naming and math help needed

[Jan]

Thanks Ken, you have taught me a new word "a twofer".  I think a similar idiom in my language may be "to kill two flies with one slap". 

In my opinion a detailed understanding how a jig works geometrically is a prerequisite for musing about its combination with the TTS-100.

In this topic you can hopefully learn something new about the Knife jig which is a necessary condition for understanding how it can be set using the modified TTS-100. To understand how the TTS-100 works is a separate issue.

My accent is always on concept because the actual trigonometrical calculations are only an exercise of secondary school math. It is a craft that is not particularly complicated and can be executed by your children or grandchildren if you've already forgotten it. 

In some instances of course it is highly desirable when everything can be accomplished in one mind.  I'm thinking about this beautiful but geometrically complicated jig.



Jan

[Ken S]

Jan,

I enjoy your critical thinking; your thoughts help me focus.

I realize some of my earlier thoughts were naive. There is no magic bullet where we can multiply a measurement by X and get the universal right number. I do not think that this discounts the whole process. Let us put together a hypothetical example:

We may have one hundred edges to sharpen. (for easy percentages) Fifty are knives; twenty are chisels; ten are plane blades; twenty are misc. woodworking, carving and turning tools. Of the fifty knives, perhaps thirty five fit easily in the Tormek knife jigs and kenjig. Of the fifteen remaining knives, half are too small, some are too thick or not shaped well for the jigs, and one is a machete.

Of our hundred edges to be sharpened, half to two thirds may be readily sharpened using either the kenjig or the TTS-100 and stop blocks. The remaining edges are more practically set up using the Anglemaster or marker with trial and error. Of this group, perhaps a majority could be easily set for future resharpenings by making careful measurements and notes.

The initial sharpening will involve the full set up time for the latter group of edges. The first samples of the first group may involve minor set up time. Let us make a wild guess that the total set up time is reduced by half using math and tools like the kenjig, Han-Jig, TTS-100, and stop blocks.

The second and following sharpenings will be even more efficient. Not only will the job be completed in less time, the results will be more consistent. We must recognize the reality that not all edges or jigs will fall into this happy category.  Hopefully the number which require more than a carefully noted initial sharpening will be small.

I do not seek perfection, merely substantial improvement based on both math and simple jigs.

Ken

[Jan]

Yes Ken, I agree with you. 

For me it is very important to have an alternative way how to set an edge angle. You have mentioned Kenjig and Han-Jig (based on TTS-100 setter modified for knifes).

I would like to add my bi-directional horizontal platform and my modified Starrett square http://forum.tormek.com/index.php?topic=2879.msg15575#msg15575
in combination with the Excel spread sheet for calculating the wheel-support distance. https://www.dropbox.com/s/ypbtaxgycgoyls0/KENJIG_wheel_support_distance_1.xlsb?dl=1

With such portfolio I am sure it is possible to set the edge angle for almost every knife. 

Jan

[Jan]

I need help with two things.

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?

Ken

Ken, I went back to your thoughts concerning proportionality between protrusion P and distance D when the bevel angle should remain constant.

If we consider one particular jig, e.g. the knife jig, then such coefficients of proportionality can really be found.

For example consider your kenjig for parameters P=139 mm, D=79 mm and bevel angle 15^o. Stone radius R=125 mm. When you have a smaller knife with protrusion P=134 mm you will have to set D=75 mm to keep the bevel angle 15^o. This means that some 80% of the decrease in protrusion is equal to the decrease in distance D between the USB and the grindstone. I hope this was your point. 

Jan

[Ken S]

Thank you, Jan. That is just what I am looking for!

If I understand you correctly,

Distance new = Distance old - [(Protrusion old - Protrusion new) x .8]

D2 = D1 - [(P1-P2) x.8]

Is this correct?

Ken

[Jan]

Yes, Ken, your formula is correct. Congrats! Your intuition was right. 

The factor 0.8 was stated as a rule of thumb. For grindstone with diameter 250 mm the factor is 0.84 and for grindstone with diameter 200 mm the factor is 0.88.

Please keep in mind that this factor it is valid only for the knife jig.

Please be so kind and test it experimentally. I have derived it as desktop exercise. 

Jan

[Ken S]

Jan,

Your patient math logic has helped me see that there is no magic X to interject in all Tormek math. If these equations help us set up quickly back and forth with different knives within acceptable or better tolerances, that is a good step forward.

I did not mean to overlook your adapted combination square tool. The English idiom "a senior moment" fits. Incidentally, I just acquired 150 and 300 mm blades for my combination squares. Less chance of conversion errors.

Ken

[Jan]

Ken, you are welcome! 

Please keep in mind that even with the more accurate figure for the proportionality factor the formula remains a rule of thumb. It means it is not strictly accurate and reliable for every situation. It is an easily applicable procedure for correcting the stone – USB distance when the protrusion is not equal to 139 mm.

When you need exact figures you can use my Excel spread sheet for calculating the wheel-support distance. https://www.dropbox.com/s/ypbtaxgycgoyls0/KENJIG_wheel_support_distance_1.xlsb?dl=1

An adapted combination square tool is very good for various settings experiments which are beyond the kenjig range, e.g. protrusion 190 mm for cleaver sharpening requires wheel-support distance 123 mm for 15^o bevel angle.
http://forum.tormek.com/index.php?topic=2879.msg15569#msg15569
Both the 12 mm Al sleeve and the Al contact block can be made of hard wood or suitable plastic also.

Jan

[Ken S]

Jan,

When I was much younger, I was a student and then an Assistant Watch Officer at the Hurricane Island Outward Bound School in Maine. A major part of the twenty six day program involved being in in thirty foot (7 meter) pulling boats for several days at a time. These were similar to lifeboats or the small boats used by whaling vessels. To measure the speed of the boat, we would drop a chip of wood next to the bow of the boat and count the seconds needed for it to pass the stern. Our friend, Mr. Euclid, would not have been impressed with the accuracy of this method, however, it was adequate for our purpose.

Our "rule of thumb" knife bevel figures strike me as also being adequate for most of our purposes. It is comforting to have more precise tools available for more critical work. We can also strive to tighten the tolerances of the rules of thumb.

Incidentally, the machinist Leroy Starrett hired to make his original combination squares thought the idea was worthless. Fortunately, Starrett was determined and today we are still using his very useful tool.

Ken

[Jan]

Ken, in this country we use similar procedure to calculate how far away is a thunderstorm centre from us. We count the seconds needed to hear the thunder after the lightning flashed through the sky. Then we divide the number of seconds by three and say that the thunder struck so many kilometres away from us. 

For you living with imperial units this rule of thumb should be modified to miles. You would have to divide the number of seconds by five and say that the thunder struck so many miles away.

The reasoning behind this rule of thumb is that sound needs three seconds to travel a distance of 1 km or 5 seconds to travel the distance of 1 mile. 

Jan

[Jan]

Ken,
in my previous post I have issued a warning that each Tormek jig is a world of its own. Nevertheless the knife jig and the square edge jig belong in my thinking to the same category, those two jigs differ in edge height above the USB. (The height is measured when the tool axis is horizontal.)

I have preliminarily addressed the question whether the proportionality factor concept will work also for the Square edge jig and to my large surprise the answer was positive. 

If you have a grindstone with 250 mm diameter and a tool protruding 50 mm from square edge jig than you have to set the stone - USB distance 32 mm for the edge angle 25^o. In this case the proportionality factor is again 0.84.
An average value of the proportionality factor X for protrusions between 50 and 75 mm is 0.86.

In the case of the square edge jig the rule of thumb is less accurate than in the knife jig case, but in principle works also. 

Jan