Geometry and Kinematics of Guided-Rod Sharpeners
- This topic has 75 replies, 11 voices, and was last updated 09/16/2014 at 7:22 pm by
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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:
Sample Animation on YouTube:
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:
http://www.mediafire.com/download/2flrqn7po9um350/Geometry_and_Sharpening_(DRAFT_1.0beta17).zipThe 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 fileThe .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
Some interesting discussion about the WEPS and recurve blades on BladeForums.com. Thanks to brplatz for his ideas and observations. Perhaps the solution suggested is cumbersome, but I was surprised and amused by it.
Here is a diagram I made for the discussion at the link above.
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. 🙂Following a suggestion, I have added three knives to the report: An 8″ chef’s knife, a 10″ khukuri, and the Spyderco LionSpy pocket knife. In the report is a new section,”Case Studies of Curved Blades on the WEPS-Gen1, WEPS-Gen2, and EP-Apex.”
You can download the new version of the report here:
https://drive.google.com/file/d/0B8rQYhU8N9ZGSENqc2Q2MlRFbTA/Alternate Download:
http://www.mediafire.com/download/2flrqn7po9um350/Geometry_and_Sharpening_(DRAFT_1.0beta17).zipIf you are just curious about the pictures and graphs, you can see them below but without much description. The report contains the details and discussion. I re-did the analysis for the khukuri with better tracing and improved spline interpolation.
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