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Re: SME V tonearm design: a success from the point of view of alignment

Posted by bkearns on December 11, 2001 at 10:24:20

In Reply to: Re: SME V tonearm design: a success from the point of view of alignment posted by dice45 on December 11, 2001 at 08:18:57:

Bernhard,

It is correct, as you said, that the offset angle will depend on the choice of cartridge, but that is not relevant: correct alignment is still achieved so long as the linear offset and the overhang are correct.

When I say correct alignment, I mean that the three arm parameters (mounting distance, effective length, offset angle) are set to achieve a particular pair of null radii.

The linear offset can be visualised by drawing a line along a projection of the cantilever on the record surface. If this line is extended back past the arm pivot, then the linear offset will be the perpendicular distance from that line to the arm pivot.

Note 1
The linear offset is equal to the product of the effective length and the sine of the offset angle. So if the linear offset is correct, and the if effective length is correct, then so too is the offset angle.

Note 2
Linear offset is also conveniently equal to the average of the two null radii – note this is my own discovery, I have not seen this statement in any of the other literature on tonearm geometry.

Note 3
The square of the effective length minus the square of the mounting distance is equal to the product of the two null radii.

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Tonearm alignment boils down to selecting a pair of null radii.

Selecting a pair of null radii determines the product of the null radii, and also determines the average of the null radii.

Consequently if the null radii are chosen (say 66.0mm and 120.9mm) then the product of the null radii is known (7979.4), and the average is also known (93.45mm). Once the null radii are selected, then a particular value of any one of the three arm parameters leads directly to the other two arm paramteters – see Note 1 Note 2 and Note 3 above.

Now lets consider two examples of setting tonearm alignment – remembering that tonearm alignment is simply a matter of adjusting the arm parameters so that particular pair of null radii are achieved.

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Case 1: fixed mounting distance, variable effective length (tonearms with slots in headshell)
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With slotted headshells, the overhang is adjusted by sliding the cartridge backwards and forwards along a line parallel to and midway between the headshell slots. The overhang is correct when the difference between the square of the effective length and the square of the mounting distance is equal to the product of the null radii. See Note 3 above. The linear offset is set to the average of the two null radii. This is normally achieved by simply ensuring the cartridge is square in the headshell – assuming the tonearm designer understood the principles involved!

Since the product of the null radii has been set to the correct value by adjusting the overhang, and since the average of the null radii has been set to the correct value by adjusting the linear offset, then the two null radii must individually be correct.

Moreover since the above procedure gives the correct effective length and the correct linear offset, it can be seen from Note 1 that the offset angle must also be correct. Hence all tonearm parameters are correct.

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Case 2 – fixed effective length variable mounting distance (SME tonearms)
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The overhang is set by adjusting the sliding base of the tonearm. The correct overhang is achieved when the difference between the square of the effective length and the square of the mounting distance is equal to the product of the null radii (as before).
The linear offset is set to the average of the two null radii. Again, this is achieved by simply ensuring the cartridge is square in the headshell.

As before, this procedure guarantees that the null radii and all three tonearm parameters are correct.

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So in either case the correct alignment can be set by adjusting overhang and linear offset. This is why linear offset together with overhand are the key adjustments for setting tonearm alignment.

Note that the procedure applies for any cartridge, and for any distance between the cartridge mounting holes and the stylus tip. Of course this is provided that in case 1, the slots in the headshell are long enough to enable setting of the correct overhang for the cartridge being aligned, and similarly that in case 2 the slider base allows enough movement.

You can find more information on the subject of tonearm alignment in the following two articles.

Part 1
http://www.audioasylum.com/audio/vinyl/messages/62571.html
Part 2
http://www.audioasylum.com/audio/vinyl/messages/62570.html

Brian

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