tonearm geometry question

I've followed the linear vs pivoted thread with some interest. Itt raises a question that someone with greater technical expertise may be able to clarify for me.

At rest, both a pivoted arm tube and an LTT tube share a common position tangent to the platter ( call it the CP line) and a common anchor ( or pivot) point (call it CAP). From there, a pivoted arm tube defines an arc across the record, while the LTT tube slides on its anchor point from the CAP along a line perpendicular to the CP line and tangent to the platter until it hits the inner groove. Call this the LTT anchor journey.

My question: Why is the pivot point on a pivoted arm not located halfway along the LTT anchor journey. Wouldn't this reduce the pivoted arm's error by half? Surely loading/removing the record can't be the reason. What am I missing?

Thanks in advance.

Walk around your turntable (closer to your left speaker) and look at it again.

Thom @ Galibier

Thanx for the quick reply.

I understand that any pivot position that puts the tube tangent to the platter
yields the same geometry, but I asked a different question:

Why is the pivoted arm mounted so that it's tube is tangent to the platter,
rather than above it. I gather that headshell offset "fixes" the
geometry, but isn't tracking error minimized for any length tube if the pivot
were located halfway along the LLT's anchor point path?

Or. put yet another way - if you took an LTT and stopped it midway through
an LP, isn't this the ideal point for a pivoted arm to start since it is a 0 degree
error position for a straight tube (even one mounted on a pivot) and the error
induced between this start spot and the first groove (to one side of the pivot)
and last groove (on the other side of the pivot is smaller for any given tube
than is therwise the case?

For an arm mounted in this fashion, the arc defined by the stylus is split left/
right from rest, rather than exclusively right (as in the typical pivoted
mounting scheme viewed from behind and above) Viewed from a user's
persective - you slide the LP under the arm, move the arm to your right and
drop it onto the record to start play.

Sorry if I'm being dense here, but I'm sitting at a round kitchen table right
now and can't figure this one.

Thanks again,

I think I understand what you are asking, and the answer is simple, but the mathematics behind the answer are not. If you use the geometry defined by Baerwald, there are actually 2 points along the arc that provide 0 tracking error. These are your null points. What I believe you propose is a single null point smack dab in the middle of the LP. This would greatly increase your tracking error. I'm posting this response from my phone...I'll try to provide more detail later.

I believe that am proposing a null at dead center. My mathematical training is limited, but intuitively, a center null would seem to minimize overall deviation relative to the radius described by a stylus moving across the record on an LTT. I would add that you it seems to me you'd also need to hold the length of the arm tube constant for a comparison of pivot placements.

BTW, if a null is a point on the radius I outlined above, how can a pivoted arm decribing an arc centered outside the platter (ie your standard pivoted arm) cross that radius line twice. I don't understand Baerwald.

Any clarification is appreciated.


Upon reflection, I can visualize 2 nulls across the radius (baerwald), but it's not intuitive that this would minimize total deviation from the desired radius - the calculus is beyond me. But, the same logic could be applied to create 2 nulls with the central pivot I describe - the tube must be longer and the pivot further away from the radius. Either way, for any given tube length. it seems to me that a cenetred pivot would reduce overall deviation.
Sorry to bother everyone, but I think the bulb just came on:

Any tube length defines an arc of a fixed degree of curvature. So long as that arc crosses any radius on the LP at the 1/3 and 2/3 points of the section of radius being tracked, total deviation should be the same. My scheme merely fixes the radius in question at the same place an LTT would.

Thanks again,

For a third option, between conventional pivoted tonearms and LT arms, try the 47 Labs RS-A1 tonearm or the headshell which can be purchased separately.
If you really want to get into the details of a Baerwald geometry, you could
check out his paper on "Analytic Treatment of Tracking Error and notes
on Optimal Pick-up Design" over at

Yeah..I'm not really looking for that level of detail, either. But there are some
great resources over at AudioAsylum in the FAQ:

In particular, check out John Elison's downloadable Excel spreadsheet for
calculating horizontal tracking error and distortion, with graphs. Very useful.
Marty, if you want a short answer, for the location you are asking about, you can set it up with 2 null points, but you will have a much larger tracking error at all the other points on the LP. By locating the radial arm at the end of the LTT these out-of-null points have a much-reduced error.

If you were to draw some circles representing the platter, and impose the radii of the two arm locations, you will see immediately what the problem is.

For any length tube it would seem that the geometry is the same (save the headshell offset), no? Now, to accomodate any "normal" tube length the pivot might have to be moved back some, but if I've (finally) got Baerwald figured out, it shouldn't matter which radius you're tracking: the radius nearer the operator as usually tracked by a pivoting arm or the radius perpendicular to the "rest" position of a pivoted arm, as tracked by an LTT. Or - alas - am I missing something again?


Well, if you think about it, as you optimize the 'new' position you will see that it has a lot in common with the 'old' position...
"For any length tube it would seem that the geometry is the same (save the headshell offset), no?"

I don't follow that. A longer arm will have a larger radius. The larger the radius, the less the tracking error/distortion between the null points.

You needn't optimize the pivot point - I'm saying you optimize the tube length to the chosen point.

I was only trying to explain that the (silly) flaw in my reasoning was that the dual point null (Baerwald) eluded me as I was focused on the particular radius tracked by an LTT. By way of explaining my (bad ) logic, I suggested an "apples to apples" (fix the tube length) comparison to illustrate that I missed a key fact:

Any radius is a radius! Or, as you say, they all start to look the same. By this logic, a 9" tube (or 10" or 12") on a pivot on an LTT designed for a straight tube of the same length should operate identically to one that is traditionally placed.

04 RDKing - I trust the above clarifies your point - I omitted the word "given".

Anyway you slice it, I just didn't get Baerwald and couldn't visualize how a pivoted arm actually traces a record.

Thanks again, guys,

I believe you're missing the forest because of the trees. A radius is not a radius. A 9" radius is not the same as a 12" radius. They are both arc's, but not the same. You keep saying "the particular radius tracked by an LTT". A LTT has no radius. It is linear.

Point is. If one were to put the pivot point in the center of the null points on a fixed head/arm, the tracking error would be gratly increased. In fact, I believe with this configuration, one would only be able to achieve one null point....... Stevenson geometery.
The perimeter of an LP is a circle. The radius I refer to is the portion of the radius of that circle (that portion between the first groove and last groove) on the LP that any tonearm will ideally track. An LTT tracks a (portion of) a particular radius that is perpendicular to the "at rest" position of a typical pivoting arm. A pivoting arm tracks a different (portion of) radius of the LP. The error of a 9" tube is constant (i think) so long as the pivot point allows 2 Baerwal nulls from any radius. This may seem painfully obvious, but I missed it anyway! My radius is the path on the LP that is ideally tracked by any arm.

You are refering to the radius defined by the length of a pivoting arm which determines the cumulative deviation from the radius on the LP to which I referred. The longer the tube of a pivoted arm, the larger your radius, the less the cumulative error - from any of my radii on the LP - so long as the pivot is optimally placed for that particular tracking path (my LP radius).. If the tube is long enough and th pivot point optimized, 2 nulls can be acheived on any radius.

Clear as mud?