Having part "wrap" to surface automatically

I have a "wire" that I want to mate and "wrap" or "fit" to a curved surface.

For example, suppose I have a sphere with a groove in it. I have a T beam
that will fit in the groove. But T is straight and the surface is curved. In
my case the surface has different curvatures and different points so I need
a way to automate it.

Also, is it possible to automatically control the length/size of a part
through a mate or two? In the above example the group has a finite length
and I'd like the "T beam" to "stretch" to fill the grove.

Thanks,
Jon

 

I would suggest that the part has two configurations: 1 for the
staright T-beam for cutting, 2 for the one to follow the groove. (1 is
made after 2).
In the assembly where the curved part with the groove is placed you
make a path curve of the groove, then the T-beam is made using feature
Sweep, the profile sketch is the T and the path is the curve from the
groove. When part 2 is made the length of the path can be measured and
then be used for the cutting configuration.

BR, MGR@Martin