The Korf Blog

The inside story: our research, development and opinions

2 June 2017
Geometry Part II. Dynamic geometric errors.
This is the second post in a series dedicated to tonearm geometry. I will try to avoid repeating the obvious and the well-researched, focusing on things that are often overlooked. Korf Audio has done extensive proprietary research into the relative importance and audibility of these errors, and I'll share some of the conclusions.

In the previous post, we focused on the static errors -- they do not change as the stylus makes its progress from the outer radius of a disc to the inner groove, or change smoothly and gradually. Today, we'll focus on errors that appear as the tonearm traces the disc's wobbles, warps and bumps. These are:

  • Scrubbing motion in horizontal plane
  • Scrubbing motion in vertical plane
  • Angular motion in both planes
  • Motion in the frontal (azimuth) plane
Scrubbing motion in horizontal plane happens as the arm is tracing the warp or eccentricity of a disc. As cantilever is deflected and angle α is introduced, effective length of a cantilever changes from a to a'.

As the suspension is imperfectly damped, the change in cantilever effective length ("scrubbing") will be repeated with diminishing amplitude.

It has been extensively covered in "PHONO ARM DAMPING REVISITED" by C. R. Anderson of Shure Corp. He has clearly shown that the amplitude of scrubbing motion is proportional to an offset angle. Reducing this offset by making arm longer (or eliminating it altogether by implementing linear tracking) significantly reduces the scrubbing motion.
Scrubbing motion in vertical plane appears when the arm is tracing the bump. Compliance of the cartridge's suspension results in the change of the cantilever's effective length from a to a' and back.

It is easy to see that, exactly like in the horizontal plane, the amplitude of scrubbing motion can be decreased by using arm geometry (b) where the stylus drag force is applied on the same line as the reaction force of the arm's pivot. In fact, the reduction of scrubbing will be even more noticeable as the geometry (b) keeps the downforce on the stylus independent of stylus drag.
Both horizonal and vertical scrubbing result in frequency modulation distortion. It's one of the most audible ones. The lower level of FM distortion, and not the lower tracking error, is the main reason why linear tracking tonearms sound different from pivoted arms, and why 12" arms sound different from 9" arms.

The scrubbing motion in both planes also rotates the stylus out of its optimal position.

The azimuth plane motion happens mainly for 2 reasons. First is torsional twisting of the cantilever and its suspension. It is caused by an offset angle and is exceedingly difficult to measure. I have tried estimating it by glueing a tiny speck of mirror foil to the cantilever, shining the laser at it and then observing the movement of the reflection. Its existence and scale (up to a full degree) is one more argument for smaller offset angles in tonearms.

Second only happens in tonearms where the cantilever is not perpendicular to the horizontal rotation axis. It is easier to show on an illustration than to explain in words. This dynamic azimuth error is easily preventable by using the correct geometry.

If the horizontal axis of an arm is parallel to the plane of the stylus (or perpendicular to the cantilever, which is the same), then the vertical deflection of an arm does not introduce an azimuth error.

Here the horizontal axis of an arm is perpendicular to the armtube. It is easy to see that the vertical deflection results in an azimuth error.

In the next post, I will talk about the impact static and dynamic geometric errors have on sound.
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