Abstract

Maxwell’s counting rule is traditionally used to decide the degrees of freedom for bar-joint frames. However, it has been observed some structure frames with special geometries violate this rule. One typical example is the “locally isostatic” repetitive frameworks, which are those have the same number of constraints as degrees of freedom locally. “Locally isostatic” frameworks in two dimensions are guaranteed to have one degree of freedom, and have a finite kinematic path. However, certain configurations have many more degrees of kinematic freedom – these are often associated with high symmetry configurations. In this project, we are trying to investigate the reasons, and find out how symmetries influence the flexibility of complicated frameworks. The possible applications include understanding the kinematics of complicated crystallographic structures, such as zeolites, and explaining mysterious properties such as negative thermal expansion coefficients.