What you are looking for is a function that can smoothly transform from a
line to an arc while always passing through to given points?   An eclipse
could do that as its eccentricity changes.  The problem is the amount of
computation required.

Cheaper to draw both the final and starting lines and take a weighted
average.  Keep moving how much weight to give to each line.  Still a lot of
computation but it's easier and after all we do all have computers.

But what most do is cut at the final line in increasing waterline depth,
then make a final finishing cut to remove the last .0005  That is what most
CAM software would do.

On Sun, Sep 18, 2016 at 1:32 PM, Gene Heskett <ghesk...@shentel.net> wrote:

> Greetings all;
> I am trying to carve the curve/arc in the toolpost base that replaces the
> bad compound in this Sheldon.  Currently mounted about 3/4" off center
> so I am basically cutting away anything on the front of the base that a
> workpiece could hit. I did this in 1/4 size, for TLM, and that, plus the
> tapered gibs almost make TLM a decent but smallish lathe. Any remaining
> tendency to chatter seems to be in the flexing of the spindle itself.
> My code at the instant starts out with a huge radii in order to start
> with a light enough cut TLM can power thru it. The start and end points
> are fixed, and this of course is hard on the tool insert as it dulls and
> starts skidding before it starts cutting at both ends.  Next pass
> reduces the radii, but I cannot get a straight line increase in the
> belly of the curve, which is about a 60 degree arc section.
> Is there a math function that would give me a uniform increase in the
> belly of the center of the arc?, which I am now convinced was a error in
> my concept of how to do it.
> So, should I just give up and use a fixed radii curve, but move its xz
> anchor radii point? That would get me a constant depth of cut, and would
> likely be easier on the tool insert too. I haven't a clue whats in this
> cast, intended for large car wheel hubs, but its tough, and abrasive
> stuff. You could call it found iron I guess.
> H&K casting where I got it, probably considers that proprietary info
> since its a contract that specifies the alloy's ingredients.
> I think the reason I didn't originally was that I was running out of out
> x motion to use a fixed offset for cutting the starter angle.
> What say you folks, how would you do it? Keeping in mind TLM cannot pull
> more that about a .4mm cut at this nearly 4" working diameter, at about
> 150 rpms.
> I need to take about 1/4" off the top of this yet, so while the "hive
> mind" is cogitating, I'll go do that, with a nominal 2 thou dish in the
> center so that big Phase-II toolpost is sitting on its outside corners
> and much more capable of resisting turning forces in the middle of a
> boring bar job.  I did a 1 thou dish on the smaller post I made for TLM
> and that little QC holder hasn't moved on the post since.
> Thanks for any advice everybody.
> Cheers, Gene Heskett
> --
> "There are four boxes to be used in defense of liberty:
>  soap, ballot, jury, and ammo. Please use in that order."
> -Ed Howdershelt (Author)
> Genes Web page <http://geneslinuxbox.net:6309/gene>
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Chris Albertson
Redondo Beach, California
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