Structural rigidity

Summary

Rigidity theory studies when a framework of rigid bars joined at flexible joints cannot be deformed except by moving it as a whole. A framework is a graph together with positions of its vertices in Euclidean space, with each edge a bar of fixed length. The subject links geometry, combinatorics and linear algebra, and it is used in engineering, chemistry and robotics. Classical results include Cauchy's rigidity theorem for convex polyhedra and Laman's characterisation of generically rigid graphs in the plane.