If you place a plate of thickness, t, between one jaw of a 3-jaw chuck and now bore a hole, what is the offset of that hole from the center of the original rod (diameter, D).
One source says it is 2/3 of t. This might be = 1 / (1 + cos 60 deg) but I failed to derive this with trig.
Anyone know how to derive this mathematically? Anyone know if this is true?
thanks
-- - - - - - - - - - - - - - - - - Bill Graves RKBA! snipped-for-privacy@ix.netcom.com
The formula is a good bit more complicated than that. Take a look at the ECCENT.ZIP archive on my website for a program that implements the correct formula.
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things
Thanks for the posting. Years ago my boss and I tried to figure out a formula to figure out how much the offset would be for a certain sized shim in a three jaw chuck. Neither of us being math whizes didn't deter us. Nevertheless we never did figure out and exact way to determine the offset. I made up a chart from actual measurements but I've been bugged for a long time about this problem. Cheers, Eric
It's a lovely exercise in trigonometry...
For the benefit of folks who want the actual formula:
w = width of chuck jaws d = diameter of workpiece e = required eccentric offset r = d/2 root3 = sqrt(3) p = required packing thickness
if (w > root3*e)
{p=1.5*e}
else
{p=1.5*e-r+0.5*sqrt(4*r*r-3*e*e+2*e*w*root3-w*w)}
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things
A really excellent set of useful utilities!
One question on the ECCENT program.
This needs accurate knowledge of the width of w - the little flat part at the end of the jaw that contacts the workpiece. This is fiendishly difficult to directly measure accurately. Your program has an elegant way of avoiding this problem by making the spacer in the form of a slotted tube.
However it's not always convenient to find or fabricate a suitable tube. I think that an alternative possibility is to simply find the largest size drill rod that will enter the fully closed jaws of the three jaw chuck. The effective jaw width w would then be accurately defined by the sides of the equilateral triangle that circumscribes that drill rod size.
Is this a reasonable approach and could it be incorporated in your program?
Jim
I hadn't thought of that technique for determining 'w', but it makes sense.
If:
d = diameter of largest rod that will enter closed jaws
then:
w = d*sqrt(3)
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things
Thanks, Marv. although I was not able to derive a formula - I see that I had completely missed the bit about the width of the chuck jaws. This gets interesting as I assume the compensation is because the jaws are no longer tangent to the workpiece. In my case, the jaws have a slight curvature!
I will take a look at the C source code you so nicely provided and see if I can follow the math. thanks a lot for your work.
-- - - - - - - - - - - - - - - - - Bill Graves RKBA! snipped-for-privacy@ix.netcom.com
The source code isn't going to help you much since all it does is implement the final, very messy equation.
I still have my derivation of the equation and will send it along to you via email after I scan it.
If your email address is false or you don't hear from me, drop me an email at mklotz alum mit edu.
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things
It's because the *centers* of the "other two" jaws are no longer the points of tangency to the workpiece.
Depending on how precise your offset needs to be, it may be safe to ignore the curvature.
-jc-
The second case seems to involve the edges of two of the chuck jaws digging into the workpiece. That would render the formula inaccurate: if the edges are blunted they won't be where calculated, and if they're sharp they'll dig in, so the workpiece won't be where calculated. It might also damage the workpiece, although in some contexts that would be completely acceptable.
Making eccentrics by shimming on a three jaw is at best a bodge. If one wants to do it correctly, a four jaw is the tool of choice. The program is aimed at newbies who still haven't equipped their lathes properly.
If they must use a three jaw, the technique of using a slotted tube is far more accurate and safer. A program for this technique is included in the archive that contains the program described above.
Regards, Marv
Marv, I must disagree about the bodge. If a small offset, say .030", is needed then shimming a three jaw is much faster. In fact I'd say up about .125" offste is best accomplished with a three jaw. Of course, I'm talking about adjustable three jaw chucks, where it is possible to indicate the part. Sort of a 4 jaw, but much faster. ERS
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