Equation of Line Closest to Three Arcs

[darrennewell]

If I have three arcs of a known position and radius, how do I find the equation of the line closest to these arcs?

Any help would be much appreciated.

Thank you very much.

EDIT:

I apologise for not being clearer in stating the problem. This problem is based on Mohr's circle: a theory widely used in engineering. Ideally if a material is tested for stress and strain under different conditions you could generate three (or as many as you wanted) arcs and fit a line that would be tangential to all three arcs. However, this is only a theory and when you actually test materials the line is not tangential to all three arcs. So the aim is to fit a line that is "tangentially" as close as possible to the three arcs.

The line may pass either side of the arc, so it's the absolute value that's important. The arcs (semi-circles) are located on the x-axis (y=0) in this case, but that shouldn't affect the true solution.

Hope that helps.

 

[Deleted member 4993]

If I have three arcs of a known position and radius, how do I find the equation of the line closest to these arcs?

Any help would be much appreciated.

Thank you very much.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[pka]

If I have three arcs of a known position and radius, how do I find the equation of the line closest to these arcs? Any help would be much appreciated.

I think that you need to carefully reword this question.
Reason: any line that intersects all three arcs meets that requirement. If a line intersects a set of points, its distance to that set is zero.

 

[pka]

You're not very clear, Darren.
Are the arcs always semi-circles?
Do they always lie on a horizontal line?
If the line crosses the arc (creates a chord), is that a negative
"distance", and how in heck is such a distance calculated?

Come on Dennis, distance is a metric measure. Therefore it is never negative.

 

[darrennewell]

Clarification

Sorry that I wasn't clear in stating the problem. If you have a look at the image that I've uploaded, I'm trying to find the minimum value of the summation of L1,L2,L3 (these are absolute values).

So the equation of the line, may or may not pass through the arcs (which are semi-circles).

As background, these are Mohr circles. Theoretically, a line would be tangential to all three circles, but my circles have been obtained from testing which I need to find the line of best fit.

I hope that clarifies the problem.

Thanks for your time.