I am trying to generate a bulged planar curve by introducing two control points to a straigth line and dragging them away from the line in the X-direction of a curve frame.
When moving the start end end points (sliders in red box) of the original line, the curve frames will flip their axes and the resulting curve (red blob) jumps from convex to concave.

Does anyone have an idea for a more robust solution?

The Frame component Generate a plane by having the X-Axis aligned to the curve direction then Grasshopper will do its best to determine the Y&Z axis, with your curves changing drastically, you need to find a way to control the directionality of the formed planes, one option is to use Alight plane and find a way to communicate between world XY and the resulting planes to make them aligned all the times.

Another way (attached) is to create a temporary lofted surface, in this case, you can generate a frame with X = surface U , Y=Surface V and the Z=Normal, so you can get a more predictable behavior

Align Plane. Sometimes it works well to use Z as the align vector.

Looking now… Oh, your construction plane is sideways? Confusing. So maybe Y as the alignment vector? That’s not reliable either… Very confusing with the unconventional construction plane.

Using a lofted surface to get normal vectors is a great idea, as @tay.othman suggested. Here’s another way to do that using the points on your reference line. I saw no reason for the ‘-x’ expressions so removed them and dropped the negatives on your sliders (though you can still move them to get negative values).

Using Merge instead of connecting multiple wires to an input is also highly recommended to make sure your points or curves are in proper sequence. Just be careful about data trees…

goord morning,
thanks to both of you for shading some light on the issue and for developping the workflow!
works like a charm. i will try to make the curves real planar ones, but i am not yet sure of how important this is in this case.

here´s my final solution to create planar curves.
the loft workflow also produced errors in some other situation, maybe i did not dig deep enough to understand and solve.
thanks again for the help …