Geometry and Kinematics of Guided-Rod Sharpeners

L

Lagrangian

Joined
Jun 25, 2011
Messages
400
Hi Everyone,

I've performed a very detailed mathematical analysis of the Edge Pro Apex (EP-Apex) and also the Wicked Edge Precision Sharpener (WEPS). I wanted to share the results with the general knife community.

As someone who loves mechanisms, I wondered if there are any ways to improve the EP or WEPS. Of course one could improve the precision of the EP and WEPS mechanisms with more accurate parts machined to a finer tolerance, etc.

However, after careful thinking, I realized that even if these mechanisms were _perfectly_ precise and _infinitely rigid_, that they would not always grind a perfect dihedral angle (informally known as a "V-edge"). That is, if we used a perfect EP or WEPS to sharpen a tanto knife, then the knife edge would not have a perfectly uniform dihedral angle. There will be a tiny variation in the included angle of the knife bevel.

How big is this variation in angle? To study it, I coded a computer program calculate the geometry and have written up the results here.

Topics in the report include:
(1) Tiny variations in sharpening angle in the Edge Pro Apex and also the Wicked Edge Precision Sharpener.
(2) A detailed analysis of the "Stop-Collar Trick" and how it is an approximation.
(3) For WEPS sharpening, a discussion about where to clamp the knife so that the sharpening angle is as uniform as possible over the entire knife edge.
(4) Using belt sanders to sharpen V-edges.

To pique your interest, here are some figures and one animation from the technical report.

Sample Figures:
http://imgur.com/a/1J8GP#0
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Sample Animation on YouTube:
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https://www.youtube.com/watch?v=Lg3dK_n49Gw

The full report is currently an initial draft (version 1.0.beta17), and it can be downloaded here:
https://drive.google.com/file/d/0B8rQYhU8N9ZGSENqc2Q2MlRFbTA/

Alternate Download Link:
http://www.mediafire.com/download/2flrqn7po9um350/Geometry_and_Sharpening_(DRAFT_1.0beta17).zip

The link is to a .zip file on Google Docs. The .zip file contains:
(1) A PDF file with embedded videos.
(2) Separate video files in a directory named "Movies"
(3) README file
(4) Creative Commons License file

The .zip file is huge because it contains many animation videos and figures. To view the animations within the PDF file, it is recommended that you use Adobe Reader version 9.0 or latter. Other PDF viewers will probably not play the videos. Also, you may have to give Adobe Reader permission to play the videos. If your PDF viewer cannot play videos, you can still view the .mp4 files in the folder "Movies." These files are .mp4 videos (MPEG-4/H.264) and can be played with free software such as Apple's QuickTime Player and/or VideoLAN, etc.

Please note: the slight variation in sharpening angle is VERY SMALL. In fact, it is typically around 0.1 degrees or less. In the worst case that is plausibly realistic, it is at most 0.5 degrees. In the Sample Figures above, we only really care when the sharpening stone is close to position X=0 inches, that is -1" <= X <= +1". These TINY changes in sharpening angle are virtually undetectable in practice.

Therefore this report is only interesting to:
1. Knife sharpening fanatics who like V-edges.
2. Engineers who like to study mechanisms.
3. Those of us who are insane. :)

This is still a beta version draft, so feedback is welcome.
If you have any questions, suggestions, or constructive criticism, just post to the discussion.

Sincerely,
--Anthony "Lagrangian" Yan

---------------------------------------
"What grit sharpens the mind?"
--Zen Sharpening Koan
 
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Brilliant work! I don't know that it will make a hell of a difference in my approach to sharpening (as in "Yeah... that looks about like 17°...) but it really is brilliant work and nice to actually know just how accurate these devices can be. Thanks for using your time in our best interest!

Stitchawl
 
I knew that there is a variance, but i thougt it would be much more severe.

Z6HJ3vx.png


Only 1,6deg on 4 inches. Couldnt care less.
 
Nice work, however the chief advantage of the EP system IMHO is the ability to continuously move the blade such that the area being sharpened is always in the center area of the platform, thus allowing a fairly precise angle on even larger knife blades such as chef's knives.
 
Sorry, browser stuck causing double post:(

In any case, thanks for sharing the calculation and the degree how close the tolerance is ...
 
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As an engineer, I have always had an itching that said these sharpeners were never "perfect", it's great to see some simulation/calculation to show the magnitude(or lack thereof) of the systems tolerances
 
Officer's Match said:
Nice work, however the chief advantage of the EP system IMHO is the ability to continuously move the blade such that the area being sharpened is always in the center area of the platform, thus allowing a fairly precise angle on even larger knife blades such as chef's knives.
Click to expand...

Hi Officer's Match,

This is true; by frequently adjusting the knife position, the sharpening stone will remain close to the "center line" of the knife platform. That will reduce the deviation in sharpening angle. And then if you over-lap strokes, the deviation will simply give you a slight convexing of the knife bevel, which is by no means a bad thing. :)

I think the most realistic worst-case is when you might try to sharpen a knife at 10 degrees per side. Yes, that is very very thin. But suppose you wanted to do that? Here is the graph for 10 degrees per side (see below). Since we are keeping the sharpening stone near the center-line of the knife platform, we are only interested in the graph for -1" <= X <= +1" (that is, when the center of the sharpening stone is within +/- 1 inch from the center line of the platform). From this, you can see a maximum variation of around 0.4 degrees away from 10 degrees per side.

Looking at the graph, maybe -0.4 to +0.05 degrees. I think this is as extreme as it gets for any example that is still realistic in practice. Probably does not matter in practice, but interesting I hope.

btw, this result is specifically for the Edge Pro Apex which has a more steeply inclined knife platform (about 30 degrees). For the Edge Pro Professional, the knife platform is more shallowly inclined (maybe 15 degrees), and would give different results. I haven't run the calculation, but for the Edge Pro Professional, my guess is the deviations would shrink by roughly a factor of 2x (for our example of sharpening a knife at 10 degrees per side).

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Again great work. That's close enough to call precise for me. As with most things, the operator skill is key.
 
Lagrangian said:
Therefore this report is only interesting to:
1. Knife sharpening fanatics who like V-edges.
2. Engineers who like to study mechanisms.
3. Those of us who are insane. :)
Click to expand...

Oh man, I check all three boxes :p I downloaded your report, I'm very interested in reading through it! Thanks for sharing.
 
I guess on another extreme side, the variation won't be there for a knife with 90* per side;)

When I try to comprehend such things and being lazy, I usually amplify/go to extreme. The same thing I did about frame/liner lock cutout inside/outside debate.
 
Chris "Anagarika";12915308 said:
I guess on another extreme side, the variation won't be there for a knife with 90* per side;)

When I try to comprehend such things and being lazy, I usually amplify/go to extreme. The same thing I did about frame/liner lock cutout inside/outside debate.
Click to expand...

LOL! :D

Actually, if you work through the geometry, I think the variation is huge for 90 degrees per side! The variation gets smaller close to 30 degrees per side, since the Edge Pro Apex has a 30 degree inclination for the main platform. As you move away from 30 degrees per side, the variation gets larger. I'm not sure, but I think the variation maxes out just before 30+90 = 120 degrees per side, but I'm not sure; very weird things happen when the sliding rod is (almost) parallel to the vertical mast. Not that sharpening at 90 deg per side or more makes any sense! :D

btw, for the Edge Pro Professional, the main platform is inclined at 15 degrees. So for the EP-Pro, if you sharpen close to 15 degrees per side, there is no variation. But as you sharpen at angles different from 15 degrees, then you get more variation.

Details in the report if you're curious, of course, but only for more sane sharpening angles.
 
Officer's Match said:
Again great work. That's close enough to call precise for me. As with most things, the operator skill is key.
Click to expand...

Quite, I don't have an Edge Pro but when you watch EP videos online, the blade is normally moving around all over the place, either by accident (unintentional shaking/wobbling) or intention (moving the knife to hit the full length of longer blades), so how relevant are precise mathematical measurements?
 
banksy said:
Quite, I don't have an Edge Pro but when you watch EP videos online, the blade is normally moving around all over the place, either by accident (unintentional shaking/wobbling) or intention (moving the knife to hit the full length of longer blades), so how relevant are precise mathematical measurements?
Click to expand...

I don't think this is supposed to be relevant, he even states the assumption of perfect precision and infinite rigidity. I think it is more to provide a better background understanding of the system, and to call to attention the possibility of improving current systems.
 
Excellent post Lagrangian :thumbup:

Just to be clear and sorry if I state the obvious...

Readers should aware that Lagrangian was carefully chosen a Tanto (knife with similar profile, e.g. bread knife) knife. To avoid: Blade thickness and variation it (e.g. distal taper) and blade width+variation(recurve; belly & tip) - all can cause resulting angle variations. Stop-collar + angle cube can correct one instance of sharpening arm at given thickness & width but can't dynamically adapt to continuous thickness & width variation of the blade.
 
A few brief replies:

@brplatz: If you replace the pair of joints with a spherical rod end, then the designs become perfect in a theoretical sense. Alternatively, the design can be made theoretically perfect by moving the two joints until their axes intersect, just like an a universal joint, or a gimbal. (By "theoretically," I mean idealized parts that are perfectly accurate and infinitely rigid, etc.) After either design fix, any variations in angle are due to limitations of reality: real parts are not perfectly accurate, and real parts bend and flex, etc. This is discussed in the chapter on the Edge Pro Apex, however many technical details were omitted because it would be impossible to cover all the manufacturing and engineering analysis (ie: finite element analysis (FEA)). Plus, I'm not well versed in manufacturing.

@Chris "Anagarika": I know what you mean by 90 degrees per side; that means 180 degrees inclusive. :D But surprisingly, if you try to sharpen at 90 degrees per side on an Edge Pro, weird things happen. For example, there will still be a rotation around the vertical mast, and this will cause a change in dihedral angle! Of course, in a real Edge Pro, the central mast isn't tall enough for you to get to 90 degrees per side. I think it is only when you get to 90+30=120 degrees per side that it goes back to being perfect. Crazy! :) (Discussion about the rotation of the vertical mast and how that changes the dihedral angle are in the chapter that covers the Edge Pro Apex.) One would think that any sharpener could do 90 degrees per side with no problem. But, if you clamp a knife in the usual way on the Edge Pro Apex, it will actually have problems sharpening at 90 degrees per side. So, although you were joking, your question has a hilarious answer!

@Bansky, @Officer's Match, @bpeezer: I totally agree; user skill is hugely important. So is the accuracy of the parts, etc. The point of the analysis was to see how big the deviations are from the design alone. After that is known, it can be compared to the deviations from other sources (such as user technique, "flex" and "play" in the mechanism, etc.). bpeezer is right that my motivation was to better understand the mechanism and how to improve it. If you read the introduction, you'll see that I discuss this point. Specifically, the report is irrelevant to almost all users because the deviations due to the design are probably smaller than the deviations due to "play" and user technique. So in practice, those should be addressed first, if one is serious about improving accuracy. And even if the mechanism were perfect, and one had perfect technique, the variation in angle is so small virtually no user would notice. This is why I say only V-edge fanatics, engineers, and the insane would be interested in the report. :)

@bluntcut: You're right; I wanted to study the simplest case possible, because I thought it would be the most revealing and also the most intuitive to understand.
 
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