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
Dear Raul, I agree with you - this is a complex subject. What I am aiming here is the difference between the basic tonearm geometry (for the individual tonearm) and the geometry for the interaction with a stylus (Baerwald, Loefgren, Bauer, Stevenson etc etc.).

I would like to have some light here that there are 2 tonearm geometries - NOT one. We need to fix the 1st - then proceed with any of the mentioned options in the 2nd geometry calculation.

Its this basic TONEARM-geometry I am target on.
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.