Welcome, Guest
Username: Password: Remember me

TOPIC: Geometry and Kinematics of Guided-Rod Sharpeners

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 2 weeks ago #15026

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
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 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.

Original photo of the khukuri:


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


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.

When I have time, I plan to also analyze a kitchen chef knife.
Let me know if you have other requests or suggestions. :)
Last Edit: 7 months 2 weeks ago by AnthonyYan.
The administrator has disabled public write access.
The following user(s) said Thank You: leomitch

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 2 weeks ago #15028

  • mark76
  • mark76's Avatar
  • OFFLINE
  • Administrator
  • Posts: 1193
  • Thank you received: 360
  • Karma: 86
Interesting analysis of the khukuri!

And I love the technical report, but you already knew that B) .
The administrator has disabled public write access.
The following user(s) said Thank You: AnthonyYan

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15127

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
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:
drive.google.com/file/d/0B8rQYhU8N9ZGSENqc2Q2MlRFbTA/

Alternate Download:
www.mediafire.com/download/2flrqn7po9um3...DRAFT_1.0beta17).zip

If 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.
imgur.com/a/M0QCx#0







Last Edit: 5 months 3 weeks ago by AnthonyYan. Reason: 1.0beta17
The administrator has disabled public write access.

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15134

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
Last Edit: 5 months 3 weeks ago by AnthonyYan. Reason: 1.0beta17
The administrator has disabled public write access.
The following user(s) said Thank You: johpe

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15136

  • johpe
  • johpe's Avatar
  • OFFLINE
  • Senior Boarder
  • Posts: 75
  • Thank you received: 18
  • Karma: 4
Hi there

Impressive work indeed! After looking at the case study couldn't that be more or less used as the base of a computer program to give the optimal placement of each knife in the vise?

Something in the lines of:
1) the user is asked to select the shape of his blade
2) the user is asked for the length of the blade
3) the user is asked about the height (or two or three height meassurements).

Then the program calculates the optimal placement and gives is to the user.

Seems like you already have the math and everything worked out?

BR, Johannes
The administrator has disabled public write access.
The following user(s) said Thank You: AnthonyYan

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15144

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
Hi johpe,

I've been thinking about this... There's good news and bad news.

(1) The bad news:
Currently, my program is prototyping code that is only designed to be as accurate as possible; it is typically able to satisfy kinematic constraints to a relative accuracy of around 10^-12. Almost zero consideration was given to speed. As the great Donald Knuth said,"Premature optimization is the root of all evil (or at least most of it) in programming." As a result, it can take an hour or two to do the full computation for a large knife. That is fast enough for what I wanted it for, but this is probably too slow for optimizing pivot placement. This can be fixed, but requires not only optimizing the code, but also re-thinking the algorithm.

(2) The good news:
If we simplify the mechanisms, then the computations can be done instantaneously. For example, we could pretend that the EP-Apex and WEPS-Gen1 simply use a spherical bearing instead of their more complicated pivoting mechanisms. Then computing dihedral angles becomes instantaneous. And the results would be good to about half a degree at worst. (It only becomes necessary to use (1) if you want better than 0.1 degree accuracy.)

For (2), it might not even be necessary to write a program! Instead, one could print out a series of concentric circles on paper. Then by placing the knife profile on the paper, and drawing some lines, you could probably figure out where to place the main pivot(s). I would have to explain the details about how to do this, and if it turned out to be too complicated, then a program would be better.

I guess the main question is whether (2) would be good enough? If there is sufficient interest, I can work on this, although slowly as I am getting rather busy with work.

Sincerely,
--Lagrangian
Last Edit: 7 months 1 week ago by AnthonyYan.
The administrator has disabled public write access.

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15149

  • johpe
  • johpe's Avatar
  • OFFLINE
  • Senior Boarder
  • Posts: 75
  • Thank you received: 18
  • Karma: 4
I would think that the simplification mentioned in (2) would definitely be good enough!

I would use a program like that for initial placement of a new knife and then 0.5 degree accuracy if probably better than any one would be able to notice or set by them selves without computer aide.

For the WEPS I think it would be a great help if the program for example could output info with regards to the already existing depth alignment guide (which we all already use(!?)).

Now, I've already manually "dialed in" most of my knives so for me a program like that would serve as a double-check that I've done right to begin with. But for new users it could probably help a lot to get started with knife placement in the vise.
The administrator has disabled public write access.
The following user(s) said Thank You: AnthonyYan

Geometry and Kinematics of Guided-Rod Sharpeners 7 months 1 week ago #15154

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
New version of the technical report (1.0beta17) can be downloaded here:

Download:
drive.google.com/file/d/0B8rQYhU8N9ZGSENqc2Q2MlRFbTA/

Alternate Download:
www.mediafire.com/download/2flrqn7po9um3...DRAFT_1.0beta17).zip
Last Edit: 5 months 3 weeks ago by AnthonyYan. Reason: 1.0beta17
The administrator has disabled public write access.

Geometry and Kinematics of Guided-Rod Sharpeners 6 months 3 weeks ago #15344

  • AnthonyYan
  • AnthonyYan's Avatar
  • OFFLINE
  • Expert Boarder
  • Posts: 100
  • Thank you received: 64
  • Karma: 16
@johpe:

Hmm... I'm busy-busy, but here are a few minor updates.

(1) I now have code that does the super-fast calculations, but only for spherical-joint sharpeners (like the WEPS-Gen2).
(2) I have various ideas about how to speed up the code for other sharpeners, but not exactly sure it would be worth it. Basically, the idea is to use nearby solutions solved earlier as a starting point to find new solutions. This would help a lot, but maybe not enough.
(3) My main problem is how to visualize the data:

Imagine a WEPS-Gen2 with a knife clamped in it. For a coordinate system, we can have the X-axis pointing parallel to the line of the blade edge, the Y-axis as pointing straight up, and the Z-axis as perpendicular to the plane of the knife. Now imagine, we choose an (x,y) coordinate for the location of the spherical joint. To satisfy our sharpening angle (for example, 15 deg per side), we can adjust the z coordinate until we hit 15 deg per side at a choosen calibration point on the knife edge. So the z coordinate is determined from the (x,y) coordinates. Now, with the pivot located at (x,y,z), we get a sharpening angle for every point on the knife edge. My problem is that this information needs 4 dimensions to easily visualize.

You can think of it as a 3-dimensional array:
Array(x,y,d) = a
x = x-coordinate of spherical joint
y = y-coordinate of spherical joint
d = distance along the knife edge for specifying a specific point.
a = sharpening angle at d on the knife edge, when the spherical joint is at coordinates (x,y,z). (Remember z is computed from (x,y).)

I tried a few things, but I did not find a way of visualizing this array that I liked. The best one I found, but am not so happy with, is to fix y, then make a 2d-contour plot where x and d vary. The user can then flip through frames of a movie, where each frame is a different choice for y. In each frame is drawn the 2d-contour plot. (Hope this makes sense...)

If I can find a nice way to visualize the results (3), then we can do something interesting. So if you or anyone has ideas, please let me know. The idea is to provide an (interactive?) visualization that then allows the user to pick what he thinks is best.

One thing I'm reluctant to do, is to blindly optimize for the user (say, minimize average deviation in sharpening angle, or maximal deviation in sharpening angle, etc.) because usually there are parts of the edge the user really cares about and other parts of the edge the user doesn't care about. So I think it is better to do a visualization rather than have a program run as a black box and return a single solution. If you have any thoughts on this, let us know.

Sincerely,
--Lagrangian
The administrator has disabled public write access.

Geometry and Kinematics of Guided-Rod Sharpeners 6 months 3 weeks ago #15348

  • GibCurry
  • GibCurry's Avatar
  • NOW ONLINE
  • Expert Boarder
  • Gib
  • Posts: 145
  • Thank you received: 104
  • Karma: 20
AnthonyYan wrote:
@johpe:

Hmm... I'm busy-busy, but here are a few minor updates.

(1) I now have code that does the super-fast calculations, but only for spherical-joint sharpeners (like the WEPS-Gen2).
(2) I have various ideas about how to speed up the code for other sharpeners, but not exactly sure it would be worth it. Basically, the idea is to use nearby solutions solved earlier as a starting point to find new solutions. This would help a lot, but maybe not enough.
(3) My main problem is how to visualize the data:

.........

If I can find a nice way to visualize the results (3), then we can do something interesting. So if you or anyone has ideas, please let me know. The idea is to provide an (interactive?) visualization that then allows the user to pick what he thinks is best.


Sincerely,
--Lagrangian

I'm following a healthy portion but not all of the different sciences you are combining and talking about.

But, when you mentioned looking for a way to visual the info you reminded me of an article I read earlier this week. Maybe it will be of, at least, interest, if not of some use.

I sure enjoy, consume and try to digest your posts.... and I thoroughly enjoyed this article.

bits.blogs.nytimes.com/2014/01/06/a-make...ner=rss&emc=rss&_r=0
~~~~

For Now,

Gib

Φ

"Things work out best for those who make the best out of the way things work out."

"My goal is to be a good, practical knife sharpener. My dream is to polish molecules."
The administrator has disabled public write access.
Time to create page: 0.153 seconds