Knife sharpener geometry -- spreadsheet

I have created a spreadsheet to illustrate the geometry I described in my previous post on the subject.  It can be found at: knife geometry.xls. 

Variables to play with are the radius of the arm (actually, the distance from the pivot point to the knife holder), length of the knife and the rotation angle of the knife.  If the radius is changed you will need to figure out the height of the pivot above the blade, to give you the desired bevel angle.

The spreadsheet has some warts -- some of the parameters have to be entered in several places.  To help figure out what goes where, the spreadsheet parameters are as follows:

Arm radius = 18"
Length of knife blade = 8"
Knife is rotated 12.75 degrees.

To determine the error in bevel angle halfway down the blade, just change the value in cell I50.  Right now it is set to show what the error is at the tip of the blade.  Changing it to 4 inches will show what the error is at the halfway point (in cell B46).

FYI, the angle calculations use the dot product of two normalized vectors.  If you take the dot product of two vectors whose magnitude is 1.0, the result is the cosine of the angle between the vectors.  Vectors can be normalized by dividing each component by the magnitude of the vector, which is given by:  sqrt(x^2 + y^2 + z^2), where x, y and z are the components of the vector in 3 dimensional space.

Dot products are very useful beasts, having a wide range of applications, from calculating the Fourier Transform to computer generated graphics.