DD,
In post #317, the model is incorrect. The two guides should be parallel to each other. So are the arm and one of the guides.
I corrected it and this is the new model now. Although there are still tracking errors at end of the trajectory, it is small now. The small tracking errors may be caused by the placement of the mid-guide. In any case, this version of geometry may work.
In post #317, the model is incorrect. The two guides should be parallel to each other. So are the arm and one of the guides.
I corrected it and this is the new model now. Although there are still tracking errors at end of the trajectory, it is small now. The small tracking errors may be caused by the placement of the mid-guide. In any case, this version of geometry may work.
Bon,
Your new geometry still has the same problem as the one with single guide because the rear guide rails can't precisely hold the positions. If the rear guide rails can hold the position precisely, it works. Please see the diagram below.
If you adopt DD's proposal to add a linkage, it can work although it is still very complicated without knowing if the arm skates or not. It has four moving pivots, two stationary pivots, three linkages, and one slide.
Your new geometry still has the same problem as the one with single guide because the rear guide rails can't precisely hold the positions. If the rear guide rails can hold the position precisely, it works. Please see the diagram below.
If you adopt DD's proposal to add a linkage, it can work although it is still very complicated without knowing if the arm skates or not. It has four moving pivots, two stationary pivots, three linkages, and one slide.
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Whenever I see a parallelogram or a rhombus in this type of design, I immediately thought why even bother with Thales circle when you can just do it in a straight line. A parallelogram is capable of extending out into a straight line with only one or two stationary pivots. At this point you can do away with all the fancy geometries and math. It becomes quite intuitive. You can even use a hexagonal structure to make it work, with some guiding mechanism for assistance. As long as you can extend 4 inches of playing surface, you have yourself a pivoting parallel tracker! The problem is having a cantilevered device can compromise structural integrity. A least it makes the concept simpler. The beauty of Birch style arm is that you only need two mass loaded pivot points, unless you're going for absolute zero tracking error. The guiding mechanism parts have little mass so it's not so critical.
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Yes, this is geometrically identical to the tangential geometry I describe, provided the pivot locations are the same.
The location of the guide pivot over the platter is the reason why instead I have 2 circle guides which are away from the platter. If there is a way of locating this pivot that can swing into position over the platter consistently, securely and accurately, then it can work. I never came up with an acceptable way to do this.
The inaccuracies due to improper location of the circle guides pivots should not be possible with precision construction. The distance between the guides cannot alter, which it must do to mis-align. The concerns about this occurring in practice are similar to observations that passive parallel trackers can’t work because they are never exactly radial. The question should be, how much better are they than traditional pivoting tonearms and is it worth the effort? I can’t answer this at present and I guess everyone will come to their own conclusion.
The tangential geometry conforms to the classical compass and straightedge construction principles.
https://en.wikipedia.org/wiki/Straightedge_and_compass_construction
To borrow a quote from the Wikipedia page
“… straightedge and compass constructions appear to be a parlour game, rather than a serious practical problem; but the purpose of the restriction is to ensure that constructions can be proved to be exactly correct.”
In principle, the tangential geometry proposed is actually simpler than that of a typical pivoting tonearm, which require non-elementary offset and overhang calculations to approximate tangential alignment.
I agree with directdriver. More pivots could be counterproductive in overall results. I am not mechanical engineer and only posting out of intution so pardon me.
Less pivots/moving part better. As shown in my previous post (Not 100 % accurate) We only need a V groove* plate in arc shape to constrain (Shown in red in following picture) Advantage is less friction/moving parts and added to that the movement is in almost same direction as stylus drag. Whereas extra linkages loads the contraption with resistive forces and needs to be pulled in 90 degree direction (Shown in green). How much force I dont know for sure though.
* The ballbearing in the V groove channel moves on its own axis too.
Less pivots/moving part better. As shown in my previous post (Not 100 % accurate) We only need a V groove* plate in arc shape to constrain (Shown in red in following picture) Advantage is less friction/moving parts and added to that the movement is in almost same direction as stylus drag. Whereas extra linkages loads the contraption with resistive forces and needs to be pulled in 90 degree direction (Shown in green). How much force I dont know for sure though.
* The ballbearing in the V groove channel moves on its own axis too.
Very creative idea for extending the tonearm. I now see what Ralf was referring to with the Bosch mechanism.
My first concern is there are now varying forces out of the horizontal plane which will affect the stylus downforce.
Also the pivoting cantilever must be free to collapse, all the vertical forces on the tonearm are downwards, so where does the vertical positioning come from?
At least there is only one horizontal bearing and minimal horizontal friction.
I don't know enough about the magnetic forces of the guide rail. I have seen how magnets can produce spectacular motions and configurations. It might be difficult to predict.
Up till this point I have been keeping the tangential geometry tonearm length short since there is no loss of accuracy unlike a conventional off set pivoting tonearm. However as has been pointed out, a short tonearm puts the Thales circle centre inconveniently located in the playing area of the disc. This is what prevents a simple radial arm enforcing the rolling circle guide position. Increasing the Thales circle diameter will put its centre outside the platter area and the circle guide can then be enforced with a simple rigid link as shown below. The animation shows the sliding pivot-to-outer groove distance 28 cm and Thales diameter (tonearm length) 31.58 cm. The link positions are at the 1/2 and 1/4 distance from the rear. The circle guide tracks and followers are now not required.
The rear circle guide bearings are no longer vertically supported and are cantilevered off the Thales circle pivot and the tonearm. Even with lightweight carbon fibre links, I don’t know if the bearing will support the twisting induced by the unsupported cantilevers. Solving one problem leads to another. Such is life. Constructive suggestions are welcome.
Bon,
If I were you, I might compress the movements even more so all the linkages are around the base.
I think my 6D is the best option so far. It doesn't skate, its bearings are highly efficient, and its tracking errors are completely neglectable. All the goals for a PT arm are achieved in my 6D with the simplest structure possible for a PT arm. I did an error analysis. Please see the diagram. The tracking errors are smaller than the tolerance of construction.
Jim
If I were you, I might compress the movements even more so all the linkages are around the base.
I think my 6D is the best option so far. It doesn't skate, its bearings are highly efficient, and its tracking errors are completely neglectable. All the goals for a PT arm are achieved in my 6D with the simplest structure possible for a PT arm. I did an error analysis. Please see the diagram. The tracking errors are smaller than the tolerance of construction.
Jim
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Hi super10018.
Your post is very thought provoking. On the face of it, the errors appear tiny and very encouraging for the simple geometry. However, may I suggest that you try and repeat the error analysis computing the deviation in the angular displacement from tangency at the stylus. Distance errors can be subtly different from angular errors. Even sticking with distance errors, a better measure would be the difference in the stylus-to-Thales pivot distance and the actual Thales circle radius. This is zero for perfect tangency.
Bon
Hi Jim.
I took your advice and compressed the tangential bearing structures closer to the main sliding pivot.
The tonearm can’t be too short since for build ability, the Thales circle centre has to lie off the platter area. With the tonearm link points at the 1/2 and 1/4 distance from the rear, the compressed geometry has the parallelogram link structure replaced by a kite. The included circles should be sufficient information to allow anyone interested to reproduce and modify this geometry with the aid of a virtual straightedge and compass construction. An angle bisection at the kite acute vertex may be required.
Interestingly the circle guide paths are now very short and I can see where the Birch geometry comes from and why it can give a good approximation to tangential geometry. When the circle guide paths are very short, it is reasonable to replace them by fixed points (say, at the circle paths mid-points). This allows the sliding pivot constraint to be dispensed with, together with the entire end 1/4 of the tonearm, as well as the Thales pivot link. Furthermore, with no Thales pivot link required, the tonearm structures can be moved closer to the platter, for a shorter, more compact tonearm with fewer friction points. The tonearm link paths are now circular arcs which we know is incorrect, since they are actually limacons.
I plan to obtain error estimates.
Bon