It would be better to describe it as a swept solid, an advancement over a swept profile, that is useful for motion studies. I think there is already a form of this in the motion envelope, but it isn't available as a feature in a part.
Ref http://en.wikipedia.org/wiki/Solid_sweep
Ref http://www.cc.gatech.edu/~jarek/papers/sweep.pdf
Ref http://www.cse.iitb.ac.in/~jineshmac/
Ref http://www.cse.iitb.ac.in/~jineshmac/homePage/images/germanyTalk.pdf (my favorite so far)
To make the problem more interesting, add the ability to modify the solid geometry (either a single solid part or an assembly) by using trajpar as an input to relations controlling the solid, in a way similar to the way trajpar can be used to modify the 2D section as it moves along the trajectory.