After realizing the ellipse found on my geometry is not based on the Thales circle, might as well see if Thales/LP circle geometry have their own ellipses.
Where I found the ellipses on my geometry algebraically, here I'll use analytical geometry (my favourite).
I constructed some geometry from a recent thread with a 250mm "arm" length as below.
Fitting a circle can only be done using 3 point constraints and results in the known tangency errors.
An ellipse can be fit to all the point constraints, and can be expressed as a simple function.
Below the construction geometry for the ellipse, it is orange because the centre, minor and major axis are not defined and are only constrained to the endpoints of the tangent lines of equal lengths.
In fact, no matter where, or what size I draw the Thales circle, it results in a perfect ellipse that can be expressed as a simple function, every time.
Same Thales constructiuon.
Now this does seem to make my first statement false, because if there is an ellipse on all Thales/LP geometry and there is one in my geometry, mine is based on the Thales/LP geometry also.
I feel fairly confident to say that any Thales circle related to another circle by tangent lines of equal length, will result in an ellipse that lies coincident on all end points of the tangent lines of equal length, and I think I know why.
I'm willing to bet that if you place the foci of an ellipse on the centres of the Thales and LP circle with a relation to the diameters of the circles, you might get a scaled ellipse, will have to think on this a bit more though.
Where I found the ellipses on my geometry algebraically, here I'll use analytical geometry (my favourite).
I constructed some geometry from a recent thread with a 250mm "arm" length as below.
Fitting a circle can only be done using 3 point constraints and results in the known tangency errors.
An ellipse can be fit to all the point constraints, and can be expressed as a simple function.
Below the construction geometry for the ellipse, it is orange because the centre, minor and major axis are not defined and are only constrained to the endpoints of the tangent lines of equal lengths.
In fact, no matter where, or what size I draw the Thales circle, it results in a perfect ellipse that can be expressed as a simple function, every time.
Same Thales constructiuon.
Now this does seem to make my first statement false, because if there is an ellipse on all Thales/LP geometry and there is one in my geometry, mine is based on the Thales/LP geometry also.
I feel fairly confident to say that any Thales circle related to another circle by tangent lines of equal length, will result in an ellipse that lies coincident on all end points of the tangent lines of equal length, and I think I know why.
I'm willing to bet that if you place the foci of an ellipse on the centres of the Thales and LP circle with a relation to the diameters of the circles, you might get a scaled ellipse, will have to think on this a bit more though.
Although it may be an ellipse, it is possible to deal with circles only. In the meantime, it has minimized tracking errors.
The emphasis should be on the playable area of a record only. Next, there are two parameters that need to be optimized. 1. the dimension of the primary Thales circle. 2. length of arm wand. The maximum tracking error can be as small as 0.1 degrees after optimization while a regular pivot arm's tracking error can be as large as 2 degrees. It is possible that the tracking error can be even smaller for a double Birch geometry.
The emphasis should be on the playable area of a record only. Next, there are two parameters that need to be optimized. 1. the dimension of the primary Thales circle. 2. length of arm wand. The maximum tracking error can be as small as 0.1 degrees after optimization while a regular pivot arm's tracking error can be as large as 2 degrees. It is possible that the tracking error can be even smaller for a double Birch geometry.
2wice,
This is brilliant. I'm glad you're still on the case because I can't do the math. Hell, I can barely follow the math when it's explained.
I was messing around with ellipses last week and came up with this drawing. Frank Schroeder hinted at the possibility of a way to replace the control arm in the two arm design, and it's bearings, with a string and magnet. He also said it might be possible to achieve an ellipse.
The attached drawing of an arbitrary ellipse shows how that might be built.
I went back to one of my arm drawings and traced the actual partial ellipse, but didn't know how to find the foci. I hope your discovery solves that.
This is brilliant. I'm glad you're still on the case because I can't do the math. Hell, I can barely follow the math when it's explained.
I was messing around with ellipses last week and came up with this drawing. Frank Schroeder hinted at the possibility of a way to replace the control arm in the two arm design, and it's bearings, with a string and magnet. He also said it might be possible to achieve an ellipse.
The attached drawing of an arbitrary ellipse shows how that might be built.
I went back to one of my arm drawings and traced the actual partial ellipse, but didn't know how to find the foci. I hope your discovery solves that.
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The tonearm has effective length 25 cm at the outer groove, stylus follows the Thales circle (solid red). The pivot point initially at the origin follows a prescribed path (solid red). Extending the plots to the complete Thales semi-circle (dotted red) we get the pivot path (dotted red).
I don’t see any ellipses for the pivot path. Am I missing something here?
Extending the pivot path for stylus on the Thales circle off the LP area, produces something much more exotic.
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I have been trying to get the ellipse, but no success. I can say that it is very close to an ellipse just as it is very close to a circle. In other words, if an ellipse works, so is a circle. I didn't use 250 mm effective length since I think it makes no difference.
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I don't know why it is not working for you, but I do notice that all the points not coincident are on one side of your ellipse, so it seems your ellipse is not scaling correctly to fit?
The diagrams below show the actual Thales pivot path with tonearm length 25 cm between pivot and stylus locations.
Now that it can be seen that the path concerned is a portion of the of the actual pivot path which is very different from an ellipse, maybe there is little justification for using an ellipse apart from maybe ease of calculation. It is impossible for EVERY line of length 25 cm from the Thales circle towards the pivot to lie on an ellipse. It is only possible for every line to lie on the actual pivot path. I guess it all hinges on the meaning of "consistently fit"
I don't understand what is meant by this.
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FTFY
Consistently fit = always fits
Every single line of length on a 250mm arm that I tried, lies on the curve. If you would like me to plot the lines for any another radius, I'll do that for you.
Every single end point is coincident to the ellipse, it lies on the curve, exactly. The ellipse is constrained by those points.
I only use those points between the first and last groove, and care nothing for any other points. You can plot the curve outside that, but it has no purpose for me.
I am still suspicious that it is not an ellipse, so, I tried it again. Please see the diagram. This time I used 250 mm as effective length.
Here is the diagram to show you the detail.
You can see that there are errors. I connected all the endpoints of the tonearm and got the lt. blue area. The solid black line around the blue area is the ellipse. Clearly, not all the endpoints are located on the ellipse.
In the analysis above, I didn’t consider the playable area of a record. Now, let me introduce that factor. So, I will choose the endpoints within the playable area of record only.
Here is the detailed diagram. You may see the endpoints of the arm fit the ellipse much better now.
However, it is still not perfect. There are still some errors. For practical purposes, I would agree that the path of the endpoints fits roughly A SECTION OF AN ELLIPSE. In reality, the direction and the position of such an ellipse are important since an ellipse is directional. I wouldn't agree that the path of the endpoints IS an ellipse.
In my previous post, I said if an ellipse works so does a circle. Here is a diagram to show you how a circle fits on the path of the endpoints. A circle may introduce slightly more tracking errors comparing to an ellipse. However, if you change the position of the circle, the tracking errors may be as small as an ellipse for a specific tonearm.
An externally hosted image should be here but it was not working when we last tested it.
Here is the diagram to show you the detail.
An externally hosted image should be here but it was not working when we last tested it.
You can see that there are errors. I connected all the endpoints of the tonearm and got the lt. blue area. The solid black line around the blue area is the ellipse. Clearly, not all the endpoints are located on the ellipse.
In the analysis above, I didn’t consider the playable area of a record. Now, let me introduce that factor. So, I will choose the endpoints within the playable area of record only.
Here is the detailed diagram. You may see the endpoints of the arm fit the ellipse much better now.
An externally hosted image should be here but it was not working when we last tested it.
However, it is still not perfect. There are still some errors. For practical purposes, I would agree that the path of the endpoints fits roughly A SECTION OF AN ELLIPSE. In reality, the direction and the position of such an ellipse are important since an ellipse is directional. I wouldn't agree that the path of the endpoints IS an ellipse.
In my previous post, I said if an ellipse works so does a circle. Here is a diagram to show you how a circle fits on the path of the endpoints. A circle may introduce slightly more tracking errors comparing to an ellipse. However, if you change the position of the circle, the tracking errors may be as small as an ellipse for a specific tonearm.
An externally hosted image should be here but it was not working when we last tested it.
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You have me doubting, Jim.
So I tried another geometry.
Looking at the size of your deviation from the arc of the ellipse, it still seems a gradual change in error and might point to the ellipse not being scaled correctly, compared to the high variable errors on the circle.
It was also never that all points fall on the ellipse, only that the curve made by the end points on the section of interest, lie on an ellipse.
The blue circles and lines above are either point on curve or tangent relations, and I leave the ellipse centre and major and minor axis undefined to fall as they may.
This discussion for me has only ever been an interesting observation as my geometry and cams are machined not from the ellipse but from the calculated rotated and translated tangent lines. My focus now is improving the aesthetics of my arm going forward.
Any and all work you do Jim is of interest to me and I enjoy your posts, and I'm very keen on seeing your implementation of the double arm PTT.
So I tried another geometry.
Looking at the size of your deviation from the arc of the ellipse, it still seems a gradual change in error and might point to the ellipse not being scaled correctly, compared to the high variable errors on the circle.
It was also never that all points fall on the ellipse, only that the curve made by the end points on the section of interest, lie on an ellipse.
The blue circles and lines above are either point on curve or tangent relations, and I leave the ellipse centre and major and minor axis undefined to fall as they may.
This discussion for me has only ever been an interesting observation as my geometry and cams are machined not from the ellipse but from the calculated rotated and translated tangent lines. My focus now is improving the aesthetics of my arm going forward.
Any and all work you do Jim is of interest to me and I enjoy your posts, and I'm very keen on seeing your implementation of the double arm PTT.
Exactly! All I tried to show that only a section of an ellipse will fit the path of the endpoints of the arm. You might say it somewhere else or I might misunderstand you. When you said the path is an ellipse, I thought all the points are located on the ellipse. In fact, it is not.
I understand you are not willing to show your creation here and am very interested to see it. Although I have reservations about tangential pivot arms, I am always inspired by smart ideas in creating tangential pivot arms.
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Yes, all that matters in the geometry is the grooved area, that 4 inches of radius on the vinyl.
I can't wait to see your creation whenever you find suitable to reveal. This thread has spawned some creative ideas and mechanical inventions, including diy projects and possibly a few commercial products. It would please me and others tremendously to see the fruit of creativity and diy spirit in pictures.
After many hours of study of Reed 5A, I finally came up with my own proposal. I believe that the alternative version of Reed 5A geometry in another thread has fewer tracking errors than Reed 5A's. Now, I completely got rid of the geometry of Reed 5A. My new proposal has zero tracking errors within the playable area of a record. I had fun in such a mind game. My proposal is as simpler as Reed 5A if not simpler. I also dislike putting a cam in the rear of the tonearm since it may cause resonance in reality. The proposal of the tangential pivot tonearm I came up with has a bearing similar to Technics and SAT. But I am not sure if I will reveal it here from Doug's experience. I also found a couple of alternative versions of my proposal. However, the one I choose is the best. In my proposal, there is no ellipse. Very things are circles so it is easy to make.
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Hi,
I am pretty new and not a so skilled DIYer as you are, I would say a low DIYer, but allow me to have a laugh on all your show off of your technical skill, the so many secrets on building a tonearm that in reality is not such new invention, also have taken hints or idea from other manufacturer.......
And all above is quoted as a proposal in a forum for Audio DIYers. Sounds like a proposal to who? Mmmmm........yourself ?
Welcome to the principle of the DIYers and sharing for not commercial use!
Never mind, after all Italy just won the Euro 2020 and my TT is still sounding good and I spin records as the usually.... the clone of the TA Ref 1 sounds great and value more the Frank product and his sharing attitude.
Regards
Adelmo
I am pretty new and not a so skilled DIYer as you are, I would say a low DIYer, but allow me to have a laugh on all your show off of your technical skill, the so many secrets on building a tonearm that in reality is not such new invention, also have taken hints or idea from other manufacturer.......
And all above is quoted as a proposal in a forum for Audio DIYers. Sounds like a proposal to who? Mmmmm........yourself ?
Welcome to the principle of the DIYers and sharing for not commercial use!
Never mind, after all Italy just won the Euro 2020 and my TT is still sounding good and I spin records as the usually.... the clone of the TA Ref 1 sounds great and value more the Frank product and his sharing attitude.
Regards
Adelmo
It is disappointing when members consciously withold information on a DIY forum, especially after probably benefitting from the advice and information freely offered by others. I know it must be infuriating to have others use your expertise without proper acknowledgement, but obsessing over IP and patent rights relating to such a boutique activity as vinyl replay, goes against the spirit of DIY.
OTOH, there are posters who clearly are protecting personal commercial interests and professional reputations. The forums are merely a form of free advertising for them.
People can ignore those guys and avoid in giving any contribution or make comments to those show off and mean people........
I am in few forum and I have to say that each forum has his own trade mark, its own characteristic and way of participating to it. I think no forum is perfect, but amongst the few I lately read on regular base, perhaps this one is a bit less friendly and a bit more mean. The technical expertise seems higher as DIY, but not so sure about this last.
Not much talking about sounds result, most looking for technical perfection, ultimate technology to spin records, but in the end is missing the report about the sound improvements of such tweaks or building.
Wonder if most of the people do listen music, records or just try to build things.
However some good DIY project have been accomplished here therefore chapeau.
Rgds
Adelmo
I am in few forum and I have to say that each forum has his own trade mark, its own characteristic and way of participating to it. I think no forum is perfect, but amongst the few I lately read on regular base, perhaps this one is a bit less friendly and a bit more mean. The technical expertise seems higher as DIY, but not so sure about this last.
Not much talking about sounds result, most looking for technical perfection, ultimate technology to spin records, but in the end is missing the report about the sound improvements of such tweaks or building.
Wonder if most of the people do listen music, records or just try to build things.
However some good DIY project have been accomplished here therefore chapeau.
Rgds
Adelmo
To Post Or Not To Post
People have the right to show or not show their invention. I have no problem with that and I understand their concern about intellectual property. I firmly believe some commercial entities took ideas from this thread without crediting us but so what we posted this in a public forum and that's the risk we took. That's why people file a patent. The members who withhold information at least contributed into the discussion and they could have simply not post anything at all and that would be boring! This thread has been around for 11 years now and I never felt the need to pressure people to post anything they don't want to reveal. Moving on. People are welcome to post whatever pertinent to the topic and people are welcome not to post but are enjoying the reading and gleaming ideas from the posts. Just enjoy the ride.
People have the right to show or not show their invention. I have no problem with that and I understand their concern about intellectual property. I firmly believe some commercial entities took ideas from this thread without crediting us but so what we posted this in a public forum and that's the risk we took. That's why people file a patent. The members who withhold information at least contributed into the discussion and they could have simply not post anything at all and that would be boring! This thread has been around for 11 years now and I never felt the need to pressure people to post anything they don't want to reveal. Moving on. People are welcome to post whatever pertinent to the topic and people are welcome not to post but are enjoying the reading and gleaming ideas from the posts. Just enjoy the ride.