Monday, 24 September 2012

Bessler's shared drawing features

I'm posting some of my musings on the various graphical  features in much of Bessler;s work.

I noticed a comment on the besslerwheel forum regarding the drawing of a Roberval Balance parellogram on page 556v (page 169 in my published version of Maschinen Tractate). It said that Bessler's drawing showed the Roberval Balance at an angle and therefore, it looked as though the weights were not equal. 

Stewart responded thus, '... It won't self-level, and you can move the parallelogram up and down with ease and it will remain stationary when you let go. This is not a "normal balance" and is a very interesting demonstration that should be studied and understood.'  Below is Roberval's balance drawn in 1669.

I think it worth pointing out that this system was designed to allow the weight of any thing to be checked against a known weight. The object to be weighed is placed on one of the two weigh-pans and checked against some known calibrated weights on the other pan, until balance is achieved.  The big advantage is that it doesn't matter where on either pan the object to be weighed, or the calibrated weight, is placed.

With differing weights the balance will be tilted downwards by the heavier weight, but because the weights were of a similar mass the two pans were always in equilibrium, whether tilted an angle by hand, or level with each other.  

The weigh-pans on the Roberval balance are fixed to a multi-jointed parallelogram whose two other sides are pivoted in their midpoints to a vertical post.  This parallelogram bears similarities to the figures 'C' and 'D' on the 'Toys' page, (MT138-141).  It also has a passing resemblance to the lazy-tongs shown as figure 'E' on the same page.

It seems worth pointing out that the ubiquitous letter 'A' with the sometimes bent middle arm in the Maschinen Tractate, can form a parallelogram but is also similar to the pantograph, a device for replicating a design in a larger of smaller scale.  

To me the pantograph shown below and drawn in 1867 look somewhat similar to the square and compass so often attrributed to the Freemasons, but also in the second Portrait.  

Do these various depictions have any connection with each other, or do they just bear a passing resemblance to each other?




  1. The machine could be a ball runner after all. It was the type most scorned by JB 1 in MT.
    A Roberval balance is a dead end.

    1. The Machine is not a 'ball runner', we know this; this is all Sir Isaac's laws stuff. The Balance is not a 'dead end', it is a major clue as to how The Machine works


  2. Someone has been sprucing up his blog!
    There could be some significance to the letter A's and the pantograph, but aren't all the clues in the two DT portraits?

    1. Yes, the MOST important clues ARE in the two DT portraits. But, to "see" them, one must be prepared to don the eyeglasses that Bessler offers in the second portrait. One puts those glasses on by doing a Herculean amount of measuring AND building / modeling. Sadly, only a FEW in a thousand Bessler mobilists will have what it takes to put those glasses on so that his vision of Bessler's working OB PM gravity wheel design will come into razor sharp focus.

      That, however, was exactly how the Master wanted it to be...

    2. There most certainly is 'some significance' to the letter A's.

      The clues are not in the portraits in DT, they are to be found in AP, MT and the eyewitness statements.


    3. If ALL of the clues were just in AP, MT, and witness statements, then Bessler's wheels would have been duplicated CENTURIES ago. To be sure there ARE clues in those sources, but they are very vague in nature and not enough to begin reconstructing Bessler's design. With the portrait clues, it's a different story. We suddenly have mathematical information to work with: angles, ratios, and, indeed, ACTUAL numbers!

      In a previous blog entry's comment section, I tried to bring to the attention of my fellow reverse engineering Bessler mobilists (referred to as "hungry squirrels" in past comments) how one could pass a straight line through the tips of the noses of the two angels on the background organ and the center of its attached clock's dial in the second portrait. I then pointed out how one could ALSO pass another straight line from the center of the clock's dial through the tip of the Master's nose and then onward through the center of the "nose" or bridge of the eyeglasses he holds in his right hand.

      Did ANYBODY even notice (or CARE!) that these two lines form an angle? Did ANYBODY even bother to measure it? Did ANYBODY even look to see if that EXACT same angle appears anywhere else in the 2nd portrait or in the 1st portrait? IF he was lucky enough to find it, did he even wonder why that PARTICULAR angle is repeated?

      IF one can not be bothered with performing such a minor and INITIAL bit of low level analysis of the two portraits' many embedded clues, then, for all practical purposes, he will REMAIN "blind" to the rich supply of data they both contain. Furthermore, his chance of EVER duplicating BESSLER'S working OB PM gravity wheel design will also remain next to ZERO!

  3. green is nice ;)

  4. Doug, are you confusing me with TG? I'm not convinced there are any clues in the portraits, other than the presence of a pentagram.


    1. Naw, I'm just poking fun.

    2. @ JC

      Yes, there are several pentagrams in the portraits and Bessler certainly included them to suggest something IMPORTANT about his wheel's internal mechanisms to those who might one day try to duplicate his wheels. I won't bother restating what my interpretation of this important symbol is except to again emphasize that it does not indicate that ONLY 5 isolated "perpetual motion structures" were used in each of his one-directional wheels or two-directional wheel's one-directional sub wheels.

      Bessler, being a student of art, would have been well aware that other artists where embedding various geometric figures into their works to express certain of their beliefs in a covert way. That's how Bessler got the idea to do it.

  5. Arrggghhh...I'm still a bit bleary eyed from this sudden change in background color! I think I find the previous blue colors more relaxing and "eye friendly".

    Well, it's obvious that MT 143 was influenced by Roberval's balance of 1669, but, not being equipped with weighing pans, it is not intended to be used as a conventional balance. I think that Bessler included it in MT to illustrate the PRINCIPLE of counter balancing which WAS used extensively by his secret wheel mechanism.

    In MT 143, one can rotate EACH gear locked pair of weighted arms so as to move the CoM of their two end weights from one side of their gear pivots to the other and, due to their perfect torque counter balancing through their intermeshed gear teeth, the weighted arms and their CoM will REMAIN in whatever location they are placed. This can be done with the other pair of gear locked weighted arms as well. Then, due to the Roberval type parallelogram frame of the larger device, the two pairs of gear locked weighted arms can be further tilted with respect to each other and they will ALSO remain in that position. Thus, one can, as suggested in MT 143, swing BOTH of the gear locked pairs of weighted arms to the right side of the device's central vertical support piece which will then move the CoM of the four weights over to the right side of that support piece while also INDEPENDENTLY tilting the parallelogram frame's right side as high as possible and, yet, the system will REMAIN in perfect balance and be stationary.

    Why did Bessler include such a device, which is NOT intended to display PM, in his grand treatise on mechanics? Simple.

    We must remember that this work was intended to be a build up to the final illustrations of the design he found and used which DID display PM, but which, unfortunately, were removed and destroyed. That design depended upon the maintenance of the OB of the CoM of a collection of weights as the wheel's drum containing the weights continuously rotated. By including MT 143, Bessler intended to show his future students how PRECISE counter balancing could be used to CONTINUOUSLY keep the CoM of a collection of weights (only 4 used in MT 143) on ONE side of the center of motion of a movable device.

    Although MT 143 demonstrates the power of counter balancing in regulating the location of the CoM of a collection of weights, it is NOT the same method that Bessler used in his OB PM gravity wheel design. That design does not use gears or rigid connectors between its weighted levers and that is the only reason Bessler left MT 143 behind when he destroyed the woodcuts that would have produced the final pages in MT that would have showed his secret PM design.

    I would not make too big a deal over the variations in the letter "A" that Bessler uses in his MT illustrations. We do not know what the exact TIME order was that the various MT illustrations were completed in. We see only the order suggested by their arrangement IN THE WORK and then ASSUME that was ALSO the time order of their creation. Perhaps ALL of the illustrations containing the decorative "A's" with the right angle corner as a cross bar were completed during a time period when Bessler was temporarily obsessed with freemasonry and its symbolism. Maybe, like a fever, that obsession eventually passed and he then began to use the regular looking "A's" again. Not wanting to redo all of his previous woodcuts with the decorative "A's" in them, he left them. I don't consider this "clue" to have any real significance and I don't waste time trying to attach anything "deeper" to it.

  6. Replies
    1. Yes John, Happily I can agree with TG for once, this colour is much better (and more appropriate), the green was 'nice' as others commented, however this colour is much easier on the eye.


  7. Ahhhhhh....that's better, much better, John. My eyeballs are profoundly grateful!

    The tan background sort of reminds me of more "Bessler appropriate" things like maybe the color of a faded parchment document containing some really important information like the secret of Bessler's OB PM gravity wheel design! I'm also happy to see the entry page's dandelion replaced with the birds in flight. Why have Bessler associated with an undesirable garden WEED when he can be associated with birds apparently defying the laws of gravity? If you could have found something depicting ROTARY motion, like a water or wind mill, then than would have been nice too.

  8. The A is definitely very conspicuous in many of the drawings, but I must say that the T pendulum is also in many of the drawings and wood carvings. Both are common throughout, but what is he trying to tell us?

    1. He is telling us that the 'A' and the 'T' are pro forma (in the engineering sense) shapes/elements of The Machine.


    2. You have a point there. From a machine design viewpoint, if pins (simple pivots) are placed at all joints in the "A" with the bent middle arm, you have an example of the "four-bar linkage", which is in general a very sophisticated, versatile and useful kind of linkage, (where the arms move relative to each other). The Roberval balance, pantograph and the "toys page" illustrations are other examples.

      On the other hand, if pins are placed at all joints in the "A" with a single straight middle arm, you get a triangle, where no relative movement of its parts is possible.

    3. Thanks Arktos,

      Thanks for acknowledging my ‘point’

      I’ve been working with “pins (simple pivots) placed at all joints in the "A" with the bent middle arm” for a few years now (see my sculpture: An Overbalancing Beam 2008).
      I first posted this idea; this arrangement of levers, on my website 18 months ago, in my drawing titled ‘Two Types of Letter A’; highlighting the difference between the A’s ‘the right way up’ and the A’s ‘up side down’, (together with The Flail Arm: The Small Weight Armature pro forma)
      The A’s ‘fall open’ (when the point of the A is pointing to 12 o’clock) and they ‘fall shut’ (when the point of the A is pointing to 6 o’clock). This is an interesting difference!!
      I played a little game in my drawing by placing them ‘the wrong way around’ (I was after all re-presenting Bessler’s Clues and taking into account all that that entails)
      There are several other good ‘points’ on my website:
      You could take another look.

    4. "I’ve been working with “pins (simple pivots) placed at all joints in the "A" with the bent middle arm” for a few years now..."

      That "A’s ‘the right way up’ and the A’s ‘up side down’" effect could just as easily be achieved by replacing the A's center horizontal folding cross bar with a simple piece of chain or a cord. Does Bessler, anywhere in all of MT, ever show one of the straight center cross bars on an "A" that is inverted? If not, then, obviously, HE did not attach that much importance to this "effect" that YOU have "discovered".

    5. A chain or cord is flexible, so the effect wouldn't be the same as a rigid bent crossarm in A's.
      The pantograph and roberval balance could be in the DT portraits.
      It's almost a sure bet they are there.

    6. @ Doug

      There are a lot of drafting tools in the second DT portrait whereby Bessler suggests that the reader actually USE them in making measurements on the items IN that portait. Sadly, only a few in 1000 Bessler mobilist ever will! As far as the pantograph and roberval balance are concerned, they are not to be found in the portraits.

  9. the parallelogram toys are drawn twice and notated twice CC : DD, 'a pair of pairs' ?

    1. The fundamental 'self-moving' element of The Gravity Wheel is The Overbalancing Beam; two overbalancing beams constituting a 'minimum wheel'(the type that "does not have the normal type of rim"), and so, yes, Jon Anonymous, you are right, The Mechanism is truly constantly a pair of pairs.

    2. "The Mechanism is truly constantly a pair of pairs."

      Good luck trying to maintain the OB of just 4 weights!

    3. @ Doug

      I'm not sure exactly what the minimum number required would be, but I don't think it can be done with only 2 to 4 weighted levers based on my previous failed attempts to do. Maybe the minimum number to maintain OB is 6. I'm SURE it can be done with 8 weighted levers, however, and that is the number I routinely work with.

      Meanwhile, my continuing analysis of the DT portrait clues has suggested a previously UNsuspected modification to my "magic" lever design which, at first glance, seems VERY odd, but which has really piqued my interest.

      Currently, my research focus is on getting the 9:00 going to 10:30 weighted lever to "rise in a flash" as the 7:30 going to 9:00 weighted lever swings CCW during a 45 degree increment of CW drum rotation and its weight moves closer to the axle. I've concluded that when Bessler wrote "in a flash" he meant that the 9:00 going to 10:30 lever's weight would SM0OTHLY and continuously draw closer to its rim stop (but not contact it yet) THOROUGHOUT the entire 45 degree increment of drum rotation. This means that its lever had to start swinging CW about its pivot just as soon as that pivot passed the 9:00 position of the drum. This requires that the 9:00 going to 10:30 position lever's weight must be supplied with sufficient energy / mass as soon as possible and that can only be done if the transfer begins immediately and is as efficient as possible to achieve mechanically.

      All of my previous attempts to achieve this effect have failed, but those were done with the "old" magic lever design which I've worked with for about the last year or so and which I now realize is NOT the most efficient for either transfering OR receiving energy / mass. This new lever design suggested by the DT portrait clues looks VERY promising and I should know in a few more days if I've have finally found THE magic lever that Bessler used!

      As the Sherlock Holmes character once said, "When you eliminate the impossible, whatever remains, however improbable, must be the truth."

  10. Would be great if we could add graphics in with the text or add attachments.

    1. The only way that could be done is if you were to send them to me and I could post them.


    2. Unfortunately, these blogs don't allow visitors to use html coding in their comments so that they can "call" images hosted on other sites into their comments. Also, they are apparently not interested in providing the extra storage space needed so that visitors can directly upload their own images into their comments.

      If one really needs to post an image, he should do so on a free host site like and then just provide the link to the image there in his comment. Those who are really interested will find it.

  11. I have animated the above drawing (#1) and the motion it is meant to depict . You guys are "thinking" of these drawings in a static sense when they were intended to depict motion . The upright is swaying side to side with it's fulcrum at the base . The weights are geared together at their pivot points and follow the sway of the upright somewhat delayed but synchronously . The horizontals are no more than a framework to support the weights in their positions and are of little assist to the motion .

    1. "The upright is swaying side to side with it's fulcrum at the base.

      I don't see any indication in MT 143 that the main vertical support is supposed to move relative to its base.

    2. So far as I am aware, there is no MT143, Bessler's images end with MT140 don't they?


  12. The 'toys' page, which is numbered 138, 139, 140 and 141 is the last page in the book. The other un-numbered pages were included because they formed part of the collection, which were all unbounded pages, found in the museum library at Kassel.


    1. After Bessler's arrest, it must have been the four woodcuts for pages 138 to 141 which were the ones he "burned and buried" and which contained four nice illustrations of his working OB PM gravity wheels. Most likely 138 and 139 originally showed the ONE-directional wheel's internal details and 140 and 141 the TWO-directional wheel's internal details. Perhaps out of some sense of religious guilt and to aid future reverse engineering mobilists working from a posthumously published work (which is would be), Bessler quickly made up the single "toys page" which only VERY generally HINTS at the KINDS of actions that went on inside of his wheels and then inserted it to take the place of the destroyed pages.

      Why two illustrations per wheel?

      Logically, there would have been two illustrations per wheel in order to show two views of each wheel: one "full face" or looking along the length of its axle and the other "profile" or looking in a direction perpendicular to its axle.

      The full face views would have shown the shapes of the "magic" levers and the "Connectedness Principle's" system of interconnecting cords between the weighted levers as well as the attachment points of the lever return springs. The profile views would have shown the "layering" system Bessler used to keep the cords within each wheel from rubbing against each other, fraying, and failing during drum rotation. The profile views would also have shown that his two-directional wheels were, in fact, made from two one-directional wheels whose "preferred" directions of rotation were opposed. It would also have been obvious that the two-directional wheels required additional latches be installed in order to lock down the weights against their rim stops when their particular "sub wheel" was undergoing retrograde rotation.

      What the actual intended order of any UNnumbered pages in the work was supposed to be is anybody's guess. Perhaps the correct order, using our arbitrary numbering, would have been: 142, 143, 138, 139, 140, and 141. I can't see any purpose to putting 142 and 143 last as we now do.

  13. @ TG and Doug,

    You guys have misconstrued/misunderstood what I said. I was responding to Jon Anonymous’s observation: to His Way of phrasing The Problem: to his basically correct interpretation of a visual clue.

    Have you temporarily forgotten that Bessler said the weights are arranged in pairs such that as one moves closer to the axle, the other moves further away?

    I could have phrased my response to Jon better. The Mechanism is pairs of pairs of pairs, whether that is weights, levers bearings or whatever. Jon correctly identified one such pairing and also touched on a basic principle.

    I do prefer it when we can agree TG. Your comment that “Maybe the minimum number to obtain OB is 6” is one that I can happily go along with. To be clear, that means 3 pairs of weighted levers.


    1. No, JW, we have not forgotten that he wrote:

      "I’d like, at this point, to give a brief description of it. 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."..."At present, as far as I’m concerned, anyone who wants can go on about the wonderful doing of these weights, alternatively gravitating to the center and climbing back up again, for I can’t put the matter more clearly." (AP, pgs. 295-296)

      It's important to realize here that in this quote Bessler is describing a "pair" as consisting of two DIAMETRICALLY opposed weights on OPPOSITE sides of the drum's axle. He is NOT describing two weights that are in close proximity to each other near the rim on ONE side of the drum. IF the latter was the case, then, as one weight moved closer to the axle and the other farther from it, there would be NO change in the distance of their CoM from the axle and, therefore, no effect on the composite CoM of ALL of the weights within the drum. ONLY by describing diametrically opposed pairs of weights can the shifting motion he describes result in a change in the location of their CoM and, therefore, the location of the CoM of ALL of the weights within a wheel.

      Geometrically speaking, one can certainly consider an 8 weighted lever wheel to be made up of 4 diametrically opposed pairs of weights each of whose connecting diameter intersects its nearest opposed pairs' diameters at 45 degree angles. BUT, that kind of image tends to make one think that there were DIRECT mechanical connections between the weights in each of these pairs. That can not be the case because such direct connections would require the connecting rods or cords involved to pass directly through the drum's interior axle section or very near to it. IF that had been the case, however, then those "no track" skeptics viewing Bessler's wheels that were permitted to reach into their drums and feel their interior axle sections would have felt these directly interconnecting rods or cords and, no doubt, we would also find statements about this by others who examined the drums during their "official" examinations.

      IMO, one should, when reverse engineering Bessler's wheels, avoid trying to make "perpetual motion structures" consisting of single "isolated" weights or simply interconnected, buy still basically isolated, "pairs" of weights. Bessler's "Connectedness Principle" connected ALL of the 8 weighted levers within a one-directional wheel or sub wheel together via a unique system of cords that, literally, completely encircled a drum's axle near its periphery. There were no isolated "perpetual motion structures" within Bessler's drum because ALL 8 weighted levers worked together SIMULTANEOUSLY during drum rotation so as to keep their CoM always located on the drum's descending side.

      While one should, of course, seek simplicity when reverse engineering Bessler's wheels, there is, unfortunately, the constant danger of making things TOO simple! Most of those basing their designs SOLELY on the designs found in MT are, unfortunately, doing exactly that!

    2. "It's important to realize here that in this quote Bessler is describing a "pair" as consisting of two DIAMETRICALLY opposed weights on OPPOSITE sides of the drum's axle. He is NOT describing two weights that are in close proximity to each other near the rim on ONE side of the drum. IF the latter was the case, then, as one weight moved closer to the axle and the other farther from it, there would be NO change in the distance of their CoM from the axle and, therefore, no effect on the composite CoM of ALL of the weights within the drum. ONLY by describing diametrically opposed pairs of weights can the shifting motion he describes result in a change in the location of their CoM ... "

      Well done. You express this important point very clearly.

    3. Thanks, Frank. I always try to state things as clearly as possible so that as many people as possible will understand what I'm trying to say. Unfortunately, this sometimes requires me to be a bit more "wordy" than some feel is necessary.

      Well, I have some preliminary "good" news to report about that "new" magic lever design that I am currently working with.

      When I put certain of the levers in the Merseburg wheel's one-directional sub wheel's design I have into the interval repeating configuration that is required of them (determined by the DT portrait clues, of course), I immediately noticed a BIG improvement in the location of the CoM of ALL of the 8 weights because of the new magic lever. In fact, the CoM of the design's 8 weights shifted from about 0.8 inches out onto the drum's descending side to about 1.24 inches out measured horizontally away from a vertical line passed through the center of the axle.

      This might not sound like much, but it translates into a 55% INCREASE in the torque that drives the drum! (There's that number AGAIN!!!) My new driving torque for the Merseburg wheel now becomes 39.7 lb-inches. This means that if the axle was 2.5 inches in radius, then this torque would be sufficient to CONTINUOUSLY lift any weight with a mass less than about 15.9 lbs via a rope wrapped DIRECTLY around the axle. Using a block and tackle that had been "reduced 5 times" would allow the wheel to continuously lift any weight with a mass less than about 79 lbs. This would, obviously, explain why the Merseburg wheel was reported to do exactly that with a 70 lb load although, of course, the lifting rate was very low.

      I still have much testing to do. Mainly, I want to see if this new lever will make my 9:00 going to 10:30 levers' weights "rise in a flash" which just means that they will CONTINUOUSLY approach their rim stops THROUGHOUT each 45 degree increment of CW drum rotation (but not touch them). This a CRITICAL condition that MUST be met otherwise it is NOT possible to maintain the CoM of all of the 8 weights on the drum's descending side.

      Ultimately, this is what Bessler wheel research is really all about: finding THE design the Master found that would keep the CoM of 8 weights continuously on a drum's descending side as it rotated. If Bessler research was an Olympic event, then doing that would certainly earn one a gold medal. Finding ANY design that does that OTHER than THE one Bessler found is also a MAJOR achievement, but I would only give a silver medal out for that since it would not be THE one (by this standard, I would have to give Asa Jackson a silver medal). Who would I give the bronze medal to? Well, I think those should go to all of the tens of thousands of sincere mobilists out there, past and present, who spent such large portions of their lives pursuing the "Holy Grail of Mechanics" without success. They, too, deserve some recognition for their sacrifices.

  14. @TG

    There really aren’t many references to the axle of The Mechanism in either AP DT or GB. The quote you refer to in support of your ideas says:

    “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 (meaning it is not a divided axle). Rather, it has many compartments, and is pierced all over with various holes”

    If you are right TG, why did Bessler create “many compartments” in his axle?
    Why did he spend time, effort and money making compartments in order not to use them for some purpose? Did he just make some empty compartments for the fun of it?

    Are you also proposing that Bessler made an axle “pierced all over with various holes” for absolutely no reason at all?


  15. We covered this issue months ago.

    In the quote "Rather, it has many compartments, and is pierced all over with various holes", the word "it" does NOT refer to the axle, but, rather, to the drum of the wheel. That drum, when uncovered would, because of its sets of parallel radial support members, appear to be divided into 8 octants or wedge-shaped sectors or "compartments". If any of Bessler's axles had actually been "pierced all over with various holes", they would have been too fragile to support the weight of the drum and the weighted levers it carried. The "holes" refer to the 8 circular inspection holes that Bessler cut into the cloth layers covering ONE side of the drum.

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