Axelwahl
You are assuming attitude is important but it isnt.
Consider the frame of reference of the tonearm with its pivot point as the origin and the arm lying along the y axis. The stylus frictional reaction force vector runs directly from the stylus tip in the direction of groove motion. The restraining force vector runs directly from the stylus tip to the tonearm pivot. The sum of these two vectors is the net force on the stylus.
The angle between the groove tangent and the x axis is the true offset angle. The stylus reaction force vector can be resolved into x and y components equal to its magnitude multiplied by the cosine and sine of this angle respectively. Since the x translational degree of freedom is constrained, the sum of forces in the x direction must be zero so the restraining force must be equal to the x component of the stylus reaction force vector.
For the y translational degree of freedom also to be constrained (eg the stylus not skip out of the groove) there must be a force which balances the y component, this force is either supplied by a reaction force on the groove wall or by antiskate.
IFF the force is supplied by reaction against the groove wall then the fact that that reaction force is not purely in the Y direction creates complexities but we can assume that the arm has been designed by someone who knew what he was doing so it has antiskate therefore we can ignore this: designing a pivoted arm with no antiskate is prima facie evidence of incompetence. The antiskate can be applied as a torque to the arm pivot or a force to a point somewhere on the arm, its all the same as long as the vectors resolve.
The argument from attitude rests on a falsehood which is that the stylus frictional reaction force somehow depends on the attitude of the stylus to the groove wall. A misalignment of say 10 degrees would result in a displacement betwen contact patches of about 25 microns for an elliptical stylus 7mil across, for a spherical sylus there would be no displacement at all since the contact areas between a sphere and a plane are always normal to the radius of the sphere.
This torque arm would result in a torque of about 0,5 uNm at 20 mN VTF where the actual skating torque is around 1mNmm, a difference of 2000 to one.
The issue which Id like to resolve is that of the influence of stylus shape. Amontons law for rigid bodies breaks down if one body is much softer than the other, which is definitely the case with vinyl and diamond. The breakdown takes the form of a pressure dependent coefficient of friction; the coefficient decreases with increasing pressure this seems counterintuitive but think about a car tyre: wider tyre, lower pressure, better grip. Since elliptical styli have greater contact pressure than spherical, the friction will be less for them and this was reflected in many tonearms having separate scales for elliptical and spherical styli back in the day. Check the owners manual for the Torens TD160 mk2 for an example. Since a line contact has, by design, a larger contact area the skating force should increase not decrease as our befuddled friend supposed.
Mark Kelly
You are assuming attitude is important but it isnt.
Consider the frame of reference of the tonearm with its pivot point as the origin and the arm lying along the y axis. The stylus frictional reaction force vector runs directly from the stylus tip in the direction of groove motion. The restraining force vector runs directly from the stylus tip to the tonearm pivot. The sum of these two vectors is the net force on the stylus.
The angle between the groove tangent and the x axis is the true offset angle. The stylus reaction force vector can be resolved into x and y components equal to its magnitude multiplied by the cosine and sine of this angle respectively. Since the x translational degree of freedom is constrained, the sum of forces in the x direction must be zero so the restraining force must be equal to the x component of the stylus reaction force vector.
For the y translational degree of freedom also to be constrained (eg the stylus not skip out of the groove) there must be a force which balances the y component, this force is either supplied by a reaction force on the groove wall or by antiskate.
IFF the force is supplied by reaction against the groove wall then the fact that that reaction force is not purely in the Y direction creates complexities but we can assume that the arm has been designed by someone who knew what he was doing so it has antiskate therefore we can ignore this: designing a pivoted arm with no antiskate is prima facie evidence of incompetence. The antiskate can be applied as a torque to the arm pivot or a force to a point somewhere on the arm, its all the same as long as the vectors resolve.
The argument from attitude rests on a falsehood which is that the stylus frictional reaction force somehow depends on the attitude of the stylus to the groove wall. A misalignment of say 10 degrees would result in a displacement betwen contact patches of about 25 microns for an elliptical stylus 7mil across, for a spherical sylus there would be no displacement at all since the contact areas between a sphere and a plane are always normal to the radius of the sphere.
This torque arm would result in a torque of about 0,5 uNm at 20 mN VTF where the actual skating torque is around 1mNmm, a difference of 2000 to one.
The issue which Id like to resolve is that of the influence of stylus shape. Amontons law for rigid bodies breaks down if one body is much softer than the other, which is definitely the case with vinyl and diamond. The breakdown takes the form of a pressure dependent coefficient of friction; the coefficient decreases with increasing pressure this seems counterintuitive but think about a car tyre: wider tyre, lower pressure, better grip. Since elliptical styli have greater contact pressure than spherical, the friction will be less for them and this was reflected in many tonearms having separate scales for elliptical and spherical styli back in the day. Check the owners manual for the Torens TD160 mk2 for an example. Since a line contact has, by design, a larger contact area the skating force should increase not decrease as our befuddled friend supposed.
Mark Kelly