B-spline / NURBS to model linear motion and generate a cam

[bos10]

I am building a C#-based application that amongst other things enables the user to:
1. model linear motion via a 2D curve: time (x axis) / position (y axis)
2. simulate the linear motion
3. generate a cam profile given that represents the above curve
4. export the cam profile to a CAD/CAM program so that it can be CNC machined

I can draw the cam profile by converting the curve to polar coordinates and generating a polygon. It looks fine on screen but behind the scenes it’s just a bunch of points that were generated by incrementing the polar angle. It would seem that there would be some mathematical transformation that “wraps” the positional bspline/NURBS around the inner circle of the cam such that the cam profile is represented by closed bspline/NURBS (i.e., time (x axis) is converted to degrees and the position (y axis is converted to the radius). Any thoughts, pointers or libraries to accomplish that?

Lastly, I need to export the cam to a standard CAD/CAM program. Minimally that’s the 2D cam profile and the circle for the shaft. Ideally I’d also be able to specify the depth. There are a lot of commercial libraries that export to DXF. I found one that supports Bezier, Arc and Polyline, but no mention of b-spline or NURBS. The reason to do the transform above was so that I could export a curve rather than a bunch of points to a CAD program. I supposed that I could output a polyline and let the user trace/fit a NURBS within a real CAD program, but that seems a little silly.

Any thoughts or pointers would be appreciated.

[ger21]

It'll depend on the control that's runs the g-code, but in the end, it'll have to be converted back to arcs and straight lines (which are supported by g-code), so it would seem like your conversion wouldn't gain you anything?
.dxf files don't support Nurbs or B splines, and there are no g-codes for them anyway.

[zool]

Look at gmax and CNC Toolkit on cnc4free.org

Go to Essentials

It takes a bit to get a handle on it, and it does come slowly, but it is very versatile, though with your apparent coding orientation [complex stuff] you might just blaze through it.

I will go though and sort out the b-spline and nurbs bits for you tomorrow.

[zool]

cnc4free.org>Tutorials> chapters 4,5,6 and 7.

What is in those chapters will get you as close as possible to what you apparently need.

Though like Gerry said nothing in any g-code for b-splines and nurbs.

And look at this PDF: http://tom.cs.byu.edu/~455/bs.pdf , especially part 5 [page 6].

[schmidtmotorwor]

A couple of things to know:

1. Unless the follower is a pointed knife edge simple translation to polar coordinates will be wrong, you need to consider the radius of the follower (a very large radius if it is flat).

2. To cut it, you just need to make the polar coordinates close enough together to achieve the desired accuracy. Fitting arcs or splines will make more problems than it will solve, particularly if very smooth motion is required.