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TOPIC: Dihedral Angles in Knife Sharpening

Re: Dihedral Angles in Knife Sharpening 2 years 2 months ago #4229

  • AnthonyYan
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razoredgeknives wrote:
I did notice that you said in the end of your post that "In general, though, a knife belly is not perfectly circular, or the pivot is not lined up with the center, etc. So there will be some variation. But the straight part of the knife edge will be fine, and you can put the pivot at a point which is aligned with the center of a best-fit circle to the knife belly. So in practice, it is still pretty good."

I do agree with this... there will be variation when you have a knife edge that is completely straight vs a knife edge that is in a perfect circle to the pivot point. the latter will have a perfectly consistant angle on the edge whereas a knife that is straight edged and long (let's say 2' long) the angle will change and become more narrow the further out you get (both directions) from the center, correct?

Hi razoredgeknives,

Sorry... I didn't understand your question(s). Maybe this will answer them? Consider a knife which has a straight edge that continues to a circular bend at the tip. In this diagram, I have drawn a side view of the knife, including the full circle and the circle's center which is marked by a cross hair.

For sharpening, if you align the pivot with the circle center, then both the straight and curved part of this knife will be sharpened to the same constant angle. That is, if you perpendicularly project the pivot onto the plane of the knife, then you land on the circle center (the cross-hair). This only works because the belly of the knife is circular, and the straight edge of the knife is tangent to the circle.

In the general case, the belly is not circular, and/or if the knife has a tanto edge, there is a corner, so that the straight part and the tip are not tangent. Then the sharpening angle will likely vary along the edge.

Hope that answers your questions.

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Re: Dihedral Angles in Knife Sharpening 2 years 2 months ago #4234

  • mark76
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Thanks again, Anthony! This proof absolutely rulez because of its simplicity. And what I also like is that you approach it with linear algebra. I really thought it would take geometry, which probably would have made it much more complex.
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Re: Dihedral Angles in Knife Sharpening 2 years 2 months ago #4235

  • cbwx34
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So, a quick check, or for the "Field & Sport" model that doesn't have the guide setup, would be to take a quick measurement to insure the tip is approx. the same distance from the pivot as the straight part of the blade.


p.s. The ruler is just for the photo, you could use the stone itself... make a mark, or just make sure it hits approx. the same spot.
Last Edit: 2 years 2 months ago by cbwx34.
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