naming and math help needed

[Ken S]

I need help with two things.

First, I would like a better term for the process we have been developing to set bevel angles. "Kenjig" is just a tool which uses the trig. (Incidentally, for the newcomers, I originally named it KS-150, meaning Knife Setting, 150mm length, following the Tormek convention. Sweden thought this name might be confused to imply that it was an actual Tormek product, so I had a forum contest for a new name. Any resemblance between KS and my initials was purely coincidental.    )

"Torig" sounds too much like a British political party. "Trigmek" misses the mark, also. I would like us to coin a word which would indicate the process without scaring away the majority of members and guests who, like me, are somewhat math challenged. (Jan's term "Mr. Euclid" has a nice ring to me.)

The second area where I need help is in expanding the concept to a more general level. I want to include other tools, not just for knives where a 139mm protrusion is convenient.

Looking at the grinding bevel set up as a triangle: one side would be the distance from the top of the universal support to the surface of the grinding wheel. Let's call it D (distance). One side would be the protrusion of the combined jig and blade from the back of the universal support to the grinding wheel. Let's call it P (Protrusion). The third side is actually not a straight line. It is the arc of the grinding wheel as measured from the two points of intersection. Let's call it G (Grinding wheel).

Using our knife set up, the angle formed by P and G is 15°. In Tormekese, this is called the bevel angle. If we increase P or D and keep the bevel angle constant, the increases in the sides should be proportional. As an example, if we have a small carving chisel with a protrusion (P) of 25mm, how would we determine the distance (D)?

I tried unsuccessfully using Dutchman's tables, dividing one side into the other, to determine a factor. Wouldn't it be convenient to multiply P by factor X and calculate D?

If that doesn't work, having a table where the rows represented Distance; the columns represented Bevel Angles; and the intersection numbers represented Protrusion would make set up much more efficient. We would have to factor in grinding wheel diameter changes somehow. Using the TTS-100 or Han-Jig might eliminate the need for multiple tables.

Using the carving chisel as an example, if the Protrusion was set at 25mm by use of a stop block or rule; by using the table, we would match the Protrusion with the desired Bevel Angle and obtain the Distance.

In the ideal, perhaps unrealistically simple world, we would just multiply 25mm by the Distance factor for 15° to get the answer.

We should be able to use this concept with almost any tool. I know where I want to get; I just don't know how to do the math. Any help from the Forum Mathematics Department will be most appreciated.

Thanks.

Ken

[Jan]

Ken, I admire your tireless efforts to generalize and simplify the grinding setup process.   

The explanation of your unsuccessful application of Dutchmen's tables to define parameters for your carving chisel is simple.  Each Tormek jig is to some degree world of its own and has to be considered separately.

It is not possible to expect that a relation between two quantities (e.g. P, D) characterizing Knife jig setting is directly applicable to Square edge jig or some other jig.

From geometrical point of view there are simpler jigs (e.g. Knife jig and Square edge jig) and more complicated jigs e.g. the Gauge jigs. 

You are correct expecting that it is possible to calculate  tables relating selected setting parameters with stone diameter and desired bevel angle which would make set up more efficient. Each jig will have its own table/tables. 

Jan

[Ken S]

Jan

Thanks for your reply. The project may be more involved than I realize, however, I believe the benefits will justify the effort!

Ken

[Herman Trivilino]

Looking at the grinding bevel set up as a triangle: one side would be the distance from the top of the universal support to the surface of the grinding wheel. Let's call it D (distance). One side would be the protrusion of the combined jig and blade from the back of the universal support to the grinding wheel. Let's call it P (Protrusion). The third side is actually not a straight line. It is the arc of the grinding wheel as measured from the two points of intersection. Let's call it G (Grinding wheel).

I would need to see a drawing of this "triangle". I tried to make one, but P and D don't meet to form a corner of the "triangle". Rather, they intersect somewhere inside the Universal Support rod.

[Ken S]

Herman, the end result is setting the Distance and Protrusion, either with a gage block or combination square (or similar tool). I would draw the triangle from the point on the universal support where the stock of the square rests to the point on the wheel where the blade rests. Drawing a line across the grinding wheel, as is used with skews, and then lining it up with the knife edge will determine where the Protrusion side is drawn. The Distance line would be from where the square's stock rests on the universal support to the point where the square's blade intersects the grinding wheel.

Ken

[Herman Trivilino]

Hmmm... I'm having trouble understanding your description, Ken. This is a case where a picture really would be worth a thousand words.

[Ken S]

Good point, Herman. I'll work on some photos.

Ken

[Ken S]

Herman,

Here is my attempt at posting

[Ken S]

Herman,

The first image shows a knife in the jig. The Protrusion is 139mm, as I use with the kenjig.



The second image shows a combination square substituted for the knife and jig. (Sorry the rule is not metric; I don't have a metric blade for my square.) This shows what I want the Protrusion side of the triangle to be. The end result is being measured by the combination square or the line on the kenjig.



The third image shows the combination square being used to measure the Distance. In this case it is 80mm, s per Dutchman's tables. like the Protrusion side, the Distance side of the triangle has an end product of being measured with the combination square or the groove in the kenjig.



These points may not exactly fit orthodox trig, however, they are practical for the use.

Ken

ps to Grepper.......Thanks for your photo bucket help!!!!!!!!

[Ken S]

Jan,

I have been thinking about your comment about the differences in the Tormek jigs. I think the jigs which might benefit from this angle approach fall into two groups:
1) Jigs which are used by being attached through the universal support. Probably the only jigs of this type to pursue are the versions of the square edge jig. Protrusion is the total of jig protrusion and tool protrusion. As the jig protrusion remains constant, we can measure just the tool projection. Tormek pursued this path with the gouge jig and TTS-100.

2) Jigs which are pressed against the back of the universal support. In this case, with the notable exception of the knife jigs, jig protrusion is zero and tool protrusion equals Protrusion. The short tool jig, multitool jig and the knife jigs are this type of jig. As the knife jigs are not attached to the universal support, a combination measurement is easily obtained. Case in point is my 139mm figure.

Essentially, the only difference between the two types of jigs for calculation purposes is that the "through jigs" have a two step protrusion and the "to" jigs have only one step.

I grant that these jigs will not cover every tool, however, they do cover most tools commonly used.

Protrusion and Distance can be obtained by using trig tables. They can also be obtained by conventional setting methods (Anglemaster, black marker, etc). Probably the easiest method for most of us would be to make up a simple file card with the tool, jig and grinding wheel used (including coarse or fine with the SG), and the Distance and protrusion measurements. Once recorded, these measurements could either speed up future setups or be the basis for a kenjig for that tool.

Ken

[Jan]

Yes, Ken, I agree with you. 

Another parameter that distinguishes Tormek jigs is the height of the tool edge above the USB. For the Knife jig it is 6 mm, while for the Square edge jig it is some 25 mm. 



Jan

[Herman Trivilino]

D'(D'+2R)=P'(P'+2R sin ß)

where D'=D-r
and P'=P-r

and r =6 mm, the radius of the Universal Support rod,
and ß is the bevel angle.

And R is the radius of the grindstone (125 mm for a new one with no wear).

[Jan]

D'(D'+2R)=P'(P'+2R sin ß)

where D'=D-r
and P'=P-r

and r =6 mm, the radius of the Universal Support rod,
and ß is the bevel angle.

And R is the radius of the grindstone (125 mm for a new one with no wear).

Herman, thanks for the formula. 

Please did you check whether your formula gives the same results as the Dutchmen tables? Kenjig uses P=139 mm, D=80 mm, R=125 mm and β=15^o.

Jan

P.S.: Your formula will be in compliance with Dutchman tables only when D'=D. After this correction your formula can be converted to the initial Dutchman's equation F0. This formula is approximate.  The approximation concerns the way how we measure the distance D between USB and the grindstone.

Hopefully exact set of Kenjig parameters is following: P=139 mm, D=78,9 67 mm, R=125 mm and  β=15^o  .

[Ken S]

Herman,

I have been working with your formula. Some quiet time when the grandchildren are not with us should produce better understanding. I'll keep you  posted.

Ken

[Herman Trivilino]

P.S.: Your formula will be in compliance with Dutchman tables only when D'=D. After this correction your formula can be converted to the initial Dutchman's equation F0. This formula is approximate.  The approximation concerns the way how we measure the distance D between USB and the grindstone.

Hopefully exact set of Kenjig parameters is following: P=139 mm, D=78,67 mm, R=125 mm and  β=15^o  .

Do you mean the Dutchman tables give approximate figures? Because I'm not aware of any approximations made in the derivation of the formula I posted.