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Proof needed to show that an angle remains constant along a line

  1. Aug 26, 2010 #1
    This is my problem:

    On my knife sharpener, there is a Clamp that holds the blade vertically, edge up. At the base of the clamp and perpendicular to the blade, there is a Base Rod with a Pivot Point that slides along the Base Rod to establish an angle relative to the blade. The third side of the triangle is created by the sharpening media sliding on a Guide Rod, anchored at the Pivot Point. T triangle could be described as follows: Side A = height of the Clamp + height of blade above the clamp. Side B = Distance along Base Rod between the Pivot Point and Side A. We can calculate the angle AC knowing that angle AB is a right angle and knowing the length of Side A and Side B. Where I run into problems is proving that the angle of the sharpening media will remain constant along the length of the blade. The diagrams below help illustrate the issue.

    [PLAIN][PLAIN]http://www.wickededgeusa.com/graphics/Constant [Broken][/URL][/URL] Angle- pt 1.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/graphics/Constant [Broken][/URL][/URL] Angle- pt 2.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/graphics/Constant [Broken][/URL][/URL] Angle- pt 3.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/graphics/Constant [Broken][/URL][/URL] Angle- pt 4.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/graphics/Constant [Broken][/URL][/URL] Angle- pt 5.png[/PLAIN] [Broken]

    In the diagrams, the Clamp is 6" and the distance of the Pivot Point from the clamp is 6". The height of the knife above the clamp is 1". I can see that the sharpening medium stays in the same plane relative to the knife, I just can't remember a way to prove it.

    Any help would be most appreciated.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 26, 2010 #2
    Another couple of pictures to illustrate the problem:

    [PLAIN]http://www.wickededgeusa.com/photos/angle-change-at-0-inches-sm.jpg [Broken]
    [PLAIN]http://www.wickededgeusa.com/photos/angle-change-at-5-inches-sm.jpg [Broken]

    If it helps to see the sharpener in action, you can see it here: http://www.wickededgeusa.com" [Broken]
    ***I'm not trying to promote the product just supplying the link if seeing the sharpener will help with the math.
     
    Last edited by a moderator: May 4, 2017
  4. Sep 2, 2010 #3
    Since there are no replies yet, I'm thinking of offering a prize. Any interest?
     
  5. Sep 2, 2010 #4

    Office_Shredder

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    It might help for clarity's sake if you labeled your diagram with what side A is, what the pivot point is etc. It's not really clear to me what it is you're trying to solve (perhaps because of my unfamiliarity with knife sharpeners)
     
  6. Sep 2, 2010 #5

    Chronos

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    The 40.601 degree angle with identical (6.000) leg lengths has me baffled.
     
  7. Sep 2, 2010 #6
    Thank you, sorry for the lack of clarity. I've been out of school and away from maths so long that I'm sure my question seems a mess. Here are a few more images, labeled a little more clearly.

    [PLAIN][PLAIN]http://www.wickededgeusa.com/blog/images/constant [Broken][/URL][/URL] angle 1.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/blog/images/constant [Broken][/URL][/URL] angle 2.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/blog/images/constant [Broken][/URL][/URL] angle 5.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/blog/images/constant [Broken][/URL][/URL] angle 4.png[/PLAIN] [Broken]
    [PLAIN][PLAIN]http://www.wickededgeusa.com/blog/images/constant [Broken][/URL][/URL] angle 3.png[/PLAIN] [Broken]

    The stone is shown moving in relation to the blade, the plane staying constant, keeping the sharpening angle constant.
     
    Last edited by a moderator: May 4, 2017
  8. Sep 2, 2010 #7
    That was 6" for the height of the clamp + 1" for the height of the knife, making the overall length of the side 7".

    Again, sorry for the messy first posting. I had forgotten to pull out the dimensions since they were arbitrary.
     
  9. Jun 24, 2012 #8
    Simple. The arc described by your "guide rod" lies in a plane. The "pivot point" lies in that plane and the straight line, which in this case is the edge of your knife blade, lies in that plane as well. Since planes are flat, at least in Newtonian physics they are, last time I checked, the angle between the blade and the plane must remain constant. I hope you are now unbaffled!
     
  10. Jun 24, 2012 #9

    haruspex

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    Where does the OP say the edge of the knife is straight? Isn't that exactly the problem? Most knives have curved edges. Unfortunately I can't seem to view the diagrams, but the only way I can imagine that the sharpener could maintain a constant angle to the plane of the blade is if it has some fancy device for detecting the curve of the knife and adjusting the distance to the pivot accordingly. And I very much doubt it has that.
    Rather, I should think it depends on the fact that the distance from pivot to knife edge is large compared with the variation in blade height, so although the angle changes it won't be by much.
     
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