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Sketch constraint along segmented curve?

I am creating a sketch layout of an assembly and want one point to be constrained along a series of connected (but not collinear) line segments with the height of the point set by a configuration variable. I have the line segments defined in a separate sketch. A coincident constraint to one of the lines wouldn't work. I've tried turning the segments into a composite curve or extruding them to form a surface, but only the linear edges are allowed to be selected to form the constraint. Is there any way to constrain the point along this path?
Lead Mechanical Engineer @ Healing Innovations
Comments
You won't be able to make it "perfect", but you could create a spline approximation of your segmented curve that might be good enough?
https://cad.onshape.com/documents/c771dca24fe1a86ad33411f9/w/9e54b9971485defba25981e6/e/4b76a342521dda1ca9fb8410?renderMode=0&tangentEdgeStyle=1&uiState=679d1b643e58d148047d7600
That's what I've ended up doing - it's good enough for my purposes.
Lead Mechanical Engineer @ Healing Innovations