  Gluck (1975) has proven that triangulated 2-spheres are generically 3-rigid.
Equivalently, planar graphs are generically 3-stress free. We show that
linklessly embeddable graphs are generically 4-stress free. Both of these
results are corollaries of the following theorem: every K_{r+2}-minor free
graph is generically r-stress free for 0<r<5. (This assertion is false for
r>5.) We give an equivalent formulation of this theorem in the language of
symmetric algebraic shifting and show that its analogue for exterior algebraic
shifting also holds. Some further extensions are detailed.
