Turntable physics questions-velocity of tangential arm?

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Many years ago before I got sick I made a linear tracking arm that travelled at a fixed speed across the record. There was some slop in the arm to prevent skipping.

What surprised me most was that, once I had played a few records and adjusted the fixed speed (if that makes sense) to get the best tracking, how little slop was actually needed and in fact I was able to play many records with a rigid arm (no slop) so I suppose the cantilever took care of any variation.

Sorry for a long winded response but my experience is that the stylus speed across the record is much closer to constant than many might expect.

sp

PS no eccentric records of course
 
I used a cheap linear tracking turntable, i think it was a radioshack and the arm was part of the lid, but this was mainly to get information on how the record was traversed by the stylus. The arm i had a design for was not actually a linear tracker and for a number of reasons i did not pursue the idea.

Now i just listen to internet radio.

Cheers sp
 
There is a frictional component to the stylus drag, ie that due to a silent groove, and there is a dynamic component to the drag caused by the work done moving the stylus from side to side and up and down.

The physics for the latter is probably very complex alas, involving the stylus geometry and 3D compliance of its mounting...

Its probably simpler to just measure the frictional force using an anti-skating balance, and estimating the magnitude of the dynamic component with a test pressing with test signals at high amplitude.

Solid friction is roughly proportional to tracking force, and you can probably measure the coefficient by placing a diamond on a plain piece of vinyl and measuring the angle at which it starts to slide. You have to factor in the groove geometry which means the actual surface forces are greater by sqrt(2) than the tracking force.
 
You can put some limits on a lot of this by noting that the geometry of the cutting head means that there is a hard limit on the modulation velocity at high frequency (Basically it cannot ever exceed the linear velocity of the disk at the cutting diameter due to a 45 degree back angle on the cutting stylus, go past this and the back of the cutter trashes the groove you have just cut).

The other limit at high frequency is acceleration due to the size of the osculating circle of the playback stylus, and note that generally the operator doing the cutting HAS to assume a worst case here, you might have some variant on a line contact or hyper elliptical that is not too worn, if the cutter assumes that there are going to be many complaints of unplayable records from Hipsters with Crossleys...

Usually there is a de-esser in chain that is setup to limit the HF to maintain velocity (+6dB/Octave) and acceleration (+12dB octave) within cuttable limits.

Most cutting heads have a hard displacement (low frequency groove amplitude) limit of about 150um or so, which is less then the groove spacing during the spiral in to the lock groove.

Be thankful that the forces on replay are MUCH smaller then the ones when cutting, there is a reason a playback deck has nothing in common bearing wise with a purpose designed lathe (Ands that the SP 10 is generally considered the one really useful turntable is building a lathe).
 
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