Tool Path Equation 2

[sreid]

This is really a math question but I don't know where else to ask it.

I need the equation (if there is one)of the curve for the path of the center of a circle which is rolling around an ellipse. Any suggestions for math forums would also be appreciated.

 

[EnglishMuffin]

zekeman : Oh - I didn't say there was anything wrong with a parametric equation - its just that a parametric equation seemed so obvious that sreid's "if there is one" suggested to me that he was looking for an explicit solution. It's still not clear what he wants it for - if its for machining then the parametric equation would be OK, but as jbel and myself have suggested, just about any decent NC software can do this anyway.

 

[zekeman]

english muffin,

Point well taken.
I do think some of these problems are real engineering situations and others are purely academic and the author should indicate as such so that people like you can address the problem properly.

 

[Kapitan]

Agreed, far too often we are not told the full story by the author or left with cybersilence, or both.

Whether or not there is any NC machining involved here I don't know and there is no shortage of CAD and NC programming packages to define geometry, but it is surely better to have some understanding of what's happening. It's very easy to just be an operator of such systems and not much more.

If a cutter is inside the ellipse, then an immediate and exact value of it's largest radius can be found ;

Minimum radius of Ellipse on major axis,
Rmin = B^2 / A
and if needed, the other case,
Rmax = A^2 / B

 

[nbucska]

If you want to calculate it, you don't need the equation:
If you have a computer, you can solve a problem many ways
even by trial and error.

Else you can blow the result( for fix numbers ) into
a PROM or you can add a small computer module just to
calculate it. See jkmicro or bagotronics ( <

http://www....com>

of course ) both make lowcost PC compatible singleboard computer cards.

<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032

 

[sreid]

I'm happy to see that this question peaked peoples interest. I did find a really elegant solution at Math World for Parallel Curves

http://mathworld.wolfram.com/ParallelCurves.html

The reason for the question is that we machine a lot of ellipse sections and we create our own tool path code. Clearly as others have suggested it's not hard to calculate the required tool center but they are kind of klunky. It's usually nice to be able to plug a number into an equation and get and answer.