Let me say at the beginning that I have made 9" and 12" arms, and am not promoting either the use of anti-skate mechanisms or otherwise. I would just like to see some unbiased discussion which deals in known quantities.
The stylus contacts the groove on two areas, one on each face of the groove, and the downforce is distributed between them. As these faces are also at 45 degrees to the horizontal, the force acts not only downwards but sideways, towards the centre for the inside slope and away from the centre for the outside.
In a linear tracking arm these sideways and downwards forces are equal (except for the force required to move the arm as the groove spirals in). As the record turns, there is friction where the stylus and the groove faces touch. This friction force is proportional to downforce times the coefficient of friction between stylus and the moving groove, and it acts such as to try and pull the stylus along the groove, directly opposite to the bearing.
However, in a pivoted arm, the sideways and downwards forces are not equal. This is because, unlike in a linear tracking arm, the arm pivot, the stylus, and the groove tangent are not in a straight line. The reason for this is that, in order to minimise the tracking error and the accompanying distortion, the stylus has to overhang the spindle and the cartridge be angled inwards so that the cantilever is positioned to align with the groove.
Consequently the force along the groove tangent causes the arm, due to the fixed pivot, to rotate towards the centre of the record. In general, the more overhang there is, more angled the alignment is, and the more the arm is forced to turn. This causes the inside face of the groove to bear more against the stylus. As it does so, the stylus climbs the face because it is pushed upwards and outwards due to the fact of the face being at an angle.
It is often thought that skating forces put an inward bias on the stylus, and the stylus wants to skate inward but is constrained by the inner groove wall.
This is a misconception and is incorrect. It is the arm that pivots inwards because of the resultant force produced by stylus friction in the direction tangent to the groove and the restraining force in the direction of the arm pivot. But the stylus, on the other hand, is actually being pushed upwards and outwards (relative to the cartridge body) against the compliance of the suspension as the cantilever pivot moves inwards.
As the stylus is pushed up the 45 degree slope of the groove, the VTF on the opposite face decreases.
Applying antiskate pulls the arm (and therefore the cantilever pivot) outwards thus equalising the VTF on both channels. The inward and outward forces are then equal at both the stylus and the cantilever pivot, as they are joined by the cantilever, and the plane of movement of the cantilever is therefore vertical.
If there is no antiskate (intentional, or otherwise, via wiring) then the forces must be unequal. And with enough VTF, while the stylus may track correctly without the distortion due to low VTF on the right channel, that channel will still have less tracking force than the left. Any alteration of VTF will still vary downforce disproportionately.
As the force on one face increases the force on the other face decreases, because the VTF remains the same. Note there are no values attributed to VTF. This description is independent of the value.
If the coefficient of friction is unchanged, increasing the VTF increases the frictional force. Decreasing the VTF decreases the frictional force. This is the nature of friction.
As the frictional force increases, the inwards force increases. As the frictional force decreases, the inwards force decreases, until, obviously, at 0 VTF there is no inwards force, because there is no friction because the stylus is floating just above the record surface.
As the pivot /stylus/groove tangent angle changes from 0 degrees (as in a linear tracker or infinitely long arm) towards 90 degrees (when pivot and spindle and stylus align), the inwards force increases.
Stylus quality and shape also affect the friction, so that the skating force, as it is known, is not the same for all arms and cartridges. However there is always friction and hence always a skating force.
In a modulated groove there are forces on the stylus which act normal to one groove face and parallel to the other, and so have an upwards resultant. Therefore there is a minimum downforce which keeps the stylus in the groove, and which depends on the severity of the groove modulation. This effect can be seen by using test record torture tracks, and applies to both linear trackers and pivoted arms.
There is also a maximum downforce value, where the cantilever suspension is compressed, the generator system becomes unacceptibly non linear, the VTA/ stylus rake angle alters markedly, and records wear faster due to the increased friction.
In a pivoted arm with the additional sideways skating force which results in less downforce on one face, the minimum force needed is greater. There is still an imbalance, still in the same ratio, for nothing has changed other than an increase in VTF which is distributed unequally as before, but now the forces on each face are increased. As the VTF is further increased, the points regarding suspension etc, above, apply. The sideways force, the skating force, doesn't disappear, it is not counterbalanced in any way, is simply overwhelmed by an excessive downwards force. (The analogy here (but not to be taken too literally) is if you are standing with a 20kg weight on your left foot and a 10kg on the other, and can't move the left foot (representing good contact with the inner groove face) but can move the right (representing mistracking of the outer face), adding 10kg to both will stop the movement. Both feet are firmly on the floor, (representing stylus firmly in the groove) but you still feel 30kg on one and 20kg on the other. This represents one channel having more VTF than the other. In this analogy, applying anti-skate would add 10kg to only the right, thereby equalising the forces
The fact that the stylus remains in the groove does not mean there are no forces trying to push it up the inside face. Only that the resultant of the force pushing down (VTF) is enough to counteract it, at the expense of extra friction.
The magnitude of the skating force depends initially on the quality and shape of stylus, the overhang and offset, and the VTF. Typical values would be between 10 and 30% of VTF. If we allow for the change in tracking error across the record, the force would decrease towards the middle tracking error maximum by 5 to 10% from its starting value, and then increase towards the runout groove.
However, studies have shown that, due to a number of factors such as inertial drag, cantilever drag, modulation drag, the force increases as the radius reduces. Also elliptical stylii produce more sideways force. So a typical anti-skate would start at around say 15% of VTF and gradually increase to say 25% at the inner groove.
Therefore an anti-skate mechanism should allow for options including the facility to apply a variable force from 0 to, say, 50% of VTF, which can reduce, or increase across the record, so as to best compensate for variation in stylus profile and recorded radii.
Using a longer arm reduces the overhang and offset angle, and so reduces the sideways force, hence the amount of counterforce needed is also reduced. Using anti-skate allows lower VTF.
Some arms use no anti-skate but have wiring which contributes an unspecified amount of drag depending on the degree of twist (AR, VPI, and others). There are also advocates of high VTF and no anti-skate, which will allow cartridges to track but obviously does not eliminate the skating force. If you actually draw force vector diagrams it will nicely illustrate the point.
