Geometry for pivot tonearms - calculation errors??


During several threads in Audiogon's Analog forum the question of pivot tonearm geometry was discussed widely and wildly the past weeks. There seems to be a great confusion about the interelation - and interaction - between overhang, offset, effective length, mounting distance and the position of the 2 zero-error points on the arc over the LP's grooved area.
However - the correct tonearm geometry is paramount for the performance of any analog sourced High-end system.

Do we need a new calculation of these parameters?
Is mounting distance a variable factor in a given pivot tonearms geometry?
Can overhang serve as the fixed parameter for a pivot tonearm?
Is effective length a variable or a fixed parameter in pivot tonearm geometry?
Is there anything like an optimum geometry for a given cartridge/pivot tonearm set-up?

I invite all interested in this complex and very important topic to contribute their thoughts. If possible please do include the geometrical derivation for any given theory and opinion.
This might be difficult in some examples, but please try.
By doing so, - this will keep this thread on terms and will make it more valueable for all.
dertonarm
Raul-thanks, and maybe all the info and links I presented-*in one post*-will help others to start studying the issue.

Dertonarm-Well, for me-I'm no math wizard-the combination of the JE and CH programs allow me to take alignment theory as far as I want to go. When you've got one program that will allow you to manipulate any of the parameters of the pivot-arm geometry, display the null points in graph form, and then show the percentage of distortion of the stylus through that arc, and *then* use the CH program to immediately print out a protractor that displays that alignment-that's as far as I can go. I'll leave it to others smarter than I to come up with 'new' interpretations and methodology for tracing a pivot stylus over an LP. Saying that, I'll keep reading this thread and to see at what you arrive. (-:
Dear Dertonarm: Could you share your " finds " /thoughts n that 1st geometry for we can understand and try to help about?, because both have an intimate relationship.

Regards and enjoy the music.
Raul.
Dear Raul, - let me put it in a few "axioms":

1) offset, overhang and effective length do relate to each other and CAN be CHANGED WITHOUT changing the PIVOT-BEARING DISTANCE. Offset, overhang and effective length do change when you align to a different arc-calculation (say - change from Baerwald to Loefgren).

2) If you change the pivot-bearing distance you change the WHOLE GEOMETRY of the given tonearm.

3) you usually get the very best results with the recommended pivot-bearing (= mounting distance) as specified by the manufacturer, because the whole geometry of the given tonearm builds on that one parameter.

4) whether you choose Loefgren, Bauer, Baerwald, Stevenson or whatever calculation for the alignment of the stylus (and these calculations are onyl aiming at the position of the stylus - not at the position of the tonearm !!) is INDEPENDENT from the geometry of the tonearm itself. These alignments can all be done at the headshell alone without moving the base (and thus the pivot-bearing distance). And they should be done without moving the base because that way you can be sure that the basic geometry of your given tonearm is as specified by the manufacturer.

I think we must clearly put a line here between the geometry of the tonearm WITHOUT a cartridge.

This is the basic geometry of the tonearm itself = 1st geometry.
This is step 1.
Then there is the geometry of the stylus in a given tonearm = 2nd geometry. This is step 2.
Here we have the option to align to whatever calculation does fit our needs best (for instance more modern pressings with long run-out-grooves or pressings from the early 1960ies with the inner grooves running close to the label - these need different alignments - one rather Loefgren - one rather IEC). Here we lay the position of the 2 zero-error points and the maxima and minima derivation. This 2nd alignment does have variations in the offset, overhang and effective length (not much, but some) - but NOT in the pivot-bearing (mounting) distance.

Thank you for your direct email. I will put together a few "basics"/standards for LP-quality and will email to you in the next 2 days.
Dertonarm, How then do you feel about the SME tonearms, which utilize a sliding pivot point in order to achieve pivot to stylus adjustments? In the process the pivot to bearing or spindle distance is also altered pari passu.
Dear Lewm,
the SME 300 series (including SME V and IV) is one of the very few tonearms which does come with a kind of "fixed" geometry in ALL parameters. Given its unability to adjust offset, overhang (we can just move the base - which we shouldn't... - NOT the cartridge ) and effective length, it surely is a fairly unique sample.

Make no mistake - the SME V was designed for a specific mounting distance spindle to pivot-bearing! The SME sliding base is often mistaken for being an "invitation" to "adjust" the base "freely" to whatever alignment you want.

Not so.

SME does specify a mounting distance of 215.35 mm.
See here:

http://www.sme.ltd.uk/content/Series-V-1330.shtml

They did not give this very precise figure out of the blue........

SME took for granted all industry standards of its day (early 1980ies) and said:

"well, if all cartridge designers do obey to and follow the standards given and if all LPs are cut following the new IEC standard, then evrything will be perfect with our new tonearm - it will be the "best tonearm in the world"............"

But the world is an imperfect one and many people do want to go their own ways.

The new SME surely was the LEAST UNIVERSAL tonearm ever designed .......
It is for sure the one tonearm which gives almost no possibilities to adjust to specific cartridge needs or to different arcs.

The SME V was a child of its day and was regarded when introduced as the first tonearm which took all (some of them fairly new...) industry standards for record-cutting and cartridge dimensions serious.
Too serious.

Only a cartridge with 100% orientated cantilever and 100% standard horizontal distance mounting holes-stylus can be correctly aligned in a SME V and can only be aligned to ONE standard cuve/arc - the IEC.

Offset can not be aligned in an SME - thats why the SME template does FORCE the user into one possible geometry only.
Thats why the MINT tractor is so very effective with a SME V and a specific cartridge.

In a biological sense the SME V (and its offsprings with fixed headshell and fixed mounting holes) is the very opposite of evolutionary versatile.
It can not "adjust" to any change in the "enviromental conditions".
With the "right" cartridge, it is a VERY serious tonearm.
But there are so very few "right" (read: 100% following IEC standards) cartridges for the SME V around.......