I've offered my observations re Bessler's toys C/D previously but in order to best make the case here, I need to start by touching on them again..
Toy A/B is clearly a recognizable one...but a toy that needs to be viewed from two angles to have any real chance of ever recognizing it....thus A & B. This toy, a Jacob's Ladder, displays/employs a flopping motion from side to side.
A too casual glimpse at C/D might easily lead one to assume likewise....the same toy shown from two angles...not front/side as per A/B but left/right C/D..a flopping from side to side also.
However, it soon enough becomes very obvious that C/D are actually two different toys. Bessler has taken every possible opportunity to change the graphical details....different handles, different characters, different everything as such.
So...C, like A/B, we recognize & know well. D looks like the C we know but it has one mysterious & obvious difference...the two twisted characters.
D apparently has some kind of twisted element to it beyond the C we know.
The repeat of the letters C & D within both parallelograms suggests that it is here that C/D differ...here where something twisted happens to a C, so's to become a D.
All that said, then here is what I've established re a twisted toy C...
TOY `D`
Take a square (ABCD) & twist any two opposite sides (A/B & C/D chosen) through 90 degree ....to thus form four edges of a six edged regular tetrahedron.
Twisting A/B & C/D against each other in one direction will result in the two joining struts (A/C & B/D) Twisting in the reverse direction will result in the two thinly shown struts A/D & B/C instead.
Again, the essence of what we're dealing with here (Tetrahedron) I have eluded to before. I'll not go into the proof of it again, although I gladly will if requested. For now I will just stick to a statement of fact, that being that a regular tetrahedron is the geometric construct formed where double helix's, one from each of the three dimensions, meet/cross.
Choose any two opposite edges of a tetrahedron as the spokes to support a double helix & the remaining four edges form that double helix supported. There are three options when choosing any two opposite edges...one in each of the three dimensions.
So...in essence, what we have here is one half of a double helix, a helix, held along/around an axle.
As we are only addressing the one helix of a double then this construct, should it turn at all, will turn in one direction only. As stated above....twist the original square in the opposite direction and one is then addressing the other helix of the double, to now turn in the opposite direction.
It's entirely possible, by design, to construct a means whereby all four struts (both helix's) can be addressed in the same unit. In this instance then one helix is addressed in one direction of turn, the other rendered inoperative....& visa versa.
Hopefully this is all as easy to comprehend thus far as I'm hoping for? If you're confused/unsure then this would have to be a failure in my presentation as it's very simple, for sure.
Onward then....
We have a helix formed by two strands/struts (A/C & B/D). These are supported by two spokes (A/B & C/D) set centrally on an axle & these two spokes are able to sway on that axle. Connected as they are to each other by way of the two strands/struts of the helix, then clearly, if one sways so the other must follow suite..& if one is set to sway in the vertical then just as obvious, the other must sway in the horizontal.
The whole construct here is `the weight`...'tho I could suggest a few simple ways in which to add specific weights at specific locations...t'would make no difference. But...just for ease on the imagination purposes, I'd ask you to imagine that the two struts are `the weights`....all else being of little/no significance.
We have then, nothing more than the two heavy strands of a helix wrapped along/around an axle....& these two strands can be manipulated by way of the two spokes it sits upon being able to sway.
As we're dealing with a turning helix about an axle then in addition I need only point out the following re the two heavy strands/struts.....
When sat centrally across the 3 o'clock position a strut is sloped across the axle, the horizontal therefore, in one direction & sloped in the opposite direction to the axle/horizontal when at the 9 o'clock position. Both struts are only in the horizontal plane when sat at the 6/12 o'clock positions, the point at which they both switch their slopes from one way to another, through the horizontal plane.
And that sounds unnecessarily complicated really..'tis the aspect of a turning spiral that most every inquisitive kid notes, nothing more.
Whatever...we have our helix mounted on an axle & its spokes can execute a swaying, back & forth through a midpoint...where both spokes are perpendicular to the axle...the regular tetrahedron point.
How then to effect this swaying motion?
The Sabu disc offers the principle characteristics required...consisting of six 60 degree sections around, three raised up, three dipped in. Please imagine that Bessler's wheel engraving is likewise..let's say the black sections are the raised up, simply mounds for Bessler rather than petals & the white sections are simply cut-out sections. But keep in mind that it's 6 x 60 degree sections...not as Bessler shows in his engraving.
Place two of these on an axle, facing & independent oF each other. Align them such that looking along the axle, mound is directly opposite mound, cut-out opposite cut-out.
Turn either one through 90 degree in either direction...NOW you have Bessler's wheel engraving.
If you take a rod, its length the diameter of a Sabu disc or similar and sit that rod across the diameter of said disc then clearly it cannot sit straight....one end of the rod will be raised by a petal/mound, the other end will be in a dip/cut-out.
Were you to turn the rod about the axle then it would reach a straight/mid-point situation & go on to reach the situation whereby it is now slanted in the opposite direction.
Again...over complicated perhaps. Press gently down on the rod ends, turn it & the rod performs a turning/see-saw motion as it negotiates the up/downs of the disc.
Ok...we extend the axle of fig one to accommodate a disc at either end, device snugly between. Viewed sideways on we have a spoke to the left, swayed..it's one end on the very top of a mound/petal, it's other in a dip/cut-out. It is at the full extent of it's sway in one direction.
It's the case therefore, that the other spoke must also be swayed to its full extent...in a cut-out/on a mound. Clearly this cut-out/mound must be at 90 degree around from the first disc's cut-out/mound. Thus the Bessler engraving position outlined above when viewed along the axle.
From this position the device can be swayed back through its central/tetrahedron point, over to the other side.
Right...this is the only potentially tricky process to attempt to describe but...
Reach between the two discs, grab a hold of the two struts & manually shunt them against each other, thus manually swaying the two spokes through the central/tetrahedron point & on, over fully to the other side.
In doing so the helix is not turning about the axle....so the discs have to turn. If you held the discs firm then the helix would turn.
However, it's deeper than that...& to be honest, I've barely got a grasp of it myself, not so's I'd be able to put it to words with any success though.
I'll attempt a little insight....
If a spoke is fully swayed, one of it's ends in a cut-out, the other on a mound, then in order for it to reverse that situation either it...or the disc...or both...needs to rotate around by 60 degree. And here we have two spokes, connected, that therefore need to both move in relation to their discs by 60 degree in order to fully sway over in one direction.
The fact that these two spokes act twisted, 90 degree twisted...& the Bessler engraving point viewed along the axle that results when fully swayed in either direction, plays a part.
The helix is turning about the axle in one direction, swaying from side to side as it goes...& it must therefore be turning in the two discs in order to do so. However, these two discs are not themselves stationary.
They turn in one direction..but with a sway.
So, viewed along the axle...the Bessler engraving will morph to a regular 6x60 around, onward to the engraving again...'cept it now appears 180 degree around...upside down.
The discs turn but in a creeping fashion, from side to side, each one constantly overtaking the other. Crab does indeed spring to mind by way of example.
And...that's it folks!
It being what I've established re a twisted toy C....& nothing more.
I'm not going anywhere near as to why this thing might perpetuate. As often stated, I've no clue, nor great interest, in all the energies/forces that are at play here....Over to you if you can be bothered?
I must argue tho' that you should be....'cos the joining of the dots here strongly suggests a picture of intrigue & possible advance rather than the same old, same old & perpetual stagnation?
Nah?
(sighs) "Oh well"
Gill :)
