulum setup, except without the caos.

Looks interesting to me. Also looks like a lot off work on
my part to bootstrap up my understanding of pendulum physics
to where I could begin to ponder a working device.

May I offer words of encouragement to continue this thread.

Please make the animated GIF you were talking about.

[ruggerodk]

PathFinder:

In a paralellogram the weights will be in balance (Desaguliers) and you will not have the expected seesaw effect, which I believe is the main function of your setup.

regards
ruggero ;-)

[path_finder]

Dear Bill_Mothershead,
Please be patient, I will build the animation asap.

Dear ruggerodk,
You are absolutely right on the full balance of this assembly, wich is in fact a big advantage and in particular at 6:00/12:00 when the shift occurs.
The acceleration obtained in this suggested design is coming not from the gravity (like for a common unbalanced wheel), but by the change of the pendulum's length (acting each as 'parametric pendulum').
I don't know if Bessler like a lot of christian people at that time was once a pilgrim to Santiago do Compostella, and if he saw the Botafumeiro.
Perhaps just someone explained to him how this pendulum was working.
In any case my intent was to use the Botafumeiro principle, not for just one pendulum but with two pendula in opposite direction.
If you made the test yourself with the Java animation, you should find the way for accelerating the botafumeiro: shorting the pendulum at 6:00 and elongating it at 12:00.
Fortunately these two actions can be taken together by the same mechanism (the last part not yet solved today, see below).
The purpose of the parallelogram frame is only to assume the parallelism of each pendulum against the plate (a single rod, even rigid, will not be able to keep the good position instead).

Now the question of the seesaw motion:
A first level solution could be to use a simple cam, fixed at the center of the wheel, and to link an arm of the parallelogram with a rolling digit.
What is strange with the shape of this cam, is the maximum size allowed for the two parts wich finally gives the famous 'yin-yang' pattern.
Basically the monks (those pulling the rope) had their shoes on the floor. But IMO they brought some additional energy from outside. If we want to obtain an autonomous system we need to find the shifting energy inside the assembly.
I think I found a mechanical way much more efficient than an use of a centered cam, wich brings too much friction.
This mechanism is based on two 'geneva stop', a kind of mechanism already in use by the clockmakers at the time of Bessler.

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Hereafter is the animation showing the motion of the two pendula in opposite position.
The red pins are the rotation axles of the pendulum arms.
The length of these arms is variable because the rotation of the seesaw (not shown here) included in the mechanical frame.
This mechanical frame (seesaw, parallelogram, gears and 'geneva stop') has been replaced by this virtual black rods, in view do not complexify the explained principle (two botafumeiros rotating a full 360 grades turn)

[path_finder]

What can be the mechanism able to move the both pendula
(in the vertical plane and in accordance with the reference path shown in the above drawing)?
We need a mechanism giving a translation.
The following first animation shows one solution but not directly usable.
This translation occurs at the right time (12:00 and 6:00) but is horizontal.
How to convert this horizontal translation into a vertical one?
We should better say: into two opposite vertical translations, one UP for the pendulum at 6:00, and one DOWN for the pendulum at 12:00.
The theoretical answer is: by a rotation of (respectively)minus and plus 90 grades.
This rotation can be obtained by using an extension for the original legs, by the way of an additional leg orthogonally linked with the main one.
On the second animation below the modified legs are in red.
The ends of the orthogonal red legs are linked with a rigid (blue) rod. This rod is not absolutely needed, but it contributes with the rigidity of the mechanism, and it's middle point follows the vertical plane.
The blue arrows show the two accessed positions.
Only the 12:00/6:00 moving positions have been represented on this animation.
This mechanism is simple and efficient, but does not respect the ideal path: the opposite pendula must have an opposite motion, wich is not the case at this level with the suggested mechanism (the both extremities are moving in the same direction). Any idea?
One more time the spirit of the MT138 workers is shadowing this forum. Hum!...
On another hand this mechanism is similar with the translator used inside the pipe organ. Hum!...
Should we are on the right path?...

[AB Hammer]

path_finder

Look at it "side ways" and you will see the problem. One weight in the middle and one at 6:00
I have built this before in my earlier experiments.

[path_finder]

Dear AB_Hammer,
Here is the situation you are refering (I presume).
This the shifted 12:00 position, followed by a 90 grade clockwise rotation.
Can you precise your comment?
Many thanks in advance.

[AB Hammer]

path_finder

I will look through my older wheels and post the one where I use them as shifters to the your blue line was a weight in this design. I am not sure if I have a photos on just the connection. I did photo everything.


edit addition. I am going to have to go to by old back up CDs to find it. It is not on my flash drives. This may take awhile.

[path_finder]

Dear AB_Hammer,
Many thanks for your comments.
This above mechanism is not intended to be a part of a primemover.
The blue rod is just a mean to rigidify the mechanism, wich in addition must be the lightest as possible.
It's purpose is just to shift the 'double parametric pendulum' at 12:00 and 6;00.
Because this 'double parametric pendulum' is always balanced, the energy needed for the shift is enough low to be taken from the rotational motion.
I want to confirm this within the next weeks.
Your experiments will be useful for sure.

[path_finder]

The previous animation shows the way for lift-up the 6:00 weight, but not to fall-down the 12;00 weight.
The question now is: What could be another mechanism able to invert the previous one?
The solution is easy: we need to add a true seesaw (teeter-totter) at the center of the wheel and link it with the previous mechanism.
The next drawing shows the principle (first position in red, second position in blue).
The weights are located at A/A' and B/B'
The both mechanisms shall be combined.
Now it's time to make an animation combining all these parts (be patient).

[path_finder]

Some animated examples of useful cam mechanisms:
http://www.flying-pig.co.uk/mechanisms/pages/cam.html
http://www.technologystudent.com/cams/camdex.htm
Readable with your navigator (IE, Firefox, Opera, etc) if supplied with the Flash plugin.
If not, the Flash Player software is loadable here http://get.adobe.com/flashplayer/

First animation: a complementary mechanism for the motion of the MT138 workers?
PJ: mechanisms_cam4.swf

second animation: “Jeeves, where’s my tea?!�
PJ: mechanisms_cam5.swf: the bellcrank, a mechanism also very often used inside the pipe organs.

Third animation: a rotating plate making an angle with the vertical axis
PJ: mechanisms_cam8.gif (for some reasons this gif animation is not well displayed, click on it for a better view)

[path_finder]

For memory, an old thread in relation with the same cam mechanism:
http://www.besslerwheel.com/forum/downl ... 2c9db33db1
Just imagine this MT124 crown as a vertical cam.

Thanks to jim_mich.
But the suggestion given for the black ribbon (a shadow) is not correct in my humble opinion. I prefer to think about the reflection in a mirror, indicating that this mechanism should be doubled (the second unit shall be inverted).

[DrWhat]

path_finder, you need to look at the paths the balls follow. It is like an optical illusion diagram. You'd think that the balls go fully around the track, eg if pushed. But they don't. They fall off because the paths disappear!
Have a good look!