Here is a bit from my undergraduate honors thesis work at the University of Dayton. The objective was to design a mechanically adaptable light reflector that moves five panels through five parabolic design profiles. The video below also shows designs for a shape-changing seat, cam, and face.
M. Plecnik, Design of a Shape-Changing Rigid-Body Parabolic Light Reflector, Honors Thesis, University of Dayton, 2010. (pdf)