Re: Math for constant speed ellipse

--- In CAD_CAM_EDM_DRO@yahoogroups.com, "Todd Fleming" <todd@f...>
wrote:

> I was trying to figure out how to machine an ellipse at constant

speed when

> I ran into a differential equation that I can't solve. Is there

anyone with

> a nice symbolic math package that's willing to try this eq? I

posted an

> image of the equation here:
>
> http://www.flemingcnc.com/Papers/help_de.png
>
> Thanks!
>
> Todd Fleming
> flemingcnc.com

Dear Todd:

Your request is an interesting one. This afternoon I made an ellipse
on my CNC "just for the heck of it". It came out well but the
tangential speeds were related to the height (2) and width (10). I
started with a circle and scaled down the outout from the Y
interpolator.

In considering what was going on, I consluded that if one were to
scale the clock frequency according to:

f = _____________fo_____________________
SQR((COS theta)^2 + (SIN theta/R)^2)

This will result in constant instantaneous velocity. Theta is the
angle which an equivalent circle would have (height = width), f is
the new clock frequency, R is the ratio of Width to Height.

I haven't tried the frequency portion yet so I can't prove it OK, but
the numbers on paper work out.

I would be interested in details of your requirement. What speed
will you run, what resolution, what ratio Width to Height, what is
your increment of motion?

Regards,
Jack C. Cain