Geometry and Kinematics of Guided-Rod Sharpeners

@brplatz:

Oh, i forgot to mention that for a tanto knife, the WEPS will sharpen the long edge as a perfect dihedral (in theory). And if you upgrade the WEPS with the Pro-Pack II so that it uses spherical joints, then it can sharpen both the main edge and the tip as a perfect dihedral (in theory). Details about this can be found in the chapter about the WEPS and also the chapter on optimal pivot placement.

The EP can sharpen a perfect dihedral angle, if you are sharpening at 30 degrees per side on the Edge Pro Apex, and 15 degrees per side for the Edge Pro Professional. Details about this are in the chapter about the Edge Pro Apex.

The chapter about the Edge Pro Apex also talks about modifications to the designs that would make them perfect in theory.
 
Lagrangian said:
@brplatz:

Oh, i forgot to mention that for a tanto knife, the WEPS will sharpen the long edge as a perfect dihedral (in theory). And if you upgrade the WEPS with the Pro-Pack II so that it uses spherical joints, then it can sharpen both the main edge and the tip as a perfect dihedral (in theory). Details about this can be found in the chapter about the WEPS and also the chapter on optimal pivot placement.

The EP can sharpen a perfect dihedral angle, if you are sharpening at 30 degrees per side on the Edge Pro Apex, and 15 degrees per side for the Edge Pro Professional. Details about this are in the chapter about the Edge Pro Apex.

The chapter about the Edge Pro Apex also talks about modifications to the designs that would make them perfect in theory.
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@Langrangian

I downloaded the report and am looking forward to reading it later today/tonight. Perhaps this will push me to customize/improve on my EP.

I am also trying to think about how a flat stone would effectively sharpen a recurve blade such as my ZT0350. I am assuming that even at the 30 degrees per side of a EPA, two points of the stone are touching on the convex portion, then one point when it bends around to the "normal" portion.

Brian
 
brplatz said:
I am also trying to think about how a flat stone would effectively sharpen a recurve blade such as my ZT0350. I am assuming that even at the 30 degrees per side of a EPA, two points of the stone are touching on the convex portion, then one point when it bends around to the "normal" portion.

Brian
Click to expand...

Even if so, not a problem. Look at the triangular "stones" of the Spydie Sharpmaker.
 
Officer's Match said:
Even if so, not a problem. Look at the triangular "stones" of the Spydie Sharpmaker.
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I agree it's not a problem, but just another interaction to consider due to the geometry of the convex edge of the recurve and the theoretical planar sharpening stone. I'm not saying the change is significant, but could add to the report
 
Thank you for your under estimated amount of patience. I tried doing this for my kinematics class years ago and lost it
 
@brplatz:

Hmm... I haven't thought too much about recurves. However, it seems that WickedEdge has. I don't know the details, but they sell some sharpening stones for the WEPS that are convex and specifically designed for sharpening recurves. At least I think they do. From what I remember, they do the right thing, where the sharpening stone surface is a cylinder with axis centered and aligned with the guide rod axis, and the radius is the distance from the axis to the stone surface. So in effect, you would be sharpening with a big cylindrical stone which is aligned with the guide rod. Because it is effectively a cylinder, any "twist" along the cylinder axis doesn't make a difference in sharpening angle.

I suppose if you had a rectangular sharpening stone, it would work OK too, so long as the 90-degree edges were well rounded off, and in general you had a two-point contact with the knife edge (ie: two rounded edges in contact with the recurve) so that the orientation of the stone is completely determined. The cylinder idea from Wicked Edge is interesting, because the "twist" part of the orientation doesn't matter; turning a cylinder along its axis doesn't change anything. But for a rectangular stone, it matters: Sharpening on the "flat" of the stone can produce a different angle than sharpening where one is sharpening only with the rounded edge on one side (like, you do a 45 degree twist along the guide rod).

Sorry, I'm not explaining this very well. If you're confused, let me know, and I'll see if I can make a diagram for it.

From the math, I don't think it is possible for the EP or WEPS to sharpen a recurve at a constant dihedral angle. In the chapter on optimal pivot placement, the only knife shapes that can be sharpened at a constant angle are ones with a straight segment followed by a circular arc, and then followed by a straight segment again. The spherical joint of the WEPS would have be located so that its perpendicular projection lands on the center of the circle for the arc. In the chapter, I try to explain that there are no other possible shapes, only a circular arc with straight segments on each side of the arc. (If the straight sides are zero length, then the arc could can be extended into a full circular blade.) I'm probably explaining this poorly here too. I think I did a better job in the report, so maybe have a look at that. If that is confusing, then ask me again, and we can sort it out.
 
fervens said:
Thank you for your under estimated amount of patience. I tried doing this for my kinematics class years ago and lost it
Click to expand...

Whoa.... When you say "my kinematics class" do you mean a class you attended, or a class you taught?

I suppose one could write a kinematic solver specifically for the Edge Pro, and then a separate solver for the WEPS. And then in each case take advantage of their specific geometries. This would be much simpler. But I didn't want to do that. So I wrote a general kinematics solver.

So I wrote a program to solve loop-closure for a general kinematic chain with three revolute joints followed by a prismatic joint. This was non-trivial! I involved a whole bunch of stuff, and I ended up working really hard on it, but it was really fun. In the end, I used the exact same program to analyze the EP and also the WEPS, or any other similar system.
 
Lagrangian said:
@brplatz:

Hmm... I haven't thought too much about recurves. However, it seems that WickedEdge has. I don't know the details, but they sell some sharpening stones for the WEPS that are convex and specifically designed for sharpening recurves. At least I think they do. From what I remember, they do the right thing, where the sharpening stone surface is a cylinder with axis centered and aligned with the guide rod axis, and the radius is the distance from the axis to the stone surface. So in effect, you would be sharpening with a big cylindrical stone which is aligned with the guide rod. Because it is effectively a cylinder, any "twist" along the cylinder axis doesn't make a difference in sharpening angle.

I suppose if you had a rectangular sharpening stone, it would work OK too, so long as the 90-degree edges were well rounded off, and in general you had a two-point contact with the knife edge (ie: two rounded edges in contact with the recurve) so that the orientation of the stone is completely determined. The cylinder idea from Wicked Edge is interesting, because the "twist" part of the orientation doesn't matter; turning a cylinder along its axis doesn't change anything. But for a rectangular stone, it matters: Sharpening on the "flat" of the stone can produce a different angle than sharpening where one is sharpening only with the rounded edge on one side (like, you do a 45 degree twist along the guide rod).

Sorry, I'm not explaining this very well. If you're confused, let me know, and I'll see if I can make a diagram for it.

From the math, I don't think it is possible for the EP or WEPS to sharpen a recurve at a constant dihedral angle. In the chapter on optimal pivot placement, the only knife shapes that can be sharpened at a constant angle are ones with a straight segment followed by a circular arc, and then followed by a straight segment again. The spherical joint of the WEPS would have be located so that its perpendicular projection lands on the center of the circle for the arc. In the chapter, I try to explain that there are no other possible shapes, only a circular arc with straight segments on each side of the arc. (If the straight sides are zero length, then the arc could can be extended into a full circular blade.) I'm probably explaining this poorly here too. I think I did a better job in the report, so maybe have a look at that. If that is confusing, then ask me again, and we can sort it out.
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Your explanation is very understandable! I feel that the only way to have a constant dihedral on a recurve or other odd curve, the pivot point about the y axis would have to be normal to the point on the edge. In your optimal pivot placement section you show that a pivot point along the curve section is a center location of the arc, but on a recurve that center location is on the wrong side. On a recurve it seems to me that the pivot point would have to follow a concentric angle to the curve of the recurve to be constantly dihedral.

I hope that makes some sort of sense, perhaps I'll draw a diagram.

Regardless of the magnitude of change (or lack thereof) I find it interesting and fun to come up with theoretical perfect situations for stuff like this.
 
Lagrangian said:
Whoa.... When you say "my kinematics class" do you mean a class you attended, or a class you taught?
Click to expand...

Poor wording on my part. The kinematics class i attended would be more accurate. Used to talking to other students about "their" classes. The way you did it sounds much easier than on paper, but that's only comparatively. Not saying it was easy at all.
 
brplatz said:
but on a recurve that center location is on the wrong side. On a recurve it seems to me that the pivot point would have to follow a concentric angle to the curve of the recurve to be constantly dihedral.

I hope that makes some sort of sense, perhaps I'll draw a diagram.

Regardless of the magnitude of change (or lack thereof) I find it interesting and fun to come up with theoretical perfect situations for stuff like this.
Click to expand...

Oh! You are right. :) It would be on the other side because that's where the center of the circle is. I understand your point.

So in a WEPS type set-up, the spherical joint would have to be above the knife! Because if the the recurve follows a circular arc, then the circle's center is above the knife. Hilariously, then the spherical joint on the right side of the knife is used to sharpen the left side of the knife!

Kind of one of those "Gee, why didn't I think of that!" moments. :)

On the other hand, it's a hilariously unusual set-up for a WEPS type sharpener. In the real-world, you would clamp the knife upside-down (blade cutting towards the ground) and then have to awkwardly get the right-side guide-rod to sharpen the left-side of the knife and vice-versa. Probably way too cmbersome to be practical.

LrBESoC.png
 
fervens said:
Poor wording on my part. The kinematics class i attended would be more accurate. Used to talking to other students about "their" classes. The way you did it sounds much easier than on paper, but that's only comparatively. Not saying it was easy at all.
Click to expand...

Hi fervens,

I'm curious... for your class, how did you solve it?

Oh... by "on paper" did you mean solve it analytically, like with pencil and paper? That's super cool! There is a ton of advanced related math for all that (algebraic geometry, etc.), but I didn't want to do something so tricky. So I opted for a "hybrid" solution that solves for all but one variable analytically, but then uses numerical methods to solve for the last variable.

Did you manage to solve it completely with pencil and paper? If so, I would be fascinated to learn more about how you did it.
 
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I drew a model in cad of a lansky type clamp holding a knife, then figures the distances form the upright of the clamp to the tip of the edge at intervals along the edge. I followed up with trig to get the varying angles. I didn't include stone thickness. Like i said, i lost patience for it. What inspired me was the edge pro with it's off center axis.
 
@fervens: I also thought about using trigonometry to calculate the change in angle. But it got to be incredibly tedious, and somehow not that interesting because the formula would be specific to the Edge Pro. To me, it was more exciting to write a program to solve the general case (which would cover the Edge Pro, WEPS, etc.). While this was more challenging, it was also a lot more fun.
 
You might all laugh at this, but I made a sharpener many years ago that was similar to the wicked edge but with rails instead of pivots, so that as you sharpened one side you could slide the rail as you honed, keeping the rod angle correct/straight instead of pivoting. I also had stops built in so they could be set at the end of the straight portion of the blade that way it would follow the curve at closer to the proper radius. I used it for a while, but it ended up buried in the garage attic I think after I got better at freehanding.
 
@eKretz:

Rails aren't bad! For the straight part of the main edge, there is no problem if the rail is parallel to the edge; it will sharpen a perfect dihedral angle. For the curved part or the tip of the knife, it would require some skill/practice to get right. I think it is a reasonable solution, and I think I've seen at least a couple of sharpening set-ups that use it.
 
Well, it had pivots at the rail interface, so once the slide rail hit the stop at the end of the straight part of the blade, it would pivot from there to follow the radius. It worked great, and I did it for sharpening longer knives as well as being able to keep the angles more uniform and being able to keep the scratch pattern more uniform on the whole edge.
 
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