A Framework is rigid Iff continuous motion of the points of the configuration maintaining the bar constraints comes from a family of motions of all Euclidean Space which are distance-preserving. A Graph is (generically) -rigid if, for almost all (i.e., an open dense set of) Configurations of , the Framework is rigid in .

One of the first results in rigidity theory was the Rigidity Theorem by Cauchy in 1813. Although rigidity problems
were of immense interest to engineers, intensive mathematical study of these types of problems has occurred only
relatively recently (Connelly 1993, Graver *et al. *1993).

**References**

Connelly, R. ``Rigidity.'' Ch. 1.7 in *Handbook of Convex Geometry, Vol. A* (Ed. P. M. Gruber and J. M. Wills).
Amsterdam, Netherlands: North-Holland, pp. 223-271, 1993.

Crapo, H. and Whiteley, W. ``Statics of Frameworks and Motions of Panel Structures, A Projective Geometry
Introduction.'' *Structural Topology* **6**, 43-82, 1982.

Graver, J.; Servatius, B.; and Servatius, H. *Combinatorial Rigidity.* Providence, RI: Amer. Math. Soc., 1993.

© 1996-9

1999-05-25