Re: [CAD_CAM_EDM_DRO] Math for constant speed ellipse

Yo Les;

It sounds like what you need is some sort of dedicated add on hardware solution,
that does only math. Failing that, if you have a spare PC for a Linux/Unix box,
I would recommend looking into, "bc", or it's RPN brother program, (can't recall
it'a name at the moment). It's basically a calculator language that can run in
it's own shell environment, or independently, does macros, matrix math, floating
point to N decimal places, and has a number of interesting features. You can
script it from the outside, piping numbers to/from it, redirect it's output, and
is relatively quick. If you get one of the old versions that only does single
letter, rather than named variables, I can slide you the latest sources.

Bill

On Sun Dec 29 14:59:35 2002, Les Watts, <leswatts@...> wrote:

>Bill,
>
>The way I see it it is a question for efficient computations in cam
>programs. I note that some of my programs take a very long time
>to calculate things like spiral pockets within elliptical boundaries.
>
>That is probably because of the numerical methods used to calculate the
>path. Closed form solutions are almost always much faster if they exist,
>but I cannot find any evidence that such a thing has been discovered in
>this case. I sure can't find one. Where is Issac Newton when you need him?
>That does not mean one does not exist, but explains perhaps why
>all cam programs I have seen seem slow to do this and similar tasks.
>
>When it comes to a machine real time controller I do not see it as an issue.
>One of my most popular carved plaques is an elliptical shape and
>EMC carves it quickly, smoothly , and accurately in real time at constant
>speed.
>Does that mean it has a particularly computationally efficient algorithm?
>Actually no. It's just that real time cutting of materials is out
>of necessity fairly slow. Even at 2 + inches per second cutting
>speed there is so much time available that an old obsolete
>PC or a cheap microcontroller can just loaf along.... there is
>all the time in the world to crunch even polygon approximations.
>In EMC it is a cubic spline calculation actually.
>In my case an old 200 MHz pentium updates and corrects the
>motion every 1/1000 of an inch at 2 inches per second-
>far better than I really need.
>
>I think a modern multi-gigaHertz PC could control a whole room full of
>3 axis cnc machines simultaneously in real time even using mostly
>floating point calculations for iterative solutions.
>
>But I don't want to wait that long in the office doing cam to generate the
>tool
>path. I have had circularly interpolated elliptical tool paths take several
>minutes to
>crunch. Since I am not slowed down there by the mechanics of actually
>physically cutting stuff I would prefer to click "ok" and bing- it's done
>in the blink of an eye. A closed form solution could do this, if it exists.
>But there is no "cookbook" recipe like variation of parameters to solve
>nonlinear differential equations.
>
>It's kind of neat in that it gives one a tiny bit of insight in the lifetime
>of financial ruin, family, and political problems that Kepler went through
>just to figure out the elliptical motion of planets. We have it easier
>though...
>we have calculus!
>
>Les
>
>Leslie Watts
>L M Watts Furniture
>Tiger, Georgia USA
>http://www.alltel.net/~leswatts/wattsfurniturewp.html
>engineering page:
>http://www.alltel.net/~leswatts/shop.html
>Surplus cnc for sale:
>http://www.alltel.net/~leswatts/forsale.html
>----- Original Message -----
>From: "Bill Vance" <ccq@...>
>
>
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