Knife sharpening fixture

This entry contains some preliminary work I've done to build a knife sharpening fixture.  No photos as yet, but there probably will be some in a future post.  This time I'm just outlining the geometry of the fixture, variations in the bevel angle along the blade due to the geometry, and approaches to minimize the variations.

Below is a simple figure showing the basic fixture from the side:

 

The vertical mast has a pivot (the circle) whose height can be adjusted.  The line passing through the pivot depicts a rod, whose opposite end has a sharpening stone attached to it (the green line).  The knife is shown in magenta.  Hardware for holding the knife is not shown.  The whole thing is assembled on a base, shown by the thick horizontal black line.

The basic idea is as follows.  The pivot is above the plane of the knife by a distance dictated by the desired bevel angle and distance between the mast and knife.  We can calculate the bevel angle using this:  tan(theta) = H/L, where theta is the desired angle, H is the height of the pivot above the knife, and L is the distance from the mast to the edge of the knife.  If we know theta and L, then H = L*tan(theta).  Caution:  many spreadsheets assume radians, not degrees, are the argument to trig functions.  To convert degrees to radians, remember that 2*pi radians = 360 degrees.  (2*pi/360) * degrees gives you the radians.

There is an interesting aspect of this.  My online searching revealed that most everyone seems to be building fixtures that create a specific half-angle -- not the full angle between the two sides of the bevel.  So, if you're sharpening a knife to a "20 degree bevel", the angle between the two sides of the bevel is twice that -- 40 degrees.  Not that it matters, it's just different relative to the usage found in general machining practice.

Anyway, back to the fixture.  While it might seem to ensure you are sharpening your knife to a specific bevel, that is incorrect.  Take a look at the diagram below.

 The diagram shows the fixture looking down from the top.  The magenta rectangle is the knife and the thin black lines show the position of the rod (plus sharpening stone) over two positions on the knife.  Observation tells us that the bottom line is the shortest line and the top line is longer.  The difference depends on the size of the knife.  This variation in distance causes a variation in the effective bevel angle that will be ground into the knife.  How much of a difference are we talking about here?

Let's do some calculations based on a fixture design I found on the web.  In that design, the shortest distance was set to 10 inches.  Probably to keep the fixture small and easily transported.  If we want a 20 degree bevel, trig tells us that the pivot point must be 3.65 inches above the knife blade.  If we are sharpening an 8" chef's knife, the tip of the knife is further away from the pivot, and as a result the bevel angle is reduced to 15.9 degrees!  Ouch.

How can we improve this situation?  The easiest approach is to increase the distance between the pivot and knife.  Let's increase the distance to 18 inches.  We have to raise the pivot point to 6.55 inches to get a bevel angle of 20 degrees.  This change reduces the variation in bevel angle to 1.6 degrees.

But we can do better than this if we want.  Since the change in bevel angle is due to the increased distance, let's rotate the tip of the knife toward the pivot point to reduce the distance.  It turns out that a rotation of 12.8 degrees will reduce the error to close to zero.  Nice, huh?  Not so fast.  What about the bevel angle at the midpoint of the knife?  With this rotation, the error is .4 degrees.  Still, not too bad.  Zero rotation gives us a MINUS error of about the same magnitude, so that's a wash.

Figuring out the optimum rotation angle of the knife may seem like a mysterious process.  But it's not, and actually is easy to set up.  In the case of our 18"-long fixture, let's use a very large compass to draw a circle around the support mast for the pivot.  The circle will have an 18" radius.  Now, loosely install your knife in the holder and rotate the tip so it just intersects the 18" circle you just drew.  That's the angle you need, because the circle denotes a constant 18" distance from the pivot!  Tighten the holder down and start sharpening, with the assurance that the variation in your bevel angle along the length of your 8" knife is no more than .4 degrees.  Shorter knives will have less variation.  If you are sharpening 10-inchers or longer, maybe you should think about an even bigger fixture, maybe with a baseline of 20 inches or more.  Even so, it still will have a footprint less than 2 feet deep.

The downside of a setup that requires you to rotate the knife has some design complications you may not want to bother with.  For one, you probably need to have a knife holder than can rotate, too.  Then be easily locked into position without engaging in an excessively-complicated procedure.  And for longer blades you probably want some sort of support partway down the blade to keep the blade from flexing (or popping the knife out of the holder).  But to accommodate different blade lengths, the support has to be movable -- the knife rotation angle will change.  Or you will need to fabricate custom holders for each size of knife you have.  Mmm, more tradeoffs.  But that's the fun of design -- addressing problems like this in as elegant a manner as practical.  No, I didn't say "as possible" -- that's not engineering.  The art and fun of engineering is finding the balance between performance and practicality.