Geometry and Kinematics of Guided-Rod Sharpening Systems

[jackknifeh]

About my previous post. When wanting VERY light strokes sometimes the weight of the stone is too much pressure. The last few strokes, especially the final stroke I lift up on the know so that less pressure is on the blade edge than what you get with the weight of the stone. For me, the need for extremely light pressure has proved to be a requirement for really sharp edges. I've heard lots of people emphasize this but hearing it or reading it or even knowing it is different than when you actually do it. Using less pressure than the weight of the stone is like using less pressure than the knife blade on a stone when free hand sharpening. This can be controlled easier with free hand sharpening because yor can change the weight of the blade on a stone by holding the knife at a different spot on the handle. Gently holding the knife in different places based on the balance point of the knife will change the amount of pressure the blade puts on a stone. Holding a knife closer to the balance point will in effect lessen the amount of pressure the blace puts on the stone. This is a great advantage to free hand sharpening IMO and why I like to do quick touchups free hand.

Jack

[jackknifeh]

@ Langranian. I read your post that happened while I was typing my last. :) Your knowledg and terminology is far above my experience. To understand a lot about what you say might require as many night school classes as I'd have to take to understand Cliff Stamp's posts. :) His knowledge of steel is so much higher than mine I don't know what he is talking about. He says steel "A" is different from steel "B". That's about all I get. When he starts explaining why I get lost. So I just pretty much believe what he says and leave it be. :D You do provide pictures (for dummies) so that's good. :D :D :D

Jack

[Philo Beddoe]

The math and science behind it is cool and they might not be 100% accurate but in the real world those systems can get knives insanely sharp..

I briefly had a Para2 that been sharpened on the WE and that was the sharpest knife I've ever seen or had.

I can hand sharpen decently but I've never been able to get one as sharp as that Para2 was..

[jackknifeh]

Ok, I read your first post and as I thought I didnt' understand the math. I don't know what imperfection you tried to explain about a dihedral something. V edge? I believe you were referring to variations in angle at different points along the edge. I'll tell you what I'm thinking and you tell me it I'm even thinking of the same thing you are talking about. Let's assume there is no play in any moving parts of an Edge Pro. Oh yeah, CAN ANYONE ELSE WHO HAS AN EDGE PRO APEX AND AN ANGLE CUBE MEASURE THE ANGLE CHANGE WHEN YOU LET THE STONE SIT ON THE END OF THE BLADE TABLE WITH ONE END OF THE STONE ON THE TABLE AND ANOTHER READING WHEN THE OTHER END OF THE STONE IS RESTING ON THE TABLE? I'm going to re-read mine because I was hurried earlier. Anyway, about the dihedral ???, are you talking about an angle change because the edge where the stone is touching the knife edge is closer or farther away from the pivot post? The farther away from the center of the blade table the edge of a knife is the lower the angle will get. Picture a 33 lp (if you are old enough :) ). If it is perfectly round and you slid the pivot rod through the hole and lowered the stone onto the outside edge and rotated the stone 360 degrees around the record the angle would be the same all the way around the record. But, if the record were shaped like an egg the angle would change dramatically as the stone rotated around the shape. Did I make sense and is that what you are referring to? Here's a better example. I have sharpened knives with a dramatic curve (belly) right near the tip. If you don't move the knife the edge gets closer to the center rod making the angle higher at the tip than it was at the beginning of the belly. Or my 10" plain edge bread knife. It has a straight edge and if I place the center of the blade on the blade table and don't move the knife the edge angles at the tip and heel will be lower than the edge angle at the center because the distance from the pivot rod is greater. Am I close to your thoughts?

About the minor inaccuracy of using the stop collar. My collar gets the angle VERY close when changing stones of different thicknesses. The only time I SEE inaccuracy is when using stones that remove such a tiny amount of steel per stroke. I tried to explain this earlier. But, I don't think, at my level of understanding math and/or geometry, that this inaccuracy has anything to do with math. I zero my angle cube with it sitting on the blade table base. When I put the cube on the stone arm I determine the angle between the stone arm and the base. This is a given. Then if the stone gets thicker it raised this part of the stone arm. If we then raise the pivot location the EXACTLY same amount shouldn't the angle be EXACTLY the same? My understanding is that it should be exactly the same. Am I correct in this? I'll assume I am and continue. So, any inaccuracy would be due to human error when re-setting the pivot or the thickness of a stone or the position of the moon or anything other than math. In my case I think my collar itself is a somewhat inaccurate item. The set screw is on one side of the collar. The collar has a larger than 5/16" internal measurement so it moves easily on the rod. You set it using a set screw. When I tighten the screw I think I can feel the collar twist a tiny bit instead of the top and bottom being at a perfect 90 degree angle with the pivot rod. This slight twist will raise the bar at the pifot point a tiny tiny bit. Any difference there will be equal where the stone makes contact. So the micro adjustments I need to do when using finer grit stones is because of the inaccuracy of my stop collar. Again, did that make sense. I wish we were in the same room with the EP, WE, and knives so we couls actually see what we are talking about.

Jack

[jackknifeh]

Oops, forgot. I just took my time and did several readings on the change in angle based on inaccuracy of the pivot variance. I'll call the end of the stone nearest me the rear end. When the rear end of a stone is resting on the end of the blade table the angle measured 15.00 degrees. Then I pull the stone arm and rest the frond end of the stone on the blade table. When it is here the rod in the pivot moves to the top of the hole. The hole is a tiny bit larger than the 1/16" rod. At this position with the rod at the top of the hole the angle is 15.30 degrees. So the difference is consistantly .3 degrees off, not .5 degrees. But when trying to put the VERY last strokes on an edge this amount of difference matters.

This amount of angle difference seems to matter when putting the final strokes on an edge when searching for the ultra sharp edge. But, I think it was Evil who said something about free hand sharpening at a margin of error of .1 degrees.. I know my accuracy free hand is not that accurate. But, I can get the hair popping ultra sharp edge free hand also. So if the .3 degrees on the EP matters to the point it keeps me from getting the ultra sharp edge how can I claim this when I get the ultra sharp edge free hand when I KNOW my accuracy is less. Now, I have less confidence in the theory I had developed or believed. I have to close because I need to pull hairs out of my head. :)

Jack

[Evil D]

When I'm putting my last finishing touches on an edge, I'm always just slightly higher than the bevel is anyway. As long as the variance works in that direction, I'm fine with it. If it goes the other way, I'll know because I won't get the results I'm looking for. The important thing to remember here is, these are known and very controllable variables.

[phillipsted]

Hey, Lagrangian - nice work! I really enjoyed reading the BF thread on your sharpening rig a couple of years ago. Brilliant!

TedP

[Lagrangian]

@jackknifeh:

Hi, I think you have the right idea, but I'm not 100% sure. I wasn't able to completely decode your explanation. Could you try reading the first few chapters of the report itself? There is virtually zero math in them; instead everything is illustrated by pictures and animations. About 2/3rds of the report are just pictures and animations. I worked pretty hard to make them clear. Because you've been thinking about it very carefully, and I think you have the right idea, you should be able to read through easily? If the report isn't clear, then just ask questions, and I'll try to answer.

Download Link:
https://drive.google.com/file/d/0B8rQYh ... Q2MlRFbTA/

Alternate Download Link:
http://www.mediafire.com/download/2flrq ... eta17).zip

I'm reluctant to reproduce all of the explanations here, when I've already spent a lot of time trying to explain them clearly in the report. :)

If you're impatient :) then please check out these two YouTube videos, which are animations from the report. If you understand these two, then you have got the essential idea. If these YouTubes don't make sense to you, then probably worth reading the report, which explains them in detail. Please watch these in order.

(1) https://youtu.be/Lg3dK_n49Gw
(2) https://youtu.be/xtY-TTw ... e=youtu.be

The second video has 6 panels (!), so you should watch that in full-screen-mode and at as high a resolution as possible (HD).


btw, most angle-cubes (ie: digital inclinometers) are only accurate to about 0.1 degrees with about 0.1 degrees repeatability. Others are only accurate to 0.2 degrees. So it's not clear to me that they can accurately measure the effect we're describing, because the effect is typically around 0.1 degrees or smaller. There are more accurate digital inclinometers, however they are insanely expensive (many hundreds to thousands of dollars).

It might be possible to measure the angular change in a different way though, say using a machinist's spirit level (sometimes called an engineer's spirit level). Or by measuring the height of parts with a dial indicator setup.

[Lagrangian]

Hi Everyone,

Here is the latest version of the technical report, with a new section on recurve blades with ideas suggested by brplatz.

Download Link:
https://drive.google.com/file/d/0B8rQYh ... Q2MlRFbTA/

Alternate Download Link:
http://www.mediafire.com/download/2flrq ... eta17).zip

Sincerely,
--Lagrangian

[WorkingEdge]

Thx for all the hard work, Lagrangian!

Can't download file on iPad so maybe you addressed already. B can be closer approximation of A if the arm starts closer to horizontal (with the mast being checked if truly vertical). Mines is bolted on the corners so I can adjust each to get the platform in the angles I want including making the edge of the platform where knife rests being horizontal as possible.

That said, I stopped with the collar and use a iPhone app with 0.1 degree reproducibility.

Hi sensorsquare,

Not 100% sure I understand your question/point, but I think I can answer it. In the figure, the length labeled by "a" is the actual change in stone thickness. Since we changed to a thicker stone, we need to raise the pivot point on the vertical rod.

If we raise the vertical rod by the distance "b", then everything works correctly. In the figure, "b" is trapped between two parallel lines and is straight up and down. So you can slide "b" until it is over-lapping the vertical rod. It will then cover the same distance between the two red lines you drew. (Another way to think about it is to see a parallelogram where "b" is one side of the parallelogram.) I "b" drew it to the side, but maybe I should draw it on top of the rod.

In any case, you can see that "a" and "b" are not the same length. In the stop-collar trick, we approximate "b" by "a". However, typically, "a" is too small of a correction (a <= b). You can draw some triangles and do some trigonometry to find out how different they are. (Details are in the chapter about the Stop Collar Trick.)

Hope this helps?

[Lagrangian]

Hi WorkingEdge,

You are correct. :) If the central mast is vertical, and the guide rod and sharpening stone are horizontal, then the stop-collar-trick becomes perfectly accurate (in theory). Another way to say this: If the guide rod and sharpening stone are perpendicular to the mast, then the stop-collar-trick becomes perfect. I tried to describe this in the chapter on the Stop Collar Trick. Additional details are there, including a formula for calculating the error.

btw, other good things happen when the guide-rod and stone are perpendicular to the vertical mast: when this happens, the Edge Pro is also able to sharpen a perfect dihedral angle on the main edge of a tanto knife. Details about this are in the chapter on the Edge Pro.

A lot of the effects described in the report are often smaller than 0.1 degrees. So you may not be able to measure them with your iPhone, angle cube, etc. Most common digital inclinometers are only accurate and/or repeatable to about 0.1 or 0.2 degrees. There are digital inclinometers which are more accurate, but those are super expensive (many hundreds to thousands of dollars). To measure these effects in practice would require something more accurate. Maybe a machinist's level (or engineer's level), or a setup which can measure lengths very accurately, like with a machinist's dial indicator.

[Lagrangian]

I was asked to do an analysis of sharpening a khukuri knife at 10 degrees per side. The analysis here is for a WEPS-Gen1

I started with photo of a khukuri that I found from http://www.KnifeCenter.com. I then did a polygonal trace of the knife edge which was then spline interpolated with sample points at roughly every 0.25 inches. The trace was more carefully done for the blade's cutting edge, and then only roughly accurate for the spine and handle. Analysis of the results are graphed as requested.

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Original photo of the khukuri:


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Results:
Please note that the graph and the knife are vertically aligned to help visualize the results.


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Discussion:

I did not trace the knife edge perfectly, which may have caused some minor artifacts So the slight "hump" at around -4.5 <= X <= -4.0 inches is probably due to inaccurate tracing on my part. Similarly, I may have clicked slightly off on the very tip of the knife, which would cause the change at the tip of the knife at X = +3.5 inches. Likewise, the slight oscillation around 10 degrees for the main edge of the knife is almost certainly due to inaccurate tracing.

The sharp increase in degrees per side for -5 <= X <= -3 is expected from the Dihedral Triangle Theorem in the technical report. The gray line is a tangent of the knife edge near X = -5. As one can see, that tangent line travels very close to the circle center. The distance from the tangent line to the circle center is labeled "d". Because d is much smaller than the radius of the circle, the dihedral angle must be much higher. Hope this makes sense. Feel free to ask questions if it is not clear.

Although this analysis was done with a WEPS-Gen1, the results will be very similar for a WEPS-Gen2. They should only differ by a tiny fraction of a degree, so the graph will be virtually identical. If there is interest, I can run the analysis for a WEPS-Gen2 and then we can compare it to a WEPS-Gen1.

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When I have time, I plan to also analyze a kitchen chef knife.
Let me know if you have other requests or suggestions. :)

[Brock O Lee]

Thanks Lagrangian...

So, after all this math, which one of the 2 (EP or WE) is more accurate/consistent?

Have you come to any other conclusions ?

[Lagrangian]

Hi Brock O Lee,

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The Edge Pro and the Wicked Edge systems are very good. Both are accurate and consistent. It is difficult for me to say which is more accurate/consistent during actual use, because, in practice, their performance will depend on many things:

(1) Accuracy of manufactured parts
(2) How parts wear over time
(3) User technique
(4) Possible complications due to unusual knife shapes

The above could be tested, but would require more than just the theoretical analysis in the technical report. A machinist and/or tool-and-die maker with a set-up for precise measurement could do it (like with a machinist's granite surface plate, dial test indicators, etc.). Unfortunately, I don't have such equipment.

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How about what I would prefer personally, and why? I can answer this, but it is simply a matter of my own opinion and preference. But this will vary from person to person.

Edge Pro
Pros: Can easily sharpen to very thin angles (say, 10 degrees per side and lower).
Cons: May require more skill when frequently re-positioning the knife on the main platform. To sharpen to a consistent angle, one has to maintain both the distance the knife edge protrudes beyond the main platform, and also the angle between the knife edge and the edge of the platform (this is a rotation within the plane of the inclined main platform).

Wicked Edge
Pros: Typically, knife is clamped only once, and remains fixed for the entire sharpening process. This helps maintain consistency. Can sharpen to thin angles, but requires the separate thin-angle attachment.
Cons: Because the knife is fixed, the shape of the knife silhouette will affect how the angle varies along the knife edge (like in the khukuri example above).

My opinion: I'm not super skilled at sharpening, so for myself, the extra skill that may be needed for the Edge Pro is why I would choose the Wicked Edge. While the sharpening angle would vary along the edge (for the WEPS), the sharpening angle will be very consistent (repeatable). I also like the idea of alternating strokes on each side of the knife, which is much easier with the WEPS.

My opinion might be different if I were more skilled, often sharpened knives to very thin angles, or didn't like having strokes that alternated sides. I have many friends who prefer and EP and many other friends who prefer a WEPS.

[Brock O Lee]

Thanks Lagrangian, I appreciate the detailed reply...

There is one other major difference between the EP and WE (not related to geometry) which I have noticed, which might be significant.
- with the WE the user sharpen using primarily edge trailing strokes (stone moves away from the edge),
- with the the EP the user sharpen using primarily edge leading strokes (stone moves towards the edge)

From my understanding, edge leading is the preferred approach, in order to form a clean edge, cut off a burr, etc. Maybe someone with more knowledge on the subject can expand on this?

It would also be interesting to investigate/compare edge retention achieved between both sharpening systems, at the same angle and on the same knife. But that is a topic for a different discussion...

[Evil D]

Personally, I have dealt with clamp style sharpeners for too long to ever use a Wicked Edge. To me, that system is a double sided Lansky. It may do the job better and may be more adjustable, but you still have all those clamp issues to deal with. I would be willing to race anyone who uses a Wicked Edge to see who can sharpen a knife faster, and I would bet my entire knife collection and my Edge Pro that I would win, especially if the blade is over 6 inches long. Unless you're sharpening blades that are over 5 or 6 inches, there is no need to move the blade around on the table, you just hold it in one spot. This has held true for every knife I've ever handled, and I've sharpened them all the way up to the Police/Military which are among the longest blades in the catalog. You simply loosen the table guide wing nut, line up the edge with the edge of the table, and you're off. You can also sharpen extremely long blades on an Edge Pro without having to reclamp the blade in different places. I have an old commercial butcher's knife that has a 12 inch blade that I use for yard work, and it gets sharpened on my Edge Pro. The bevel may be measurably uneven according to math, but by sight the bevel is consistent and even all the way down that 12 inches of blade. If you didn't constantly move the blade around in the clamp on a WEPS, you would end up with high and low spots on the bevel because of how the bevel gets wider the further away from the clamp it gets. I couldn't see maintaining my kitchen knives on a WEPS and having to deal with moving the blade around in the clamp. The only extra skill required in using the EP is just holding the blade in one spot, which I really don't think is very hard, especially if you use the table magnets to help you along. Another thing is, blades that don't have a squared off spine are an issue with clamps. What do you do when you have to sharpen something like the Breeden Rescue or a Bench Made Pardue? On the Pardue, the spine is ground with a false edge, if you try to clamp on that the blade will either wiggle or slip out. Then you have to deal with a slew of tricks to keep the blade in there tight...gives me a headache just thinking about it.

[Brock O Lee]

To me, that system is a double sided Lansky.

LOL ... :D

My early Lansky permanently dampened my enthusiasm for any system that uses a clamp. For that reason alone I much prefer the EP.

[Evil D]

Don't get me wrong, I can put a stupid sharp edge on a Lansky, but it comes as a result of TONS of practice, trial and error. We had several very in depth threads here discussing the issues of the clamp, where to clamp, how far from the edge to clamp, and how all those things effect the actual angle that the stone hits, and then furthermore how difficult it is to repeat all those things later on when you need to touch up the edge without completely making a new bevel every time.

[senorsquare]

I'm with D on this one. I can get good results with the edge pro fairly quickly, easily and consistently with a wide variety of blade shapes and lengths.

I've got two more atomas to go before I have the complete set for the EP and since those plates are the same thickness then I should be able to pick an angle then set it and forget it.

[Lagrangian]

@Evil D
I agree; if you don't move the blade in the EP, then the skill required is much less. Also, yeah, clamping properly on the WEPS takes a little time. Personally, I don't mind that. btw, if you do not move the blade in the Edge Pro, then it has many of the same effects where the sharpening angle will vary due to both the mechanism itself, and also due to the shape of silhouette of the knife (like the khukuri example above).

@Brock O Lee
Hmm... I haven't had much experience trying an EP. But it seems to me that on both a WEPS and an EP, it is fairly easy to do both leading and trailing edge strokes? I typically do leading edge strokes on my sharpening rig (see below).

@ everyone
I built my own sharpening rig, and it can be used in the style of an EP or a WEPS. And the knife can be fully clamped (WEPS), or un-clamped on a platform (EP).

Details on sharpening rig here:
http://www.bladeforums.com/forums/showt ... Pict-Heavy

Some pictures:

"Edge Pro Mode"


"Wicked Edge Mode"


Although I can do both, I usually prefer to use it in the WEPS mode.
Like Brock O Lee, I also like leading-edge strokes.