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

[clayallison]

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.

http://www.wickededgeusa.com/graphics/Constant Angle- pt 1.png
http://www.wickededgeusa.com/graphics/Constant Angle- pt 2.png
http://www.wickededgeusa.com/graphics/Constant Angle- pt 3.png
http://www.wickededgeusa.com/graphics/Constant Angle- pt 4.png
http://www.wickededgeusa.com/graphics/Constant Angle- pt 5.png

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.

[clayallison]

Another couple of pictures to illustrate the problem:

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

If it helps to see the sharpener in action, you can see it here: Wicked Edge (http://www.wickededgeusa.com)
***I'm not trying to promote the product just supplying the link if seeing the sharpener will help with the math.

[clayallison]

Since there are no replies yet, I'm thinking of offering a prize. Any interest?

[Office_Shredder]

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)

[Chronos]

The 40.601 degree angle with identical (6.000) leg lengths has me baffled.

[clayallison]

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)

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.

http://www.wickededgeusa.com/blog/images/constant angle 1.png
http://www.wickededgeusa.com/blog/images/constant angle 2.png
http://www.wickededgeusa.com/blog/images/constant angle 5.png
http://www.wickededgeusa.com/blog/images/constant angle 4.png
http://www.wickededgeusa.com/blog/images/constant angle 3.png

The stone is shown moving in relation to the blade, the plane staying constant, keeping the sharpening angle constant.

[clayallison]

The 40.601 degree angle with identical (6.000) leg lengths has me baffled.

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.