The corollary of this is that if the third side of the triangle increases the effective length increases and the offset angle decreases.Īll arms have the above triangle embedded somewhere in their geometry. This means that the short side of this triangle remains constant, so that as the effective length increases, the offset angle decreases. The short side is the mean of the nulls, and the angle opposite, the offset angle. This can be imagined as a right angled triangle, with the effective length being the hypotenuse. 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 is worth a closer look.Īrm geometry is such that the ratio of this mean to the effective length is the sine of the offset angle. 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 approach is based on the fact that there is an interesting consequence once the minimum and maximum radii are chosen, typically IEC or DIN. 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.Ī second approach is the nominal effective length + nominal offset angle approach. 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 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. 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 approach might be called the fixed effective length + fixed offset angle approach. Together with figures for minimum and maximum recorded radius, the cartridge offset and tonearm mounting distance can be calculated from Lofgren´s equations. When an arm is being designed many designers have a particular effective length in mind, be it around 9" (230mm approx.) or 12" (300mm approx.).
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