Tuesday, 30 August 2011

J.E.E.Bessler -> W.R.R.Orffyres

Having time away from all things Bessler while on holiday, allowed me time to think and mentally review many things I had speculated upon. One of them was Bessler's use of his pseudonym - Orffyreus.

I have spoken about the fact that Bessler was born with just one forename, Elias. About the time he invented his working wheel he adopted the pseudonym, Orffyreus, using the 'Albam' method - at the same time he added two additonal forenames, Johann Ernst. I think that the Hebrew 'Albam' method of encoding these names is familiar to everyone interested in this story. I had always thought that having two 'E's as his initials was meant to point to the numbers '5' or '55' which are present in encoded form seemingly throughout his publications. However there has always been a disquieting feature to this idea which has caused me some doubt as to my interpretation of it.

For a start in this case, the fact that Bessler used the Albam alphabetic substitution rather than alphanumeric susbstitution to obtain his pseudonym, suggested that the former is to be used and not the latter, in which case the fact that 'E' is the fifth letter of the alphabet is no more than a fortunate coincidence.

In addition, converting the intials J.E.E.Bessler through 'albam' results in W.R.R.Orffyres, and the 'W' is formed from two V's which, in Roman numerals, produces the number '55' again and to suggest that the two 'E's represent the '5's too, seems almost tautological (if there is such a word!). Seriously is it likely that Bessler would have used the letter 'J' for any other reason than as part of an albam code? He could have left the 'J' out and used alphanumeric substitution to get '55'. So the letter 'J' is important but so is the letter 'R' which is derived via the 'albam method from 'E'.
You can see Bessler's own version of the letter 'W' above left, which differs from those used in the fraktur font - except when used to point a finger at his enemies, Gartner, Wagner and Borlach, taken from Apologia Poetica, the metaphorical passage!!!  It is definitely two 'V's.

So the letter 'J' leads us to the letter 'W' which points to 55. Now if the letter 'E' is not deliberately included to point to 5, then it points to 'R', its albam equivalent. Bessler routinely signed his name with a large 'O', presumably short for Orffyreus; he included a dot in the middle so it could also represent his wheel. But then he added two letter 'R's, one on either side of the 'O', the left one pointing the wrong way. This appeared to represent a wheel supported by two 'R' shaped figures.

Artistic as this may seem, there has to be more to it than sheer artistic vanity. It was important enough to add new forenames to his pseudonym, and the number 55 was of great importance to him as is clear from the many occurences of it, so one must conclude that the letter 'R' was of at least equal importance. The only thing I can conclude from my own research is that it has to refer to the path of the weights. One weight moves through a short curved circle and the other one moves through a longer less curved circle.

I have my own theory about how this helps and I am writing my ideas out in detail and I will post them when they are done. I'm considering doing another video to explain graphically what I mean, but if anyone else has any thoughts about the letter 'R' and its meaning I'd love to hear it.

JC

1. It's very obvious to me.

The "O", as you note, represents one of his wheels. The two "R's" represent the pendula that he could attach to cranks a the end of a wheel's axle. These "R's" are reversed because the pendula were counterpoised and would swing in opposite directions when a wheel was in rotation.

2. One weight moves through a short curved circle and the other one moves through a longer less curved circle.

Could you rephrase this? Less curved circle? Do you mean an ellipse?

3. R-wheel-both directional.

4. Like Technoguy here, I see, except for the R's, also two pendula at both sides of the wheel. Since old fox Bessler also indicated the axle (by the dot) in the middle of the wheel, it makes me wonder whether the little dot at the roughly 12 o'clock position (1 o'clock since the whole is slightly slanted) as well as the dot on the right of the wheel periphery, at 3 o'clock - connecting the pendulum to the wheel? - has any significance. There isn't one at the left. A clue to a key feature of the mechanism?

5. Come to think of it... this is a interesting picture. Let's ignore the left pendulum for a minute. A wheel with a pendulum as depicted on the right, temporarily (connectedness principle?) attached at the 3 o'clock position would set this wheel in motion. When disconnected at the right time, the pendulum is free to swing, and return to roughly the same location. The wheel in the meantime has rotated a number of degrees under its own momentum and the pendulum, upon completing its period, attaches again for a short while, causing further rotation. The cycle repeats. A very simple (clockwork-ish!) mechanism indeed.

The only thing missing in this scenario is something that would detach ("jettison") the temporarily attached pendulum rather forcefully at the right moment, with enough force to ensure that it will return at the same point.

The pendulum on the left side is not connected (attached) when the wheel is rotating clockwise, but would fulfill the same role as the right-hand pendulum when it is required that the wheel rotates counterclockwise.

Hmmm. Interesting. And simple, very simple. So simple a carpenters boy could construct it?

6. A bit OT, but from studying the circle, I notice that the direction of the curve of the small "tail" at the 12:30 position of the "O" indicates that this circle was drawn counter clockwise. This indicates that Bessler was probably right handed since most right handed people will draw a circle counter clockwise.

His right handedness is further demonstrated by the better formation of the long leg curl of the right side "R" as opposed to that of the left side "R". In a left handed person one would expect the left side "R's" long leg curl to be more tightly curved and drawn with better control.

7. Aleister Crowley wrote in one of his books something like "When an adept (occult practitioner) make a clear and unambiguous statement, you have definitely misunderstood the meaning".

As far as the code goes, let me add an observation. To make a code more difficult to break, add superfluous information. Or to put it another way, to make a jigsaw puzzle more difficult, you don't need to make more intricate pieces, but mix two or three similar puzzles together. If a code is presented in a mater of fact format, it's quite easy for a an elucidated man (like a scientist) to crack, but mix in a whole lot off stuff that's irrelevant but looks as if it might have something to do with it, and the learned man will tie himself in knots trying to decipher it. Alternatively, a clever fool may work it out in minutes. I'll give you and example:

Which is the odd one out:
1,2,3,5,7,8,11,12,13,15,17,22,23,40.
(This really annoyed a professor at a London university who devoted an afternoon to fruitlessly searching for a mathematical solution, whereas a fellow from the pub got it right within minutes).

Whilst I agree with, and cannot discount much of what has been discovered, it does remind me of things like the "bible code", which was supposed to unique to the first five books of the bible, but it has since been found that if the technique is applied to almost any large volume of printed text, the same sort of "discoveries" can be made. As such, things such as pentagons etc., can be found almost anywhere if one looks hard enough, which makes me think that this might be a red herring, but then again, perhaps it's not.

Another thing that I've learnt searching for illusive problems is sometimes not to look for what you've been shown, but to look for what hasn't been shown. E.g. a gold prospector may be happy to discuss prospecting in certain areas of land, but will avoid discussing areas where his own finds are located.

There's no rice with No. 22.

8. Thanks Great Bear - and thanks for the mathematical puzzle!

I agree with what you say about there possibly being superfluous clues within Bessler's work. I'm leaning towards the theory that he invented at least two different mechanisms that both worked and he included mixed clues to construct both.

Good analysis Technoguy.

Andre, we have emailed each other, thanks again.

Doug, I meant elipse, I guess, but I was just describing the letter 'R', which when drawn by Bessler has the two curves as described. I have several versions of the same signature by Bessler and they are all similar but vary in quality depending on how quickly they were drawn. So some have a squashed cirle and others don't.

JC

9. Do the 'blobs' at the end of each R letter indicate weights? Do other letter r's in his writing have the same 'blob' so pronounced?
Regards
Jon

10. To Andre and Dwayne: I've been reading your interesting exchange in the comments for the 19 June 2011 post. I've added some comments on my own experience with silux issues there (rather than here; I agree it's a bit off-topic).

11. Anon, I have about 25 versions of the, let's call it a logo, about 25 versions of the logo and they vary slightly from one to another but not by much. I would say that they all consiste of a circle with a dot in the middle and two 'R's, one on either side, pointing in opposite directions and missing the vertical straight line of an 'R'.

Some have blobs, and some have slightly overlapping circle ends such as occur commonly when drawing a circle.

JC

12. This is my fourth attempt to post some comments on my experience with silux issues. On the 19 June post I get the "comments have been published" message, and all seems OK, but when I revisit the site a minute or so later, they're gone.

Here we go again (brief version):--

Exploding models (rare but can happen): Try making all links and/or interaction constants harder. Or, make a small object of mass 1 gram or less, make it a non-member for simulation (uncheck that in the edit object box) but still interacting. The aim is to reduce the time between iteration cycles, dt. Also, avoid models with long flat surfaces bearing against each other, e.g. a long flat-sided piston in a cylinder. Keep bearing surfaces short.

Hollow objects: Use negative masses for cutouts. See how silux do this in their clockwork model. Otherwise rotational inertia will be wrong.

Micromovements: Assign correct velocity and rotational speed values for all objects, no matter how light, at the start of a simulation. Otherwise graphs will be "noisy".

Significant figures: Silux often displays only three significant figures e.g. for spring maximum force Fn. But for accurate work you can enter values to many more significant figures and silux will act on these, and will record and display to six significant figures in data associated with graphs.

Compression springs: These can display incorrect forces in graphs, but will still act correctly in models.

Dampers: Always graph damper force vs time to be sure a damper is working correctly. Either it will be, or if not, it will display zero force.

Gears: If gears are created using the silux method "Create Gear" and "Create Link Gearing" etc, this is the one case where the simulation results will probably be incorrect. Energy does not seem to transfer correctly across the gear link. If that's important, you have to model the gears as normal objects, complete with their teeth. The simulation will take longer, but it will be correct.

Saving: Never save a model with a graph minimised. You won't be able to recover the graph, and you may get an unhandled exception error which will crash the program.

I had some comments on the advantages of a Finite Differences program (like silux) over the much more common Finite Elements programs, but I'll leave that for now.

13. Sadly, ALL computer simulation programs have their little annoying "idiosyncracies" which one must painfully learn to avoid before he can build models whose movements he can trust.

But, this is really a very small price to pay considering how much more rapdily such a program allows one to test the validity of a design concept as opposed to actually having to physically build it.

For example, if Bessler had had such a program, then he might have discovered the secret of PM in only six months instead of having to struggle on for a decade to do so.

14. In my opinion Vincent’s simple contribution “R-wheel-both directional”, comes closest to the probable meaning of the ‘ROR’ logo. Do any of the 25 versions you have predate the making of the two-way wheels JC?

I think the letter ‘R’ could stand for ‘Rotating’ (Rotierend in German): that Bessler has stylised a wheel image out of rotating R’s, whilst at the same time he has used the R’s to symbolise the arms of the wheel that move in and out. The “missing vertical lines” of the R’s are not in fact missing but have been curved around to make the O: as indeed the missing (or invisible) lines of gravity will be doing in a working wheel.

The motif is very similar to the first (unidentifiable) element in his signature. Am I the only person to consider Bessler’s Signature to be a very significant clue?

I believe Bessler chose the name Johann (John) because of his religious desire to be ‘as Christ’s favoured disciple’ and to make clear that he had been ‘The recipient from an Angel of The Revelation’ (of the wheel). He chose Ernst because it means in German ‘a very serious person’ and also interestingly now, Gravity!
His given name Elias being the Hellenised version of Elijah was no less important to him hence the references in his writing to his Mantle.
I have covered all this name stuff in the second verse of my long poem ‘For the love of Eurydice’ on my website.

John

15. Arktos, thanks for your trouble of posting that very useful information. Those are typically good things to know, as apposed to "finding out the hard way". Indeed as technoguy observes, many of these programs have their own quirks and hiccups, and its good to know about them in advance. Thank you again for all your kind help!

16. Thanks to John W. for his revelations concerning Bessler's names.

Imagine the effect on Bessler's young mind of realizing that his then first name, Elias is equivalent to Elijah in Hebrew. He reads the Book of Elijah in the Old Testament and all about its "wheel within a wheel". He then becomes interested in Judaism and maybe even studies the Cabala.

Learning about codes, he analyzes the name "Bessler" and derives "Orffyre" from it and then Latinizes it to make "Orffyreus" which sounds like "Orpheus" (wasn't this the name used for him in some newspaper article of the time?).

Studying the legend of Orpheus he learns about his magic flute and the story about how it could control an ever moving wheel in Tartarus or the Greek version of Hell.

With all of this wheel imagery floating around in his subconscious mind, is it any wonder that he became the first known human to produce a working perpetual motion wheel?

I would bet that the "invigorating" dream he had probably also involved wheels!

In the final analysis, Bessler was literally programmed to find a successful PM design. He was the "right man at the right time with the right tools" and, because of his inbred tenacity, managed to fulfill his destiny.

17. Correction.

Orpheus used a magic lyre or harp given to him by the Sun god Apollo. It was Pan who had the magic flute.

18. (Perhaps this approach might educe some little, unmerited response?)

Above, JC revealed to us as follows ". . . I'm leaning towards the theory that he invented at least two different mechanisms that both worked and he included mixed clues to construct both."

". . . the theory . . ."

This must be THAT ONE discussed variously, on the Bessler Wheel forum, over the years?

It is very good to know also publicly, that you are "leaning" in such a direction, John.

Edifyingly, with every day comes some new, delightful thing to be learned about ourselves.

James

19. Perhaps my words "...leaning towards the theory", might be too strongly suggestive of the idea that I actually considered that Bessler included two differing mechanism designs within his drawings. In fact what I intended to convey was that I did not rule it out, but too infer from my words that it was an established theory of mine would be to put to strong an emphasis on it. I'm merely open to the possibility.

JC

20. Andre and technoguy etc, you're so right about "learning the hard way"! You may be interested to see www.realphysics.ch/sonar.htm for later developments, in 3D FD analysis. I'd love to get my hands on Sonar-code!

John, I tend to agree that if Bessler's logo is anything more than just artistic vanity, then it could indicate a mass path.

In "Apologia Poetica" Bessler says (in the translation in your republication, p291) "So then, a work of this kind of craftsmanship has, as its basis of motion, many separate pieces of lead. These come in pairs, such that, as one of them takes up an outer position, the other takes up a position nearer the axle. Later, they swap places, and so they go on and on changing places all the time." Later, talking again about the axle (p326) he says "Rather, it has many compartments, and is pierced all over with various holes."

I take this to mean that, in simplest form, a pair of weights, one on each end of a rod, move in and out diametrically as the wheel turns. However, I don't think the reversed-R - O - R logo can represent a *pair* of weights, because if so both weights would have to come close to the axle at the same time, near the horizontal centerline.

So maybe an R represents the path of just one weight of the pair, with the reversed-R indicating that the wheel is bidirectional, as Vincent already suggested.

21. Arktos,

When Bessler wrote "Rather, it has many compartments, and is pierced all over with various holes" that "it" refers to the drum that carried the weights, not to the drum's axle. It was the drun that was divided into sections (most likely eight) and had holes cut in its cloth covered sides so Bessler could perform occasional maintenance on the wheel's "perpetual motion structures". These holes were normally covered over with larger patches of cloth that were pinned in place and prevented anybody from getting a glimpse of a wheel's mechanisms.

In other sections he writes that all of his wheels' timbers were solid and mentions that members of the public were invited up to grasp the portion of the axle inside of the drum to verify that nothing was attached to it or passed through it. This would have been done through a smaller hole in the cloth covering near the axle.

22. technoguy,

While I agree that it's a bit hard to imagine the axle of a wheel having "compartments," I still think that in context, Bessler is referring to the axle. Here's the entire first part of the relevant paragraph from p325/6 of AP:

"Now look, Wagner, just listen carefully if you want some information from me. People say that, in your writings, you claim to have devised a Wheel which has a divided axle, held together in the middle only by a peg. Am I reporting you correctly? But people will continue to laugh until you actually produce such a machine! You further claim that my wheel is the same, but you're lying through your teeth! Ask any of those who have groped inside my Wheel and grasped its axle - and you will be assured, in no uncertain terms, that my axle is not like that. Rather, it has many compartments, and is pierced all over with various holes."

23. I've always been a bit puzzled by the comment that the axle has many compartments and is pierced all over with holes, and I came to the conclusion that the sentence refers to the wheel not the axle. He mentions in the preceeding sentence that people have grasped the axle inside the wheel and I think that the 'it' which follows is referring to the wheel and not the axle. In my opinion that makes much more sense and complies with previous statements about the axle. In German, I understand that the words do not follow the same order as in English and the nouns can often easily be associated with the wrong verbs by a non-speaker such as I.

JC

24. I believe I can throw some light on the question of axle compartments being discussed here.

That part of the mechanisms structure that is fixed to the axle effectively becomes a part of the axle, both physically and in name. In the passages already quoted Bessler describes the form of this part of the mechanism as being composed of compartments; in AP XLVI he describes a compartment as a Dogs Kennel. I would describe them as the slotted recesses that the arms of the mechanism withdraw into on the light side and extend out from on the heavy side of the wheel. They are “pierced all over with holes” because they consist of an open framework with no solid sides, base or top, not to mention the holes for bearings.

John

25. John Collins - an especially mad mobilist?

Hehehe...

26. In fairness, I had a glass or two...

27. Although my German is poor, I'm wondering whether there might have been a mis-translation, or at least an alternative translation of the key word "FÃ¤cher" (see AP p173). This seems to be the word translated as "compartment". It means "fan" literally, but can also mean "range" figuratively. So an alternative translation could be "Rather, it is pierced all over with a range of various holes".

I know that the word "Fach" without the umlaut means "compartment".

I guess it would take someone with real fluency in German to sort this out decisively.

Anyway, the most important point to me is that it seems fairly well established that the masses move in and out radially as the Wheel turns.

28. FÃ¤cher also means: pocket, division, compartment, locker etc.

Use http://dict.tu-chemnitz.de/ as an excellent German/English dictionary, Arktos. Sometimes you have to read down the page to see all the alternatives.

JC

29. How about translating it as "fan shaped section" or "cylindrical sector". I imagine the "compartments" of Bessler's wheels to be similar in shape to the 45 degree sections seen between the radial members of a small Ferris wheel that only carries eight seats

30. I personally feel that there were two sets of four compartments along side each other,45degrees out of phase.This adds up to eight weights operations per revolution.This is the only configuration that will allow the weights to swing freely without interfering with each other.
Today is my 70th birthday and I am very optimistic that I will have the wheel sown up this month.I have all the component operations in place that are essential for a wheel to work and it looks like John was right,there are five.

31. Hi Trevor, can you tell a bit more about the five mechanisms c.q. component operations? As usual, I'm extremely curious :-)

32. Happy Birthday Trevor! I hope you are right, I'm getting fed up with perpetually motionless machines.

JC

33. Happy Birthday, Trevor, and many more.

I certainly hope you have finally "cracked the nut" of the Bessler mystery. 300 years is long enough to wait for a working solution!

34. I tried to post a lot of amazing stuff I'd discovered about MT55 but this blog won't accept the posting; maybe it's too big! I've sent a copy to JC for scrutiny but with no reply I asssume it never got there. Will try to post again...

35. Happy Birthday,to Trevor.

36. Great Bear I don't know why you are having problems posting, perhaps there is a limit on size? Also I haven't received any emails from you, are you sure you are sending them to me at the right address? Try my name at gmx.com
JC

37. Happy birthday, Trevor.

To Great Bear and John C, I also had problems with a fairly large post; see my comment of 2 September 10:57 above, which is only about half of what I originally tried to post.

38. I've checked to see what problems there may be and this is what I found.

Size of Posts: Individual posts do not have a specific size limit, but very large posts may run up against the page size limit. (See the next item.)

Size of Pages: Individual pages (the main page of your blog, or your archive pages) are limited to 1 MB in size. This will allow for a few hundred pages of text, but it may be a problem if you are listing hundreds of posts on the front page of your blog. If you hit this limit, you will see an error message saying "006 Please contact Blogger Support." You can get around this error by lowering the number of posts on your main page, which will have the added benefit of making your page load faster as well.

So far no problem, but....

Finally the captcha generator (you copy it to enter a code for access) sometimes comes in to conflict with certain browsers such as firefox. There is not sufficient space to say more here but all answers can be found on google.

If I sound as if I know what I'm talking about...disabuse yourself of this conclusion! I don't, its just what I found on google.

JC

39. The posting I'd intended to put up was my analysis of MT55, which once entered upon raises many, many questions, as the deeper the analysis goes, the more questions it raises. After the realisation that these are two totally separate machines, there was the realisation that the schematic shows a cut-away of the wheel to reveal what's inside, though this does not immediately tie in with the other half of the diagram. If anyone would like the full analysis, I can try to publish it in small sections.

40. Great Bear,

I don't see the upper portion of MT55 as showing the interior of a Bessler PM wheel. Rather, it just looks like one of two variations of the same unworkable general design.

In operation, the upper and lower axles of either variation will always have to rotate in opposite directions. This will happen as each pendulum, after being released by a paddle (lower machine) or peg (upper machine), swings back through an angle of about 90°, engages its cluch mechanism with the upper axle, and then tries to rotate the upper axle in the opposite direction that the lower axle is rotating in.

The largest wheel in either variation is not one of Bessler's PM wheels, but is just a heavy metal flywheel intended to keep the lower axle in motion as it sequentially lifts and then releases the pendula hanging from the upper axle.

Such a design neglects to consider the large amount of each pendulum's gravitational potential energy that will be irretrievably lost (that is, converted into heat energy) in overcoming bearing and clutch part frictions, as well as gear train and aerodynamic drag. Such a design will always be less than unity...far less, in fact. Consequently, it will neither be self starting nor able to do any significant amount of external work. After being put into motion by an external torque, it will immediately begin slowing to a stop when the external torque is removed.

The fact that Bessler would include such obviously unworkable designs in MT makes me think that they were selected only to serve as negative examples which Bessler would then explain with later notes. (If he actually did think any of them would work, then I might even begin to question if he really did build a genuine working PM wheel!)

Anyway, I think that when we finally do rediscover the mechanism used in Bessler's PM wheels, we will see that it uses no gears or pulleys, but just incorporates small, very low friction bearings to which the weights are attached.

41. INTRODUCTION. (Part 1)
This diagram is deceiving. It may be meant to deceive but then again anyone paying close attention would have stood back and wondered.

There are two diagrams in this image. The bottom one is a "picture" and the top one seemingly a schematic.

PICTURES & SCHEMATICS
At first glance, the top one (schematic) appears to be a side in view of the picture below. Inspection however proves that they are both totally different things.
The picture (bottom) seems to show an Orffyreus wheel, driving a chain of gears to a shaft which moves paddles; motorised cricket bats if you like. This contraption rests on the ground. The gear ratio of wheel D to C is 2:3 and it is a reducing gear to power the application into moving the paddles, thus three rotations of E will produce two rotations of C resulting in each paddle being "flicked" twice, or 6 in total. I've made an assumption here that wheel C lies directly under wheel D, which from the perspective of the drawing seems to be about right, however, a disconcerting feature is that wheel C does seem to rest on, or even penetrate the ground.

SCHEMATIC
The schematic however is floating; it does not rest on anything, so I take it to be a pure diagram. It is however, not a diagram or schematic of the picture below it, though just a cursory glance implies that it might be. It consists of big two wheels (E & C), roughly of the same size and three rods (A) that intercept the inner wheel(B), which appears to be mounted on, or inside wheel C. At first sight it gives the impression that wheel E drives wheel C in the form of a reducing gear. This in turn causes the three rods A to be agitated by the six "protuberances" on wheel B, in much the same way as in the picture below.
However, this cannot be possible.
If wheel E turns clockwise, all rods, assuming they’re free to move about the axle of wheel E, will fall to the bottom and stay there; A pointless exercise.
If wheel E turns anticlockwise, the rods will all move to the top and undergo little bumps as the protrusions on wheel C agitate them. They will all do this simultaneously, which again seems a pointless exercise.
At this point it should be noted that arms A are "L" shaped hooks, orientated upwards. As only one arm can be clearly seen, it is an assumption that the others are the same. If any particular arm is different, it might be the bottom one as its end cannot be seen. This throws a different complexion on the system. It is possible, that if wheel E turns anticlockwise, the arms, or a single arm may catch upon one of the protuberances causing the wheels to lock together. If this system is mounted vertically on say a wall at the centre of wheel E, then it's possible that the locked wheels may act as a pendulum, until they have completed a swing of 180 degrees. At this point, gravity might pull the arm A downwards to free the system and for wheel C to swing back towards whence it came from.

42. HOW MANY ARMS?
However, a closer look at the system shows that Arms A do not originate from anywhere. Because they seem to come from the centre of wheel E, leads one to assume they originate from there, but no hinge or bearing is shown. As Besslers drawings are good, it is improbable that he would have forgotten to highlight such an important aspect. It was at this point when something struck me as very odd about the whole schematic and how useless or pointless such a device really is. Then I realised that the ellipse, (or football shape) in the middle is a cut-away section of the diagram. i.e. it is part of Wheel E with the covering removed allowing the observer to see what's behind it! This suggests that there are not just three arms A, but if they're set at 18 degrees apart (vertex of a pentagram, plus one in the middle, thanks JC), then there are 20 such arms contained within wheel E.
But looking at the arms again, it appears that top one is resting on a protrusion, the middle one might be resting on a protrusion, and the lower arm appears to be floating in mid-air (unless perhaps somehow hooked onto the lower protrusion). This implies that the angles between them, especially the lower two arms, is less than 18 degrees, which I cannot accurately measure because I put my school protractor away some 40 years ago. However, if it's slightly less for instance 16 degrees, then this might mean that there're 22 arms.
However, no other arms are seen in the cut-out section. This may be because they're hidden behind the rest of the wheel covering. The quadrant exposed however is (by visual inspection) a demi-semi circle section of wheel E and shows a quarter of the complete wheel. If such a section contains three arms, it might be anticipated that Wheel E contains 3 * 4 = 12 arms. An explanation may be that the cut-out is not a demi-semi circle at all but just a sector containing the trees arms as seen. My own feelings towards this are that at this stage of his book, these are illustrations to suggest possible perpetual motion machines, and not fully detailed plans that an engineer could build from. Weights and masses are not specified, neither are lengths, diameters or operational speeds etc. As such it is an illustration of a principle rather than a design that can be sent to a machine shop for building.

ARM FIXINGS
It's speculation whether the arms are rigidly fixed to the wheel axis, (which means they could turn the wheel E if weights were placed on them), or rotational, which would ensure flexibility but no visible way of turning the wheel, or maybe using a spring to allow power transfer as well as a modicum of flexibility, or maybe the entire arms are springs.

43. WHEEL OPERATION
Now the anticipated operation of the wheel becomes much clearer.
The gearing of wheel E to wheel C is 12:49. As it's difficult to draw many gear teeth precisely, maybe we should assume for now that it's 12:48 or 1:4, so as E turns four times, C turns once.
This means that 4 * 20 = 80 (or 4 * 12) arms A in wheel E move past any point (but lets say it's on the horizontal between the two wheels) during a single revolution of wheel C, where 6 Protrusions move past the same point. This seems rather silly. If the arms are meant to match up with the protrusions, there need to be 24 of them. This is the only logical figure that fits. If there were 12 arms, three of the protrusions would never be touched and would be superfluous (but more on this later). Again, if this is just an illustration, that what it shows is fine, trying to show 24 arms in a small diagram will make it cluttered beyond recognition.

LEVER ON LEVER
This gives the impression that it was meant to be a lever driving a lever mechanism. That is, that wheel E drives wheel C through the gearing system, with each degree of rotation produces a downward force on an arm A, which in turn makes wheel E go around.

L SHAPED ARMS
One problem with this explanation is that the Arms A seem to have the L shaped end pointing upwards and resting on top of the protuberances. This implies that wheel C has turned clockwise and is pushing the arms upwards, which would still make the wheel work if this sort of system works, but then why not just use straight arms without the L shapes at the end.

WHEEL MATHS
Now in four revolutions of wheel C, Wheel E would revolve just once.
In the four revolutions of C, the protuberances would have moved past (say the centre horizontal point) 4 * 6 = 24 times. Looking at things from this perspective, wheel E would need 24 arms to make full use of every opportunity to interact with wheel C.

44. GEAR RATIOS
The ratio of the gears was 12:49, which we simplified to 12:48, or 1:4. If this simple ratio was correct, it would be very important to get the starting conditions for the wheel to be exactly right, and then the two systems would be locked together with the same relative distances between each other forever. However, offsetting this by just a fraction, (the extra tooth in the cog), would mean that the wheels would never be exactly in sync, and would return to their own starting positions every 12*49 = 588 revolutions (I think), which would mean that if one or several arms were not precisely aligned, at some time they would be. But conversely, perfectly aligned arms would also loose their alignment and return to it.

At any rate, wheel C turns at slightly less than a quarter the speed of wheel E, or to look at it another way, wheel C turns marginally faster than E, and if driving wheel E, then the force on wheel E increases by 1/49 each revolution. Although this seems highly desirable, this force cannot build unabated forever, and sooner or later something is going to break, whether it's an arm, or the teeth of the cogs, or the wheel itself may distort. As it stands, it looks as if any force put on the arms gradually lessens until after 588 turns when it should return to full force again.

PROTRUBERANCES.
Six are shown, and they're assumed to be protuberances, though it's possible they could be depressions. The height of these is unknown, but I've made the assumption that they're all the same height, though they may not be. If they are not, then another layer of complexity enters the frame. If say three are half the height of the others, and the arms are not all laid out in a flat circle, than different arms will engage with different protrusions. i.e. raised or offset arms will miss the low protrusions and only make contact with the taller ones. However, if this was the case, I feel Bessler would have gone to more pains to show it.

45. THE PICTURE
I have difficulty in seeing how the picture and the schematic go together, unless all of the schematic fits into wheel E of the picture as a driving mechanism. However, then the lettering system identifying the components goes astray. If comments were intended for MT55, it would be cumbersome to describe which part any specific item referred to. I've considered that in the picture, wheels C & D might equate to wheels E & B in the schematic, but the gear ratios are so obviously different that this cannot be the case, unless the observer is meant to transcribe the ratios from the picture to the schematic (which I haven't).

CONCLUSION
This is a baffling drawing, not in the style of the others where there's one illustration per "page".
Every time I look at it I wonder what else may be staring me in the face but that the brain hasn’t registered yet, and then, if these anomalies are drawing errors or subtle hints. If I discover anything else, I'll let you know.

46. Trevor, sorry I missed the fact that you had your birthday on the 7th. Happy (belated) birthday!

47. Wow, great Bear, that's a lot to digest. I'll read and re-read your observations here, next to the picture. Interesting.

48. Hi guys,..Okay the first thing we must accept is what Bessler said,that the the pendulums are free to swing without hinderance.This is the first component of the five operations that must occur every revolution of the wheel.
As the wheel turns at say one rev per second,the pendulums begin to swing rather energetically.This property does not in any way hinder the revolutions of the wheel.Neither does the wheel revolutions hinder the pendulum swing which is free,handed to you on a plate.
The next component mechanism which you have to work out is one that can harvest work from these pendulums without actually impeding their swing.

49. I think the top drawing is the side view of the bottom. The letters match up with each other.The top drawing has 3 "layers"; the arms A , the third layer, are the same arms to the paddles in the lower drawing He probably made D bigger in the lower drawing for clarity.
Also, the lowest arm has a much thinner, longer line than the top two. I don't think it's meant to portray an arm. The "L" shape may show how the arms are attached to the paddles in the side view. It might have been more confusing to draw the complete paddle in the top drawing.
The left paddle has a cutout in the axle; that seems odd.
The left drawing of the arm shows the E axle free to turn; the arm doesn't engage other than resting on the axle.
The thing that doesn't match up between the two is the number of paddles; he could have shown three in the top drawing.

50. Something that bothers me is Count Carl's statements regarding the internals of the wheel. In particular, that a carpenters boy could have built it.
The problems I have with this are (1) What is a carpenter's boy, (2) how competent is a carpenter's boy and (3) How does Carl know what a carpenters boy is capable off.
Again using the proven adage of if you assume you make an ASS out of U and ME. I'll outline my assumptions and interpretations.
(1) I ASSUME that a carpenters boy is the term used for an apprentice. A 30 minute search of the web did not confirm this, and the nearest I could get was that a "boy" was a servant.
(2) Still, ASSUMING a carpenter's boy was an apprentice, the apprenticeship took seven years to complete (in London). This is a long time, and ranges from perhaps, a keen youngster to someone who would the next day be declared a qualified master craftsman. It's also interesting to note that (in the London guilds at any rate), due to their cost, apprenticeships were usually taken up only by the more affluent and educated classes. One could then suppose that even the youngest and greenest of boys would not have been entirely stupid, and capable of grasping the many skills required to fulfil the training. A carpenter's boy could have been quite a clever individual, especially nearing the end of his training.
(3) I wonder how count Carl, being of the nobility and enjoying the privilege of the titled classes, would know anything much about carpentry, or the people who performed this skilled work. Perhaps his remark at the inner workings of the wheel were an off-the-cuff remark rather than an analytical assessment of the construction of the workings. It is entirely possible that he had had building or renovation work done at his castle where he could have seen carpenters and their "boys" at work, but It's doubtful if he might have engaged many in conversation to ask how long they'd been apprentices, or what skills were learnt each year. I suspect that the youngest apprentices would have started off at the bottom, sweeping up after the craftsmen and the like, and then being taught basic skills such as sawing wood, planning, chisel work etc. I suspect the master carpenters may have been involved with intricate decorative carvings, marquetry, compound joints, load-bearing structures and finishing work etc.

This leaves the question of what skill level was count Carl referring to, a bright and keen youngster perhaps already competent with the basic tools, a seasoned worker who could do most things without supervision, or someone about to become a master craftsman.
Any thoughts?

51. Good analysis Great Bear; it parallels my own thinking, but I came to the conclusion that the design was readily understood and therefore easy enough for a person of average skills to copy.

I think he was trying to tell us that there was nothing too complex about it, and someone capable using carpentry tools could probably make one that worked.

JC

52. My assumption about Karl's remark about the simplicity of the mechanisms has always been the skill level for construction required was low; prompting the wording of his assessment. It would be consistent with the design of the mechanisms also being simple.
What bothers me, and others, is the fact that this simplicity of design hasn't been discovered.
That's what leads me to believe either Karl wasn't allowed to see something, or he saw something more - complicated - he had to hide for one reason or another.

53. I dare say that carpenters in those days may have very well been rather more skilled than they are these days, especially considering the rather primitive, all-manual tools they had to work with.

Also we should keep in mind that Bessler was a skilled clockmaker, with (therefore) most likely a good understanding of and feeling for mechanics. Then he was also an organ-builder - therefore familiar with the mechanics involved, and principles of resonance.

Resonance i.e. oscillation must have been key in his design.Like Trevor said, a mechanism must be devised that allow us to harvest work from these pendulums without actually impeding their swing.

There's at least one such mechanism in existence I can think of: the parametric oscillator.

54. You can't get work from a pendulum without impeding its swing.
We've had that debate once. But if you insist, we can revisit it.

We have to assume Karl knew something about carpentry. If it was a trade for more affluent people to learn, then he probably was at least knowledgeable of of the basics, being affluent himself. Having said that, if he did see something more difficult to build, he might have instead said it was simple to build to help market it to a potential buyer such as Peter.

55. By "carpenter's boy" I believe Carl was referring to an apprentice who was either in his late teens to early twenties. He would have acquired enough skills to replicate a design in wood after having studied it for awhile.

When it comes to the description of "so simple...", I do not think this describes the actual design, but rather refers to the nature of the construction it used. That is, the design used no gears or pulleys, but would have involved the same construction techniques used in organ construction.

As an example, one might look at a painting and proclaim that it was "so simple that an artist's assistant could do it after viewing it". That would be a true statement if the assistant only had to dab various colors of paint on a canvas in the same pattern previously done by the artist. But, it would probably be difficult to impossible for the assistant to created the original painting by himself without having the artist's product to guide him.

I think anyone who wants to duplicate Bessler's wheels should study the types of methods used to construct the organs of Bessler's time. When the secret is finally revealed, I'll bet that we'll see that Bessler got the idea for his "perpetual motion structures" from the craft of organmaking and not from that of clockmaking.

56. Andre,..The harvest of the pendulum equates to lift.As Bessler said ,if you can lift one pound with 4 ounces the you have a wheel that will maintain itself.What I posted on the 8th September is extreemly important.There are five complimentary components that must be in place to make up a working wheel.If you don't believe me ,just believe Bessler.
I cannot see anything in maschine tractake the will solve the wheel.I think it is there to lead people off the track.

57. Anyway thanks for the kind birthday wishes.When you get to my age you don't really look forward to the passing years especially when your trying to solve the wheel.
At least the solution is definitely in sight and I'm very optimistic as usual.

58. @Trevor, indeed, the "harvest" equates to lift, or more correctly, force. User RHEAD100 on YouTube has posted some new videos of the big oscillator he's constructing. Keeping his version of the 2-stage pendulum going requires 90 inch-pounds of force, but he's "harvesting" 2400 inch-pounds of force at the same time - without impeding the swing. Using a gearbox-ish assembly (he calls a double-Becket, not sure that's right) he's driving a PMA (permanent magnet alternator). Using a 35-pound flywheel on the PMA should keep it going nicely and smoothly. It's basically a giant version of the experiment I tried last December, which I found very compelling and interesting. Keep an eye on that guy, he's putting it all out in the open.

@Doug - we did have that discussion, yes. You were not convinced by my arguments, which is of course fine. Maybe try this: construct a small 2-stage oscillator, which is fairly easy to do. Let the pendulum swing and observe and measure the gyrations of the bar. Now block the business end of the bar while the pendulum swings. Watch what the pendulum does. Or rather, what it doesn't do. I think it will be quite obvious - there's no clear equal and opposite reaction to the blocked bar.

Bessler’s Clues Here and on Besslerwheel forum

I’ve decided to go back to my original plan which was to share everything I’ve discovered and know, or believe about Bessler’s wheel.  It ha...