Ups and Downs
So far, I’ve only looked at horizontal mode scrubbing and FM. I’ll use the same modelling methods for analyzing vertical mode scrubbing and FM. For the vertical mode I will model it generically as “Arm 3”. Zero offset angle geometry has no inherent advantage in terms of vertical mode scrubbing susceptibility.
Here is a graphic (from Shure tech notes) which shows how scrubbing that results from vertical resonance is influenced by the Vertical Tracking Angle of a typical cartridge:
[20] Shure Figure 10 Simplified Vertical Scrubbing
Shure’s graphic shows a simplified relationship between vertical motion and scrubbing along the groove and a simple formula that describes it. Here too, the scrubbing motion is asymmetrical WRT headshell/cantilever displacement. For a symmetrical vertical displacement of the headshell, the stylus scrubs more aft than it does forward.
Here’s a Linkage2 model of a typical “Arm 3” and a cartridge with a 20 degree vertical tracking angle:
[21] Arm 3 Linkage2 Model
[22] Arm 3 Linkage2 Cantilever
Here’s a video of the simulated mechanical motion during vertical resonance:
I won’t do a separate analysis for vertical mode resonance and scrubbing because it’s essentially the same concept as the 9” “Arm 1” model for horizontal mode FMD. The vertical tracking angle is in the same ballpark as the offset angle for 9/12” arms and the scrubbing behavior is comparable (see the Linkage2 video animations). Unfortunately, there’s no magic bullet for solving FM caused by vertical mode scrubbing, since you can’t eliminate the VTA built into the cartridge by the manufacturer.
There a few different options for dealing with vertical mode FM, each with its own set of compromises.
Option 1 - Raise the height of the arm pivot so that the angle of the arm WRT the record surface matches the VTA of the cartridge. This would make the vertical mode scrubbing behave in a way comparable to the horizontal mode scrubbing example of zero offset angle “Arm 2”. The RS Lab “RS-A1” is an example of this. Other not-so-obvious examples of this are the mechanism in the ReVox Bnnn linear trackers, and various mechanical and air bearing Linear Trackers, including diy efforts. I doubt that any of these designs originally had the vertical scrubbing issue in mind as a design concept, and I’ve never seen it mentioned before. The disadvantage is that, while these would be expected to perform well vis-à-vis vertical mode FMD from scrubbing, they become more susceptible to the audible effects of 0.55 Hz warp wow scrubbing. It’s an unavoidable trade-off that is one of those pick-your-poison scenarios.
[25a] RS Lab RS-A1 Simplified Vertical Scrubbing
[25b] RS Lab RS-A1
Here’s a Linkage2 model of what I’ll call “Arm 4”, inclined to match a cartridge with a 20 degree vertical tracking angle:
[27] Arm 4 Linkage2 Cantilever
Here’s a video of the simulated mechanical motion during vertical resonance:
The scrubbing in “Arm 4” is so much less than “Arm 3” that it’s difficult to see in the same scale. Here’s a close-up stylus view of the same video. Notice that in “Arm 4” the scrubbing frequency is once again double that of Fres, as in the case of “Arm 2”.
Sorry, I don’t have one of these arms to demonstrate a sound clip.
Option 2 - Apply a viscous damped brush at the cartridge end a’ la Shure. IME this is beneficial. The disadvantage is that the bristles can sometimes convey audible noise to the cartridge signal. This was not a problem on my OEM Type IV, but occasionally is on my OEM M97xE. The OEM M97xE brush bristles seem stiffer than on my OEM Type IV, likely due to the cost-conscious directive that went into the M97xE design. Unfortunately, the idea of a viscous damped brush on the cartridge never caught on with other cartridge or arm manufacturers, likely due to patent rights issues and “Not Invented Here” syndrome. Shure’s patents have since expired, so…?
Option 3 - Apply viscous damping to arm bearings or add an oil bath/paddle damping outrigger. IME this is beneficial. The disadvantage of this is that such damping is a compromise and difficult to optimize for specific arm and cartridge/stylus combinations without a lot of experimentation. Beware the “more is better” syndrome.
Option 4 – Electronic servo controlled damping. Based on user comments in various audio forums this apparently works. Wish I had one to experiment with. Servo controlled damping was offered on both varieties - conventional pivot arms and linear arms, such as the Sony Biotracer PS-X600 (pivot with offset angle) and PS-X800 (linear tracker with no offset angle).
Option 5 – Yet to be discovered clever ideas up someone’s sleeve.
Sidebar – Air Bearing and Mechanical Bearing Linear Modeling:
Strictly speaking, these arms don’t exactly form a four-bar linkage the way pivoted arms do. However, if you consider that the salient point for modeling is that if the length of Link 4 (the arm) is large compared to Link 2 (the cantilever), then you can consider link 4 to be anchored at a virtual arm “pivot” at a far distance without introducing significant error in the mathematical model. In any case the errors introduced would be conservative and the actual performance of such arms would be a bit better than the calculations indicate.
Open for discussion?
Ray K
So far, I’ve only looked at horizontal mode scrubbing and FM. I’ll use the same modelling methods for analyzing vertical mode scrubbing and FM. For the vertical mode I will model it generically as “Arm 3”. Zero offset angle geometry has no inherent advantage in terms of vertical mode scrubbing susceptibility.
Here is a graphic (from Shure tech notes) which shows how scrubbing that results from vertical resonance is influenced by the Vertical Tracking Angle of a typical cartridge:
[20] Shure Figure 10 Simplified Vertical Scrubbing
Shure’s graphic shows a simplified relationship between vertical motion and scrubbing along the groove and a simple formula that describes it. Here too, the scrubbing motion is asymmetrical WRT headshell/cantilever displacement. For a symmetrical vertical displacement of the headshell, the stylus scrubs more aft than it does forward.
Here’s a Linkage2 model of a typical “Arm 3” and a cartridge with a 20 degree vertical tracking angle:
[21] Arm 3 Linkage2 Model
[22] Arm 3 Linkage2 Cantilever
Here’s a video of the simulated mechanical motion during vertical resonance:
I won’t do a separate analysis for vertical mode resonance and scrubbing because it’s essentially the same concept as the 9” “Arm 1” model for horizontal mode FMD. The vertical tracking angle is in the same ballpark as the offset angle for 9/12” arms and the scrubbing behavior is comparable (see the Linkage2 video animations). Unfortunately, there’s no magic bullet for solving FM caused by vertical mode scrubbing, since you can’t eliminate the VTA built into the cartridge by the manufacturer.
There a few different options for dealing with vertical mode FM, each with its own set of compromises.
Option 1 - Raise the height of the arm pivot so that the angle of the arm WRT the record surface matches the VTA of the cartridge. This would make the vertical mode scrubbing behave in a way comparable to the horizontal mode scrubbing example of zero offset angle “Arm 2”. The RS Lab “RS-A1” is an example of this. Other not-so-obvious examples of this are the mechanism in the ReVox Bnnn linear trackers, and various mechanical and air bearing Linear Trackers, including diy efforts. I doubt that any of these designs originally had the vertical scrubbing issue in mind as a design concept, and I’ve never seen it mentioned before. The disadvantage is that, while these would be expected to perform well vis-à-vis vertical mode FMD from scrubbing, they become more susceptible to the audible effects of 0.55 Hz warp wow scrubbing. It’s an unavoidable trade-off that is one of those pick-your-poison scenarios.
[25a] RS Lab RS-A1 Simplified Vertical Scrubbing
[25b] RS Lab RS-A1
Here’s a Linkage2 model of what I’ll call “Arm 4”, inclined to match a cartridge with a 20 degree vertical tracking angle:
[26] Arm 4 Linkage2 Model
[27] Arm 4 Linkage2 Cantilever
Here’s a video of the simulated mechanical motion during vertical resonance:
The scrubbing in “Arm 4” is so much less than “Arm 3” that it’s difficult to see in the same scale. Here’s a close-up stylus view of the same video. Notice that in “Arm 4” the scrubbing frequency is once again double that of Fres, as in the case of “Arm 2”.
[29] ARM 4 – Linkage Stylus View
Sorry, I don’t have one of these arms to demonstrate a sound clip.
Option 2 - Apply a viscous damped brush at the cartridge end a’ la Shure. IME this is beneficial. The disadvantage is that the bristles can sometimes convey audible noise to the cartridge signal. This was not a problem on my OEM Type IV, but occasionally is on my OEM M97xE. The OEM M97xE brush bristles seem stiffer than on my OEM Type IV, likely due to the cost-conscious directive that went into the M97xE design. Unfortunately, the idea of a viscous damped brush on the cartridge never caught on with other cartridge or arm manufacturers, likely due to patent rights issues and “Not Invented Here” syndrome. Shure’s patents have since expired, so…?
Option 3 - Apply viscous damping to arm bearings or add an oil bath/paddle damping outrigger. IME this is beneficial. The disadvantage of this is that such damping is a compromise and difficult to optimize for specific arm and cartridge/stylus combinations without a lot of experimentation. Beware the “more is better” syndrome.
Option 4 – Electronic servo controlled damping. Based on user comments in various audio forums this apparently works. Wish I had one to experiment with. Servo controlled damping was offered on both varieties - conventional pivot arms and linear arms, such as the Sony Biotracer PS-X600 (pivot with offset angle) and PS-X800 (linear tracker with no offset angle).
Option 5 – Yet to be discovered clever ideas up someone’s sleeve.
Sidebar – Air Bearing and Mechanical Bearing Linear Modeling:
Strictly speaking, these arms don’t exactly form a four-bar linkage the way pivoted arms do. However, if you consider that the salient point for modeling is that if the length of Link 4 (the arm) is large compared to Link 2 (the cantilever), then you can consider link 4 to be anchored at a virtual arm “pivot” at a far distance without introducing significant error in the mathematical model. In any case the errors introduced would be conservative and the actual performance of such arms would be a bit better than the calculations indicate.
Open for discussion?
Ray K
Attachments
![[20] Shure Fig 10 Vert Scrub 500x394.gif](/community/data/attachments/779/779500-81b6bf9c1c262eff92c4c42de4d5e208.jpg?hash=gba_nBwmLv)
![[21] Arm 3 Linkage2 Model 800x78.JPG](/community/data/attachments/779/779502-2d9b2e6e769e942fef8db78bc9cfe31d.jpg?hash=LZsubnaelC)
![[22] Arm 3 Linkage 2 Cantilever 800x388.JPG](/community/data/attachments/779/779503-eb0e41f8cc6b8d73359a4abad80b8066.jpg?hash=6w5B-MxrjX)
![[25a] Vert Scrub 600x356.jpg](/community/data/attachments/779/779507-3f61d288a994e7827be49cf58e8ce8c1.jpg?hash=P2HSiKmU54)
![[26] Arm 4 Linkage2 Model 800x322.JPG](/community/data/attachments/779/779508-40e69752202e94ac7a3814cb1db1e171.jpg?hash=QOaXUiAulK)
![[25b] Rs Labs Rs-a1 800x520.jpg](/community/data/attachments/779/779512-34d0abedb358133cd343ce6e57ef4c88.jpg?hash=NNCr7bNYEz)
![[27] Arm 4 Linkage2 Cantilever 800x347.JPG](/community/data/attachments/779/779515-f36ff457bca6989c32753483cd399541.jpg?hash=82_0V7ymmJ)
In case anyone is interested, I attached the 'linkage2' model files for Arm 3 & Arm 4 in case anyone is interested in playing with these on their computer.
Ray K
Ray K
Hello Ray,
This is a very interesting series of posts. I wish I had your knowledge to be able to post like that.
Almost a year ago I filed an application for US patent with the US patent office. The application was for my "floating head-shell" invention whose purpose was to eliminate the well known tracking error. While I was writing the specifications and making the drawings, I realized that, the floating head-shell would apply to all tone arms and that it would do away with scrubbing in the horizontal plane. We'll see if the patent examiner will agree with me, or not.
Sincerely,
Ralf