Edge geometry on a wicked edge (we130)

jalapeno said:
Hi Larry, this is definitely a brain teaser. Different visual aids work better for different people, so maybe this one will help. I find it easier to visualize on a Wicked Edge type of system for whatever reason.

Think of the line of the blade’s edge that you’re grinding a bevel on as just "a line on a plane."
In the drawing I have a plane (in green). Maybe think of this as a piece of thin, inflexible plexiglass (or metal or whatever) but where you have it mounted to the pivot point of the sharpening rod (the red dot) so it’s co-planar with the sharpening rod.

Lay that plane across the blade edge (first with the blade edge horizontal). The blade is shown in orange.

The dotted red lines represent the different angles you could pivot the sharpening rod at, and these are all lines on the green plane. I also have a profile view of this setup.
167044119.W53LFIHi.jpg


The WE sharpening stones go on the rods, and the face of each sharpening stone lays flat on the plane no matter which side-to-side angle the rod is at (because the sharpening stones can rotate on the rods). As you scrub the sharpening stones up and down to abrade the edge, they stay in constant contact with the plane. Since the plane is fixed at the same angle everywhere, so too are the faces of the stones.


Now tilt the blade in the vise so it’s no longer horizontal:
167044120.Rspfx8ez.jpg


Note that the line of contact between the plane and the blade edge is still just a line on the plane. But the spherical pivot joint allows the plane to still conform to the blade's edge no matter what the tile angle is. So, while the angle of the plane itself may change slightly between the 2 drawings, it is fixed at a constant angle in both individual cases.

If you set your sharpening angle to the same in both cases (using an angle cube, not the relative angle markings on the WE angle bar scale) with the sharpening stone at the centerline of the vise, the constant sharpening angle will also be the same in both cases.

Does this help?
Click to expand...
Thank you for those diagrams. So if I’m reading and looking at those diagrams correctly, a knife is put in on a slant (as shown in the diagram) and say therefore the tip is the lower point on the right, the angle will stay the exact same at the tip(right) and closer to the handle(left) no matter how much it is slanted? If that’s the case I don’t understand why you would need to find the "sweet spot” when using a wicked edge. Thanks for everyone’s patience when explaining this to me.
 
LarryT said:
Thank you for those diagrams. So if I’m reading and looking at those diagrams correctly, a knife is put in on a slant (as shown in the diagram) and say therefore the tip is the lower point on the right, the angle will stay the exact same at the tip(right) and closer to the handle(left) no matter how much it is slanted? If that’s the case I don’t understand why you would need to find the "sweet spot” when using a wicked edge. Thanks for everyone’s patience when explaining this to me.
Click to expand...

Yes the *sharpening angle* stays constant (even though there are other angles in that 3-d geometry that do change), and if all your knives are perfectly straight blades, there isn't a sweet spot. But on a chef's knife for example, the straight portion has some slight curve to it, and then it curves more drastically toward the tip.

So, on a chef's knife, that plane wouldn't lay flat against the edge except for a small portion near the heel. And for the curve to the tip, as you can see in this next drawing (you do have to use your imagination a bit to picture it in 3-d), once you get past the straight part, the knife's edge breaks away from the plane (which means the sharpening angle begins to change).

What you want to do on this part is get the curved part to match up with a constant radius as best you can (you do that by moving the knife left or right in the clamp, and mabe even add some up or down tilt from the horizontal, depending on the shape of the curve)
167044121.24b6R3sZ.jpg
 
jalapeno said:
Yes the *sharpening angle* stays constant (even though there are other angles in that 3-d geometry that do change), and if all your knives are perfectly straight blades, there isn't a sweet spot. But on a chef's knife for example, the straight portion has some slight curve to it, and then it curves more drastically toward the tip.

So, on a chef's knife, that plane wouldn't lay flat against the edge except for a small portion near the heel. And for the curve to the tip, as you can see in this next drawing (you do have to use your imagination a bit to picture it in 3-d), once you get past the straight part, the knife's edge breaks away from the plane (which means the sharpening angle begins to change).

What you want to do on this part is get the curved part to match up with a constant radius as best you can (you do that by moving the knife left or right in the clamp, and mabe even add some up or down tilt from the horizontal, depending on the shape of the curve)
167044121.24b6R3sZ.jpg
Click to expand...
Exactly so as the belly of the knife begins to curve towards the tip after the straight portion, the angle will change right? The tip is on a lower level than the straight portion.
 
I 100% believe the angle does not change the further you go away from the pivot point. That I do I understand. However, with the blade swooping down with the belly (as if you had it clamped in a wicked edge),the tip and belly is on a lower level. Same concept as when you are sharpening a knife the more material you take away the bigger the angle gets. Example: you sharpen a knife at 18 per side. You sharpen it so much and take so much material away the angle is now 19 degrees because in theory you dropped the level of the blade. I’m applying this concept to the belly and tip of the blade because it is at a lower level that say the flat portion of an edge.
 
LarryT said:
I 100% believe the angle does not change the further you go away from the pivot point. That I do I understand. However, with the blade swooping down with the belly (as if you had it clamped in a wicked edge),the tip and belly is on a lower level. Same concept as when you are sharpening a knife the more material you take away the bigger the angle gets. Example: you sharpen a knife at 18 per side. You sharpen it so much and take so much material away the angle is now 19 degrees because in theory you dropped the level of the blade. I’m applying this concept to the belly and tip of the blade because it is at a lower level that say the flat portion of an edge.
Click to expand...
Hi
:thumbsup:
great picture of the physical thing
you've proved it, its fact :)

See also, more graphs and a video
Sharpening Angles for a Khukuri Knife on a WEPS-Gen2 (animated contour plot) - ChiralSymmetry / Lagrangian geometry-and-kinematics-of-guided-rod-sharpeners.1131476/


Its easy to get confused like me so my "simple" example in numbers so I wont forget
Code: 
                \#\
                 \#\
 15 dps edge -> /\\#\
                || \#\
                ||15\#\   <- hypotenuse (longest)
                ||   \       the abrasive
   run          ||    \
   adjacent ->  ||     \
   (long side)  ||      \
    edge-up     ||       \
    clamped     ||___   / \
    blade       ||90|   |75\
                ||__|___|___\ <-- pivot
                     ^
                     |
                  opposite/rise (short side)
                  distance from pivot arm to blade
The abrasive on a wicked edge is the hypotenuse (longest side),
which is at an angle = arctangent ( rise / run )
which is at an angle = arctangent ( opposite / adjacent )
with the rise (short side ) being the distance of pivot arm from clamp
with the opposite (short side ) being the distance of pivot arm from clamp
and the run (long side ) being the height of the edge from the table,
and the adjacent (long side ) being the height of the edge from the table,
So yes, as the edge curves at belly/tip ,
the run (long) decreases, the angle must changes
the adjacent (long) decreases, the angle must changes
Code: 
              | |
              |T|
              |A|
       /|-----|B| shrunken run/adjacent (long side), angle increased
      / |     |L|
     /  |     |E|
    /   |     | |
    |   |     | |
    |---------| | run/adjacent(long side) at initial angle setting
    |   |     | |
    |   |     | |
   \|___|/    |T|
    |   |     |A|
    (   )     |B|
    (   )     |L|
    (   )     |E|
    (___)     | |
              | |

And the actual numbers (not from a physical sharpener )
knife blade is 2inch wide 8inch long , a chef knife ( 5cm wide 20cm long )
the sharpening system pivot is 2.679 cm (rise/opposite/ short) away from blade clamp
and the height of the edge of knife in clamp is above table is 10cm (run/adjacent/ long)
arctan( 2.679 / 10 ) = 15dps
in the last 2 inches of knife edge length , the width is changed by 1 inch,
changing the height above table ( run/adjacent/ long),
shrinking the run/adjacent/long by 2.54cm
and changing the angle by almost 5 degrees

arctangent ( opposite / adjacent )
arctangent ( short / long )
arctan( 2.679 / 7.46 ) = 19.75 dps

Check the tangent to make sure arctangent was calculated correctly

tangent( angle ) = ( opposite / adjacent )
tangent( angle ) = ( rise / run )
tangent( angle ) = ( short / long )
tan(15°) = 0.2679 = 2.679 / 10
tan(19.75°) = 0.359037 = 2.679 / 7.46
 
bucketstove said:
Hi
:thumbsup:
great picture of the physical thing
you've proved it, its fact :)

See also, more graphs and a video
Sharpening Angles for a Khukuri Knife on a WEPS-Gen2 (animated contour plot) - ChiralSymmetry / Lagrangian geometry-and-kinematics-of-guided-rod-sharpeners.1131476/


Its easy to get confused like me so my "simple" example in numbers so I wont forget
Code: 
                \#\
                 \#\
 15 dps edge -> /\\#\
                || \#\
                ||15\#\   <- hypotenuse (longest)
                ||   \       the abrasive
   run          ||    \
   adjacent ->  ||     \
   (long side)  ||      \
    edge-up     ||       \
    clamped     ||___   / \
    blade       ||90|   |75\
                ||__|___|___\ <-- pivot
                     ^
                     |
                  opposite/rise (short side)
                  distance from pivot arm to blade
The abrasive on a wicked edge is the hypotenuse (longest side),
which is at an angle = arctangent ( rise / run )
which is at an angle = arctangent ( opposite / adjacent )
with the rise (short side ) being the distance of pivot arm from clamp
with the opposite (short side ) being the distance of pivot arm from clamp
and the run (long side ) being the height of the edge from the table,
and the adjacent (long side ) being the height of the edge from the table,
So yes, as the edge curves at belly/tip ,
the run (long) decreases, the angle must changes
the adjacent (long) decreases, the angle must changes
Code: 
              | |
              |T|
              |A|
       /|-----|B| shrunken run/adjacent (long side), angle increased
      / |     |L|
     /  |     |E|
    /   |     | |
    |   |     | |
    |---------| | run/adjacent(long side) at initial angle setting
    |   |     | |
    |   |     | |
   \|___|/    |T|
    |   |     |A|
    (   )     |B|
    (   )     |L|
    (   )     |E|
    (___)     | |
              | |

And the actual numbers (not from a physical sharpener )
knife blade is 2inch wide 8inch long , a chef knife ( 5cm wide 20cm long )
the sharpening system pivot is 2.679 cm (rise/opposite/ short) away from blade clamp
and the height of the edge of knife in clamp is above table is 10cm (run/adjacent/ long)
arctan( 2.679 / 10 ) = 15dps
in the last 2 inches of knife edge length , the width is changed by 1 inch,
changing the height above table ( run/adjacent/ long),
shrinking the run/adjacent/long by 2.54cm
and changing the angle by almost 5 degrees

arctangent ( opposite / adjacent )
arctangent ( short / long )
arctan( 2.679 / 7.46 ) = 19.75 dps

Check the tangent to make sure arctangent was calculated correctly

tangent( angle ) = ( opposite / adjacent )
tangent( angle ) = ( rise / run )
tangent( angle ) = ( short / long )
tan(15°) = 0.2679 = 2.679 / 10
tan(19.75°) = 0.359037 = 2.679 / 7.46
Click to expand...
So I am indeed not going crazy. I didn’t think anyone was understanding what I was trying to say. I think this theory is 100 percent true right? Jalapeño, this is what I was trying to explain. Do you agree with this?
 
bucketstove said:
Hi
:thumbsup:
great picture of the physical thing
you've proved it, its fact :)

See also, more graphs and a video
Sharpening Angles for a Khukuri Knife on a WEPS-Gen2 (animated contour plot) - ChiralSymmetry / Lagrangian geometry-and-kinematics-of-guided-rod-sharpeners.1131476/


Its easy to get confused like me so my "simple" example in numbers so I wont forget
Code: 
                \#\
                 \#\
 15 dps edge -> /\\#\
                || \#\
                ||15\#\   <- hypotenuse (longest)
                ||   \       the abrasive
   run          ||    \
   adjacent ->  ||     \
   (long side)  ||      \
    edge-up     ||       \
    clamped     ||___   / \
    blade       ||90|   |75\
                ||__|___|___\ <-- pivot
                     ^
                     |
                  opposite/rise (short side)
                  distance from pivot arm to blade
The abrasive on a wicked edge is the hypotenuse (longest side),
which is at an angle = arctangent ( rise / run )
which is at an angle = arctangent ( opposite / adjacent )
with the rise (short side ) being the distance of pivot arm from clamp
with the opposite (short side ) being the distance of pivot arm from clamp
and the run (long side ) being the height of the edge from the table,
and the adjacent (long side ) being the height of the edge from the table,
So yes, as the edge curves at belly/tip ,
the run (long) decreases, the angle must changes
the adjacent (long) decreases, the angle must changes
Code: 
              | |
              |T|
              |A|
       /|-----|B| shrunken run/adjacent (long side), angle increased
      / |     |L|
     /  |     |E|
    /   |     | |
    |   |     | |
    |---------| | run/adjacent(long side) at initial angle setting
    |   |     | |
    |   |     | |
   \|___|/    |T|
    |   |     |A|
    (   )     |B|
    (   )     |L|
    (   )     |E|
    (___)     | |
              | |

And the actual numbers (not from a physical sharpener )
knife blade is 2inch wide 8inch long , a chef knife ( 5cm wide 20cm long )
the sharpening system pivot is 2.679 cm (rise/opposite/ short) away from blade clamp
and the height of the edge of knife in clamp is above table is 10cm (run/adjacent/ long)
arctan( 2.679 / 10 ) = 15dps
in the last 2 inches of knife edge length , the width is changed by 1 inch,
changing the height above table ( run/adjacent/ long),
shrinking the run/adjacent/long by 2.54cm
and changing the angle by almost 5 degrees

arctangent ( opposite / adjacent )
arctangent ( short / long )
arctan( 2.679 / 7.46 ) = 19.75 dps

Check the tangent to make sure arctangent was calculated correctly

tangent( angle ) = ( opposite / adjacent )
tangent( angle ) = ( rise / run )
tangent( angle ) = ( short / long )
tan(15°) = 0.2679 = 2.679 / 10
tan(19.75°) = 0.359037 = 2.679 / 7.46
Click to expand...
By the way thank you for taking the time to do those diagrams. They must of taken up some time but they explain it perfectly.
 
bucketstove said:
Hi
:thumbsup:
great picture of the physical thing
you've proved it, its fact :)

See also, more graphs and a video
Sharpening Angles for a Khukuri Knife on a WEPS-Gen2 (animated contour plot) - ChiralSymmetry / Lagrangian geometry-and-kinematics-of-guided-rod-sharpeners.1131476/


Its easy to get confused like me so my "simple" example in numbers so I wont forget
Code: 
                \#\
                 \#\
 15 dps edge -> /\\#\
                || \#\
                ||15\#\   <- hypotenuse (longest)
                ||   \       the abrasive
   run          ||    \
   adjacent ->  ||     \
   (long side)  ||      \
    edge-up     ||       \
    clamped     ||___   / \
    blade       ||90|   |75\
                ||__|___|___\ <-- pivot
                     ^
                     |
                  opposite/rise (short side)
                  distance from pivot arm to blade
The abrasive on a wicked edge is the hypotenuse (longest side),
which is at an angle = arctangent ( rise / run )
which is at an angle = arctangent ( opposite / adjacent )
with the rise (short side ) being the distance of pivot arm from clamp
with the opposite (short side ) being the distance of pivot arm from clamp
and the run (long side ) being the height of the edge from the table,
and the adjacent (long side ) being the height of the edge from the table,
So yes, as the edge curves at belly/tip ,
the run (long) decreases, the angle must changes
the adjacent (long) decreases, the angle must changes
Code: 
              | |
              |T|
              |A|
       /|-----|B| shrunken run/adjacent (long side), angle increased
      / |     |L|
     /  |     |E|
    /   |     | |
    |   |     | |
    |---------| | run/adjacent(long side) at initial angle setting
    |   |     | |
    |   |     | |
   \|___|/    |T|
    |   |     |A|
    (   )     |B|
    (   )     |L|
    (   )     |E|
    (___)     | |
              | |

And the actual numbers (not from a physical sharpener )
knife blade is 2inch wide 8inch long , a chef knife ( 5cm wide 20cm long )
the sharpening system pivot is 2.679 cm (rise/opposite/ short) away from blade clamp
and the height of the edge of knife in clamp is above table is 10cm (run/adjacent/ long)
arctan( 2.679 / 10 ) = 15dps
in the last 2 inches of knife edge length , the width is changed by 1 inch,
changing the height above table ( run/adjacent/ long),
shrinking the run/adjacent/long by 2.54cm
and changing the angle by almost 5 degrees

arctangent ( opposite / adjacent )
arctangent ( short / long )
arctan( 2.679 / 7.46 ) = 19.75 dps

Check the tangent to make sure arctangent was calculated correctly

tangent( angle ) = ( opposite / adjacent )
tangent( angle ) = ( rise / run )
tangent( angle ) = ( short / long )
tan(15°) = 0.2679 = 2.679 / 10
tan(19.75°) = 0.359037 = 2.679 / 7.46
Click to expand...


So... how do you explain... that you can set the knife in the clamp, so that, as you approach the belly to tip area, the angle can get smaller?

6193_B9_DA_C0_C1_4784_A7_E2_7_BC04_DFA1279.jpg
 
cbwx34 said:
So... how do you explain... that you can set the knife in the clamp, so that, as you approach the belly to tip area, the angle can get smaller?

6193_B9_DA_C0_C1_4784_A7_E2_7_BC04_DFA1279.jpg
[/QUOTE
This might have something to do with that "sweet spot" that wicked edge users try to find. I ordered an angle cube yesterday so I can see for myself. I’ll keep you guys updated. I’ll try moving the knife away from handle and towards the handle to see if your theory is correct.
Click to expand...
 
cbwx34 said:
So... how do you explain... that you can set the knife in the clamp, so that, as you approach the belly to tip area, the angle can get smaller?

6193_B9_DA_C0_C1_4784_A7_E2_7_BC04_DFA1279.jpg
Click to expand...
The tip angles would be larger than that of the initial "straight" angle. It looks like you have it backwards.
 
This might have something to do with that "sweet spot" that wicked edge users try to find. I ordered an angle cube yesterday so I can see for myself. I’ll keep you guys updated. I’ll try moving the knife away from handle and towards the handle to see if your theory is correct.
 
LarryT said:
This might have something to do with that "sweet spot" that wicked edge users try to find. I ordered an angle cube yesterday so I can see for myself. I’ll keep you guys updated. I’ll try moving the knife away from handle and towards the handle to see if your theory is correct.
Click to expand...

Be sure you use it correctly. You might already know this, but if you got a single-axis unit, the angle is only accurate if you keep the body of the unit parallel to earth's gravity. These units are based on micro-machine accelerometers internally, and the displayed angle is based on an internal calculation using the angle the accelerometer makes with earth's gravity. The instructions probably won't tell you this.

In plain english, if you have a wicked edge and you attach it to the stones via its magnets, it will only read the correct angle when the sharpening rod is at the centerline of the vise. Swing the rod either left or right of there, and you have to twist the body of the unit so it's perpendicular to the horizontal.

edit: in the link cbwx34 provided above, you can see this in the second photo (with the sharpening arm off to the side), where the body of the angle unit is twisted off the face of the stone so that it remains perpendicular to horizontal.

If you got a dual axis unit, the one I've seen by Floureon only functions in dual-axis mode when the unit is oriented flat (which isn't the way you'd orient it to place it on a sharpening stone), and a +/- 30 degree range from flat. You have to make some special adaptations to actually use it in dual axis mode on a guided sharpening stone.
 
jalapeno said:
Be sure you use it correctly. You might already know this, but if you got a single-axis unit, the angle is only accurate if you keep the body of the unit parallel to earth's gravity. These units are based on micro-machine accelerometers internally, and the displayed angle is based on an internal calculation using the angle the accelerometer makes with earth's gravity. The instructions probably won't tell you this.

In plain english, if you have a wicked edge and you attach it to the stones via its magnets, it will only read the correct angle when the sharpening rod is at the centerline of the vise. Swing the rod either left or right of there, and you have to twist the body of the unit so it's perpendicular to the horizontal.

edit: in the link cbwx34 provided above, you can see this in the second photo (with the sharpening arm off to the side), where the body of the angle unit is twisted off the face of the stone so that it remains perpendicular to horizontal.

If you got a dual axis unit, the one I've seen by Floureon only functions in dual-axis mode when the unit is oriented flat (which isn't the way you'd orient it to place it on a sharpening stone), and a +/- 30 degree range from flat. You have to make some special adaptations to actually use it in dual axis mode on a guided sharpening stone.
Click to expand...
So you can use the angle cube to help but keep in mind you may have to twist the stone so it is parallel to get an accurate reading? That’s good info to know but it makes sense
 
cbwx34 said:
So... how do you explain... that you can set the knife in the clamp, so that, as you approach the belly to tip area, the angle can get smaller?
Click to expand...
Hi,
LOL! :D If I had coffee I'd spit it out, I actually laughed out loud :)
But, something to do with curves? :) I dunno Im sleepy
 
You must log in or register to reply here.
Back
Top