Re: [CAD_CAM_EDM_DRO] Math for constant speed ellipse

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@...>