Focal point on Parabola

[[Me...]]

Hello, our facility will soon be measuring reflector dishes and I was attempting to determine the process for the output of the focal point. We will be measuring the dish with a series of points from engineering, then best fitting these points. From that result, a value for this point is needed. Has anyone out there had experience with this process? Our CMM is an Accura, with Calypso, 5.4. Thanks.

[[Cl...]]

The dish is concave I take it? Sounds like space points will work for
you. Are you looking for the point at which all the points converge?

[[Pa...]]

no previous experience other than telescope mirror grinding, I'll take stab at it. Scan say six arcs that pass through each engineering point as shown in the diagram. Then determine the tangent line to each arc at that nominal point. The perpendicular to that tangent should point to the focus of the parabola in 2D space. Now you will have to combine all those lines to find the focus in 3D space as well as doing a "best fit" focus with those lines.
3D wise, I was thinking that you could combine each set of six arcs into a theoretical sphere and use the radii of the spheres, but the arcs do not form a true sphere; I'd stick with the perpendiculars to the tangents of the arcs at the nominal points. What accuracy are you trying to achieve? I'm assuming you are not working to the millionths of an inch required in telescope mirrors, but you may still find the small arc method above does not give you the accuracy you require.
PS - Is it possible to coat the dish with a reflective surface and do the measurement optically?

parabola measurement.pdf

[[An...]]

Mission impossible!

[[Aa...]]

The math isn't quite that simple. The line from each point to the focus is off of the tangent-perpendicular by the same angle that the tangent-perpendicular is off of the normal vector of the parabola.

My question is, in your situation, is the normal vector of the parabola known, or do you have to determine that, too? If it's already known, I would say it's not impossible to achieve (to some degree of accuracy, depending on how true-to-form the parabola is) through constructions. But it's not going to be straightforward, and will involve the use of some trig formulas.

Calypso won't let you determine a 3D line using only one point and constraining the normal vector of the line. (for some unknown reason), so you'll have to employ formulas to create a theoretical second point for each 3D line based on the known angle.

[[Aa...]]

I'm not sure, though, how effective scanning small arcs to determine the normal at each point would be.

[[Da...]]

Engineering should decide how much deviation is allowable, then a series of 3d curves and a profile tolerance would be a viable option. I'm surprised that no one offers a Parabola Pack. It's common enough.

[[An...]]

Here some thoughts in theory.
In reality the accuracy would be very low.

Parabola_Focal_point_1.pdf

[[An...]]

In addition to what was posted here.
See attached.

Parabola_and_Focal_Point_1.xlsx

[[Cl...]]

Hey if I don't know what the heck I'm talking about, let me know. Why couldn't you (if you have the model) pick a bunch of space-points on the surface, recall each point into a 3d line. Enter the vector values, and XYZ origins of the space -points into each 3d line, give it a depth. Intersect all these lines. Would that not give you the focal point?

[[Da...]]

Finding the focal point is really a reverse engineering project. If you think about it, a parabola is a constantly changing radius. Our Cmms can't really check a small section of radius with very much accuracy. If I gave you a large radius that only had say 5 degrees of arc and I asked you to find the center of that radius we couldn't do a very good job of it, could we? So with a parabola we have a series of different radii with a width of......ZERO degrees ! What are the chances of us getting ONE right ? But the parabola has a multitude of radii.

Typically when I run into this type of problem I resort to checking how far from perfect am I. Deviation from model is the only way I can see to check this part. You could tolerance the curve as a complete surface or apply zone tolerances . If you MUST produce a focal point value then maybe out put your point data to solidworks and see if it can fit a focal point to the points. That's what SW is for, it's a cad program, Calypso isn't.

That of course is only my opinion. I haven't ever tried to get a focal point.

[[Da...]]

Bump. (I'm missing the "bump topic button")
James, what was your approach at the end?