Advanced alignment guide
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Clay, After reading the: https://knife.wickededgeusa.com/forums/topic/geometry-and-kinematics-of-guided-rod-sharpeners
Relative to your post: “The knife set up looks strange so I used the clamp to hold the knife after sharpening and took measurements w/ the laser goniometer. It’s registering a solid 13° along the whole blade. Weird, but true.”
How is that possible ? My understanding is that a consistent exact angle is only possible on the “uncurved “ part of the knife.
Except the special case of having a curve which is 100% fully on the arc of a circle (I think that is quite unlikely in reality)
If you position the knife at an angle equal to the “prorated (for segment length)” average of all the tangential slopes then you <span style=”text-decoration: underline;”>may</span> be at such a position angle which would minimize the delta sharpening angle over the full length of the blade.
As Yan mentions in note 2 at the bottom of page 57 “Mathematically, we say the knife edge is a differentiable curve” and if I remember from my many calculus classes you can then determine all kinds of things. We need a mathematician to help with an App to allow you to take a picture of a knife and determine the optimal set position and angle.
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The goniometer is pretty accurate (up to about 1 degree, I’d say), but the problem lies in interpreting its results. A tiny variation in the edge grind can cause almost unexplainable laser light spots on the goniometer circular thing (that’s how the goniometer shows its results). And interpreting measurements from convex bevels is a nightmare sometimes…
Anthony’s theory is spot-on and 100% accurate. The approach I took on my blog (link) and from which the above picture was taken by ReadHeads doesn’t take the various planes into account. Nevertheless it should still be a very good approximation of Anthony’s results and it also allows you to predict angle changes on edge curves.
If the knife was clamped as in the post of 02/03/2016 at 2:42 pm by Clay, there should also be angle changes on the straight part of the edge. If that isn’t the case, I’d blame the goniometer.
Molecule Polishing: my blog about sharpening with the Wicked Edge
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The following attempts to correlate Mark76’s analysis to Anthony Yan’s. My conclusion is that for an 8 inch chef’s knife (15 DPS with a knife shape as shown in the Figures) the theoretical sharpening angle deviation over the entire length of the blade is a min of 0.7 deg and max of 5.2 deg. The min is at a spherical joint location at just before the start of the major curve (which ends at the tip of the knife) at x=-.11. The max is at a spherical joint location at the heel of the knife at x=-.4. Complete understanding can be obtained by reading Anthony Yan’s analysis at:
<span style=”color: #2f9bc1;”>https://knife.wickededgeusa.com/forums/topic/geometry-and-kinematics-of-guided-rod-sharpeners</span>Comments are desired: Collaboration is how Linux was developed and is improved. It is the backbone of the fastest supercomputers in the world.
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If the knife was clamped as in the post of 02/03/2016 at 2:42 pm by Clay, there should also be angle changes on the straight part of the edge. If that isn’t the case, I’d blame the goniometer.
Nope, there won’t be an angle change along the straight portion, even if the knife is clamped at an angle. If you think about it, the pivot doesn’t “see parallel”… it just sees a straight line.
If you need a visual, clamp a blade at an angle, then tip your whole WE until the blade is parallel (to the ground)… to the pivot it “looks” the same as if you mounted it parallel to begin with.
Edit: Here’s a picture…
If you clamp a blade at an angle (top photo), then rotate the WE so the blade is parallel to the table/ground (middle photo), it looks no different to the pivot then the blade mounted parallel to begin with (bottom photo).
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I probably could have made it easier and just did this…
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I agree for the straight section, however, in reality there is no straight section. There is only an “almost” straight section. Mathematically, a knife profile can be represented by a 4th order polynomial equation. Something like:
The knife profile is actually a bunch of circle arcs combined together. Which one to pick in order to place the spherical joint at its center is my question. When Clay rotates the knife angle he is actually changing the location of the spherical joint relative to the circle arcs. We know there are different “best locations” depending if you want more or less acute angles at the tip as well as different total delta sharpening angles. You would think there are better ways to fine tune it than a sharpie. Yet of course it depends how anal you want to get about the edge. I am treating it as a mental engineering exercise in the quest for the perfect edge (whatever that is).
You should be able to take a scaled picture of your knife, input your biased use factor, push a button and your phone tells you how to place your knife for the optimum edge.
That being said I just did a 40 min touch up of my 4.5 inch Henckel steak knife at 17 DPS in a horizontal position with the spherical joint approximated to just outside the curve using my written log from last time (tip was at B on the steel ruler). The angle cube says I have a 4 deg total delta along the total edge (this was tricky and somewhat inaccurate though because the angle cube needs to be kept in the same vertical position as you traverse the edge – which I did by eye). Result: 400 grit thru strop green and I can read the newsprint, shave my arm and fast cut bent newspaper. I am sure it will cut my steak and hopefully my kids will keep their hands off it.
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The knife profile is actually a bunch of circle arcs combined together.
Great job on the knife and thanks for your work filtering down higher math into practical usability.
The main reason I run a double riser block in my setup is to allow for a larger radius and allow it to hit closer to the “primary” circle arc of any given larger knife. If its a small knife I can remove the riser blocks to reduce the radius from ball joint to knife apex to allow for a tighter sweep(narrower cone?).
Great stuff!
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