This approach might be called the fixed effective length + fixed offset angle approach. In this case the arm must have a facility (such as headshell slots) to adjust for variations in the distance between the cartridge mounting holes and the stylus, which varies with manufacturer. This is essential, as the effective length and cartridge offset angle are fixed for the mounting distance of the arm, which on most arms is generally not adjustable and its accuracy is dependent on the installer. This illustrates the disadvantage of this design approach, because if the mounting distance is wrong and not adjustable, the effective length should be different from the specified length , and the offset angle should also be different. This can be dealt with by moving and twisting the cartridge in its slots and setting up using a universal two point protractor with appropriate nulls, or a protractor based on the Dennesen principle.
A second approach is the nominal effective length + nominal offset angle approach. This approach is based on the fact that there is an interesting consequence once the minimum and maximum radii are chosen, typically IEC or DIN. In calculating each alignment, (Lofgren A/Baerwald, LofgrenB, Stevenson) these radii are constant, and the formulae are such that the mean of the nulls is therefore constant also. This is worth a closer look.
Arm geometry is such that the ratio of this mean to the effective length is the sine of the offset angle. In other words, from the mean of the nulls divided by any given effective length you can get the offset angle for that length.
This can be imagined as a right angled triangle, with the effective length being the hypotenuse. The short side is the mean of the nulls, and the angle opposite, the offset angle.
This means that the short side of this triangle remains constant, so that as the effective length increases, the offset angle decreases. The corollary of this is that if the third side of the triangle increases the effective length increases and the offset angle decreases.
All arms have the above triangle embedded somewhere in their geometry.
The short side is called the Linear Offset and is commonly disregarded (or often misinterpreted) as applying only to the angle that the axis of the bearing for vertical movement makes with the arm tube, and important only inasmuch as it allows the vertical movement axis to be perpendicular to the cartridge cantilever.
However, unless one appreciates the importance of Linear Offset, it is impossible to have a complete grasp of tonearm geometry.
Traditionally, SME arms are fixed headshell arms, with a fixed cartridge mount and fixed headshell angle (as opposed to fixed cartridge offset angle). The later 3009 and 3012, V, V-12, and M series are designed for a LofgrenA/Baerwald IEC alignment (the early Series I arms and the newer 300 series are different - the early arms used Stevenson, and the 300 series uses an alignment close to Baerwald DIN). This means that there is a specific linear offset which pertains to them, (and all other arms, of whatever effective length, with this same alignment). Therefore for a nominal effective length of 233.15 (SME V) or 308.81 (V-12) the linear offset is the same - 93.45mm.(91.54mm for the 300 series). The headshell offset angles are different because the effective lengths are different. With the cartridge square in the headshell, the correct cartridge offset is obtained.
In terms of the embedded triangle, all that has happened in the longer arm is that the cartridge and hence the stylus has moved along the third side, thus extending the triangle. The cartridge has not twisted. It does not need to, because its offset decreases as the effective length increases, as it must do to maintain the correct angle for the alignment.
This can cause confusion among designers and commentators (some of them well known ones who should know better) when faced with cartridges of varying mounting hole to stylus distances. If one does not realise that the arm´s effective length is nominal, it is mistakenly assumed that, because there are no slots in the SME, the cartridge must twist, because the heashell angle is fixed. However, in a cartridge with, say, a longer cantilever, all that is happening is that the stylus has moved along the third side of the embedded triangle and the real cartridge offset angle has changed appropriately as the effective length increases.
To illustrate the point, if the cantilever was made longer and longer, with the cartridge square in the headshell of the SME V, the stylus would eventually end up at a point where the effective length and the cartridge offset was the same as the V -12 (or any other arm of that length using the same alignment). The same would apply to the early 3009 and 3012, as they have the same linear offset.
Of course, with a given alignment, an effective length and an offset angle, there is an appropriate mounting distance/overhang given by the equations. This distance is automatically arrived at using a two-point protractor, or one specific to the arm, the mounting distance on the SME being adjusted using the sliding base to square off the nulls which are LofgrenA/Baerwald IEC (for the V). When this is the case, the mounting distance must be correct for the effective length, whatever it may be.
The advantage of the sliding base in the SME means that mounting distance/overhang can be precisely adjusted using the nulls on a protractor. There is no need to actually know the effective length or mounting distance, as long as the arm base has been located such that it is within a few millimetres of 215mm (i.e. the approximate mounting point for the nominal 9" arm). The sliding base then sets the precise distance to square the nulls. The issue of cartridge variations is unimportant. One other point often not appreciated, is that the Lofgren B IEC alignment is easily achieved by simply sliding the base towards the spindle by approx 0.5mm thus altering overhang without having to re-adjust the cartridge mounting to also reset the offset as would be the case with a slotted headshell and fixed base.
The SME´s disadvantage is that other alignments (which have different linear offsets) depend on being able to vary the cartridge offset from the set value, and it has no facility for this other than the clearance between cartridge and headshell mounting holes. Depending on the sizes of screws and holes involved this can be a degree or more, which is often sufficient.
Of course, this argument applies to slotted headshells also, as the cartridge still has to be twisted for other alignments, and so depends on sufficient clearance in the slots. Had one hole of the SME been extended into an arc this would make the arm more versatile.
Of course, this argument applies to slotted headshells also, as the cartridge still has to be twisted for other alignments, and so depends on sufficient clearance in the slots. Had one hole of the SME been extended into an arc this would make the arm more versatile.
It would be pointless SME supplying an overhang gauge or specifying a fixed pivot to spindle distance. The whole point of the SME approach involved not having a fixed overhang, because a specific effective length would have to depend on a cartridge having exactly the mounting hole to stylus distance to achieve that length in the absence of headshell slots.
All this is partly because of the focus, in forums and by some manufacturers, on precise mounting distance being paramount, leading to the proliferation of arc protractors, (and the assumption they are more accurate, as opposed to easier to use) than two point protractors, and partly, perhaps, because of a lack of appreciation on the part of current SME staff of the subtleties and advantages of the original design, thus giving the impression by specifying the nominal effective length to two decimals, that the arm is of the fixed effective length type.
