The summary of my latest studies

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The svastika design (indian version), the prime-mover of the solution? :

As explained earlier here:http://www.besslerwheel.com/forum/viewt ... 1c26#55935
The svastika is a very old sign from the old India.
IMHO the triskelion, the ying-yang, the svastika, the david star, etc. are not only ornamental

Few years earlier I made a first attempt with the svastika, but without any practical test. The idea has been shown here:
http://www.besslerwheel.com/forum/download.php?id=6309
There is no chance for this design in that state to be successful if the svastika is used by this way.

But, but...Working recently on the 'cardan gear' mechanism, I discovered the skills of the svastika (in a strictly mechanical domain).
The animation below shows the concept, where the 'cardan gear' mechanism is multiplied by four, dephased by 90 grades.
The wheel is supposed to rotate clockwise, recovering his position every 90 grades.
The intermediate positions are not represented, a full animation should do it.
The external cogs are half size of the center one, and rotate counterclockwise at twice the speed of the main wheel.
(A reminder for those having forgotten the principle of the 'cardan gear', see here again: http://www.mechanisms101.com/cardan_gear.html)
If you look at the geometry you recognize easily the shape of the svastika (in violet on the drawing).
As indicated in the last slide of the serial, the path (the green arrows) is a full diameter.
An additional mechanism is needed for the division of this path by two, limiting the shift to a single radius during the half time.
Then we can link the end of each of the four rods to any rhombical frame, like p.e. this old one:
http://www.besslerwheel.com/forum/downl ... 992381c97a

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Hereafter some suggestions for the builders.
If you want to test the svastika concept, don't make the same errors like me.
On your plywood or plastic plate don't draw a first circle on your plate and don't make four holes for the center and the four half sized rollers: practically it will never work at all.
Even with an acceptable tolerance you don't have any chance for a good mutual position of your five cogs.
I cannot translate this in english (in french: 'rattrapage de jeu') but a correction of the mutual distance of the teeth is needed and cannot be obtained by just a fixed distance between the axles.
A dynamic correction assembly is needed.
If you refuse to use some sophisticated industrial means, CNC parts, etc (in a car gear box, it's name is the synchronization pinions), and if you consider that at the time of Bessler and earlier at the Egyptians ancient time, no such as technology was available, the old good methods are the only solution.
This simple solution has been remembered recently by Stewart (I take now the opportunity for salute his rigorist but pertinent contribution) here:
http://www.besslerwheel.com/forum/viewt ... 0c4e#80711
On a mechanical point of view this method has been shown also here:
http://www.besslerwheel.com/forum/downl ... 962a274795
Note by the way we recover perhaps the springs of Bessler, 'not used as you think'.
At the same point of the reflexion you can ask me why I used some gears with teeth when I declared earlier that IMHO Bessler did NOT used this method. The answer is simple: I'm pretty sure (not yet full tested but already a good feedback) that the flowerbowl was working with only simple rollers: even with a small shift, it still works.
IMHO Bessler used some polygons (just a personal impress).

As explained many times before I'm specially interested to replicate the 'flowerbowl'.
This is the reason why my building is of 'order three' (three 'cardan gears' at 120 grades)
But I still think Bessler used the same principle in some of his wheels, based on an order four design (four 'cardan gears' at 90 grades).

The three shots below show:
1. The sub-assembly of the first stage, including all the designations.
2. The three rollers (20 teeth each) also doubled (for a stable motion) and the three control springs.
The six links are made in thin transparent plastic, reducing the room and the friction, but strong enough for the requested effort.
They are also used as guide along the middle plane part of the fixed couple of centered gears.
3. The first stage of the building: the double centered gear, fixed to the ground, and with 40 teeth. A crank and an handle are provided for the start/stop experiments.
This 'one side' part need an elongated strong support outside of the main wheel for the two bearings.

I apologize for the bad quality of the shots, because taken in the night at the electrical light.

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The next stage of the building: the counter-rollers and the actuators
In the shot below you can see the three counter-rollers.
On the same secondary axis they are on the same shaft than the cog supporting the rotating actuator arm.
There is a mandatory for the exact respect of the squared triangle geometry of the assembly. If not fully respected the reference points will follow an elongated ellipse instead the straight segment.

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No, this is NOT a new replication of the Keenie-Buzzsaw wheel.
This is a new implementation attempt of the animation 'MT137_55b.gif' above.
See here again:http://www.besslerwheel.com/forum/viewt ... eb22#80917
You need some complementary explanation: the last picture showed a 'wrong good idea'.
The previously built frame was really interesting, giving a perfect geometrical shape (dodecagon).
See here for memory: http://www.besslerwheel.com/forum/downl ... 72cc7f76ae
But my experiments demonstrated to me the following conclusion: a simple genuine polygon is not very useful.
The rigid faces of the polygon allow an erratic slippery of the rods.
The reference position must be still kept whatever the motion of the wheel.
Thus I was unable to make the test, so many pins not keeping their reference position inside the physical corner.

I decided to review the full building.
Some previous experiments gave to me the confirmation the best way is similar with the 'cycloidal reductor'.
Remember here:http://www.besslerwheel.com/forum/downl ... 64bd1ff5e0
Thus I decided to implement this technology but by a new and particular way.
The idea is to use some small rollers at the same time for the inner rim of the wheel, and for the mobile 'jumping' rods.

- The first shot below shows the cage (main wheel) with the double set of 12 circular pins.
For a better understanding on the shot we can see two parts (at 12:00 and 6:00) simulating the both reference position of a mobile rod.
- The second shot shows the FIVE mobile rods. Note for each of these rods the four black rollers assuming the motion in the inner rim of the wheel.
Each one is located in a specific plane (five parallel planes)..
This shot lets think to the musical notation of the Bach's canon.
- The third one shows the fully equipped wheel with the FIVE rods supporting the couple of weights.

Now the motion is correct and there is no erratic slippery any more.
The bottom pin is now correctly adjusted (at the right corner of the dodecagon) between two circular pins of the external plates (the rods falls down a little bit at 5:00 inside this place).
Next step: with the springs.

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The motion of the five rods inside the wheel is similar with the 'twirling baton'.
Just for the fun, the 'twirling baton parade':
http://www.youtube.com/watch?v=57vkPCYpe6Y
The reference of Bessler for the toy of the kids on the street?

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looks amazing, I do like to see your trial builds.

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Some members recently reproached me with the display of not working designs, I had some hesitations to publish these new shots.
But as explained many times before, the truth comes from the wrong designs, which allow us to discover some aspects instead not covered before.

These shots show the final assembly of the design described in details above.
I had some difficulties to build it, in particular to adjust the exact distances in view to obtain an efficient flip at the right moment.
As you can see on the video each of the five rods flips correctly at 12:00.
In the video the wheel is moved manually by myself, the only purpose being to test the correct flipping motion.
I made all available improvements for reducing the friction, but I cannot really determine if this wheel could rotate alone (with the springs included, what is not the case in the video).
So far the best conclusion is: in that state it does NOT work alone.

But this wheel has been really useful for my understanding of what IMHO is the basic principle of any gravity wheel: the relocation of the COG.
For the good observers (they are a lot), the path of a particular point of each rod will be important.
Remember here: http://www.besslerwheel.com/forum/viewt ... 9257#59257
Indeed what I have learn from this building is:

1. A single primemover cannot be alone the solution.
This is a confirmation one time again of what I (and not only myself) repeated many times before.

2. The active primemover has no need for lifting any weight.
The purpose of this primemover is just to modify the geometry of the second (active) primemover.
In that case this primemover is always balanced, and its COG is permanently relocated

3. The second primemover is the only active part of the assembly.
The purpose of this primemover is to transform a linear motion of the weights into a rotation.
The only mechanism able to do this kind of job is the reciprocator
Remember here: http://www.besslerwheel.com/forum/download.php?id=6019

4. At the minimum two orthogonal displacements are needed.
Usually they are synchronous, but it works also sequentially (one translation at each time after one)
Therefore the role of the first primemover is to actuate alternatively the two moving parts of the reciprocator

5. The geometry of the first primemover must approach as soon as possible a circular path for the COG of the second primemover.
With a geometry too much primitive this path is a curved polygon (a deltoid per example, if based on FOUR rods).
The MT137 drawing is the visualization of this COG for a number of TEN rods.
More greater is the demultiplication of the first primemover, better is the shape of the final circular path of the second primemover's COG, but in this case the size of the wheel must be also greater for accepting this population, what in return allows a better flywheel effect.

For the moment my latest experiments are based on the second primemover (including a reciprocator) already shown here:
http://www.besslerwheel.com/forum/viewt ... 4062#74062
It will be completed by a first primemover based on the same design than on the shot below.

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My recent experiments are directly in relation with my comments to our friend Fletcher,
here: http://www.besslerwheel.com/forum/viewt ... 1759#81759 (and some other above).
The animation hereafter shows the principle developed in these topics.
I built a wheel implementing this principle, which have been almost confirmed.
The video below show the validity of this concept (a little bit short because the size is limited for the files in this forum).
Some remarks:
- the weights are all identical. They appear different in the video because the parallax effect.
- the geometry shown in this video, reflecting an temporary version, is not complete.
Some improvements are needed for a perfect auto-retriggering.
The final design will be published soon (before the 12th ton of 'Big Ben').

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As promised, the wheel built in accordance with the above animation (my last shot of 2010).
The key of the success is coming from the exchange of the COG between the two vertical arms at 12:00, allowing the passage of a virtual weight from on side of the vertical to the other side.
All these operations must be held with the COG above the rotation axle, assuming a permanent metastable state (it is the same principle used with the bike).
The string allows the anticipation, creating an permanent unbalance (on the shot not all are viewable).
The eight weights are all mounted on bearings and free to rotate during the motion of the wheel.
The four red crosses indicate the location of the four pinions were the arms are rotating.
The clue of Bessler 'who is able to lift-up a weight etc..' is assumed here four times by turn between 11:00 and 12:00.
In addition the black dot in the Bessler drawings is often NOT a single mass, but the result (COG) of two or more weights.

More infos in the next days.
Right now, I want to spend the first minutes of 2011 with the 'woman of my life' (since 1969). Happy new year 2011 for all.

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post removed (data base access error).

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This new step in the building is in direct relation with my previous explanation here:
http://www.besslerwheel.com/forum/viewt ... 1799#81799

What all this has to do with the gravity wheels?
With the Besslers's wheels, I don't know.
But with my wheels I know well where this additional term will have an action.
Perhaps you asked yourself why I took the care to mount my eight weights on some bearings.
The version in the previous shot is not complete, an important feature being not yet included.
The purpose of this mechanical improvement is to recuperate by a ratchet the additional angular momentum coming from the relative rotation between the main wheel rotation and the local inertial rotation of the weights.

Thereafter two shots of the wheel implementing these features (not the springs yet, neither the ratchet).
The first one has been taken during the horizontal setup, the second is the standalone version. Note the two different orientations of the rotation axis (the main ones in red are horizontal, the secondary in yellow are orthogonal, giving the extra torque)

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Another attempt using the same concept, but this time of order FIVE (just for verify the JC assumptions).
For a good work all built wheels using this concept must be perfectly balanced. Instead any unbalance point drives to a little bit before 360 grades.
Then there are several ways for connecting the springs.
My experiments drove me to these conclusions:
- the best place for the spring linkage is the middle of the rod
- the most efficient assembly could be this one with a large number of rods (may be few dozens) with a minimal shift for each couple.
This shot hereafter shows the version with five couples of weights (without any springs).

Note: More and more my practical experience is increased.
IMHO I could NOT have got these data from any simulation program, neither from any Bessler drawing nor clue.

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Some good news...
After several years of studies I got finally the meaning of the two parts at the right side of the MT138 drawing.

Many suggestions have been made about.
The 'cats craddle' has been invoked.
Some suggested it was a kind of 'Jacob Lader'.
In fact it is a particular chain where two consecutive elements are not equal (length and shape)
This particular configuration allows this chain (when located around the inner rim of the wheel) to act like a 'Jacob lader'.
So far when the wheel rotates clockwise, an hole of mass (where a segment is missed) is permanently shifted counterclockwise.
In the MT137 Bessler did NOT show this hole, but all the whole path. Only in another drawing (I forgot it, may be in Apologia) you can see the two sectors between 10:00 and 12:00.


This chain is constitute of two kinds of elements:
- A longer one (see the details below), made of a single rod
- a second one (with a length equal to the radius) but doubled (two parallel rods)
They are attached together at each end by some axles, in a continuous chain, alternatively, like already explained earlier here:
http://www.besslerwheel.com/forum/download.php?id=9094
(in this drawing the yellow link is the long rod, and the green double link is the shortest element, the length in the drawing being irrelevant).

How to calculate these lengths:
1. We consider a circle divided in 12 (twelve) equal parts, noted like in the clock.
2. If we link two consecutive even (or odd) points, we got the length of the shortest rod, which is equal to the radius (because as side of the equilateral triangle with the third summit at the center of the circle).
3. The largest rod has a length more difficult to calculate.
This rod links one point of the circle and not the diametrally opposite point but the next one (per example: 6:00-11:00 or 6:00-1:00).
With this choice the ratio between the lengths of the long rod and the short rod is: 1.8929

How this works?
Exactly like one old but quiet member explained yesterday: like a falling pine (greendoor will not be alone anymore to keep the secret).
or like this old video (for the fun) here: http://www.youtube.com/watch?v=IKIp-wLyV2k
Each long rod reaching a vertical position will be tilted from 11:00 to 1:00, but in its fall it will pull also the short element behind him, and by consequence also the attached previous long rod. And so on, with an avalanche effect.

The corresponding full animation after the dinner: I'm hungry, and it is not fully completed.
The motion of the chain is directly correlated with the two animations shown before here: http://www.besslerwheel.com/forum/viewt ... 0876#80876
but more complex because the number of the segments in the chain.

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After the 'foie gras, caviar, champagne' with my wife, now as promised the 'dessert'...
(wie sagen unsere deutsche Freunden: 'es ist Feier Abend!...')

edited:
in addition, a very slow version (for a better observation)

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I spent a significant time experimenting one of my four wheels (each based on a different principle).
This kind of wheel gives me some excellent results: with a strong balance adjustment I obtain more than 350 grades of self rotation at each attempt (without any push).
I suspect this can be improved until 359 grades with a more rigorous building: the bearings are not exactly aligned and I did NOT check the weight of each individual part.


In particular in view to see the eventual effect coming from the number of spokes, I made a model with FIVE rods (see the shot below) hoping a geometrical permanent dissymmetry.
This should be some good news for John Collins (we know his concern with the number five), unfortunately this new geometry don't increase the performance: we got the same result than with a four rods device (in addition the building is more complex inside, another difficulty).
I had about the same result with eight spokes. Nevertheless I guess a big number of strokes could be more successful, this will be explained why later.

An important point discovered by my experiments is: the second weight on the shortest arm (L=x) can be removed.
With this weight in place or without it the result is apparently similar. Only the weight on the largest arm (L=4x) is important
Does has this anything to do with the remark of Bessler? I don't know.

In conclusion this design (like shown in the second video 'swap_move2.mpeg' above) is excellent, even if the quality of the building must be high for the best efficiency.
But we cannot hope more than 359 grades why? Because in that state we just transform the potential and kinetic energy without adding any energy.
Therefore there is no acceleration. By the practical way this is indicated by the fact the heaviest side of the (not perfectly balanced) wheel cannot overpass 11:59

We must find an artifact for overpass this step. The way to do the job is simple: a shift of the inverted pendulum axle
(I suggested this earlier here: http://www.besslerwheel.com/forum/viewt ... 1732#81732)
Everybody knows the game of the sweep on the nose. See here per example:http://www.youtube.com/watch?v=0Texo9Edi5s.
It's exactly the same principle.
IMHO I can now explain the purpose of the toy in the MT138 drawing (next post)