Rigidity of frameworks

Summary

A framework is a graph whose vertices are placed at points of Euclidean space, with the edges read as rigid bars joined at the vertices. The framework is rigid when it cannot be deformed a little without changing some bar length, except by moving it as a whole. Rigidity theory decides this from the graph and the positions, and in the plane Laman graphs answer the question for generic positions. It belongs to distance geometry and has uses in engineering, robotics and molecular biology.