When I was designing tonearms some 30 years ago, I considered it essential to look at existing designs and into whatever theories existed regarding arm geometry. I would expect anyone designing an arm now to have done the same. It could be argued that not only arm designers, but turntable and cartridge designer should also consider how arm geometry might impact on their products, and that dealers and anyone else involved in arm set-up should do the same.
Given that SME were making arms before some current designers were born (unfortunately not in my case), it would seem a wise move to consider their designs and think about the reasons behind their design choices. However, it is apparent if anyone searches on the internet (the mis-information super-highway) that a top tonearm designer, a top cartridge designer, a top turntable designer, and a designer of a very expensive alignment tool (not to mention various dealers and others) either have a poor understanding of the basis of the SME geometry, (and as a corollary, of arm geometry generally,) or else choose for whatever reason to explain it in a negative manner which leads to misunderstanding on the part of those who might look to them for guidance.
This is the problem with the internet - how to know information is valid and reliable. Whatever you read here regarding arm geometry also, may be said by some to be inaccurate or wrong. However if I have been clear about the points raised then you should be able to locate the source information and check it for yourself. This is because the theory has been worked out a long, long time ago: you can have an opinion about which alignment is best, or which arm is best, but the basis of the alignment and the geometry of the arm are not matters of opinion, but matters of fact.
As an analogy, you may think your football team is the best, and I might disagree, but our opinions don't alter the fact of how many times either team has won the league title.
So with this in mind, consider the fact that the principle of using overhang and an offset headshell to reduce tracking error was established before I (and probably all other living tonearm designers) was born. The principle of a pivoted arm, as described by Percy Wilson in 1924, is based on knowing where, on a record, the recording begins and ends.
Once this is decided, then an important constant emerges. This is known as the Linear Offset. This parameter is unchanging for a given minimum and maximum radius, irrespective of tonearm length. Once the Linear Offset is established, then an effective length, an offset angle and mounting distance can be chosen using various formulas devised by Lofgren and adapted by others which give alignments to minimize distortion in various ways. For each and every alignment chosen, there are two points where there is zero tracking error. These vary depending on the alignment and are known as the nulls.
In other words, if you want to design a specific arm, you start by picking minimum and maximum recorded radii from a particular record, or an average from a collection, and then decide which geometry alignment you will use, then choose which parameter to base your alignment on. Often it is effective length, which then gives an offset angle and a mounting distance. But equally it could be an angle, which gives effective length then mounting distance. Or it could be mounting distance first.
The points on the arc where there is zero tracking error, the nulls, are fixed for a given alignment. As the alignment was established first of all from the maximum and minimum radii, the nulls are therefore also related to the Linear Offset. Therefore if one of either the effective length, the offset angle, or mounting distance is known, from the nulls the rest follow. See some simple formulae here.
So, knowing the Linear Offset or the nulls, the three arm parameters can be calculated.
If the concept of Linear Offset is appreciated, the principle of SME design becomes clear, as does tonearm geometry.
