Re: [CAD_CAM_EDM_DRO] Re: Math for constant speed ellipse

> 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.

If I understand your equation, f = d theta / dt. Since I'm interested in
theta as a function of t, this is a D.E. similar to the one I found; we're
back to square one again.

I tried finding a power series expansion of the D.E., but I can't find a way
to get the D.E. into a suitable form.

> 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?

All of these are variables; I want to design a controller that can handle
any reasonable variation.

> Regards,
> Jack C. Cain

Todd Fleming
flemingcnc.com