Rigidity of frameworks / Daud Mohamad

The term "frameworks" is normally referred to a collection of rods and Connectors/hinges. However, some people tend to used terms such as linkages, linkworks and mechanisms. basically, in mathematics, a framework consists of two sets, a finite set of vertices and a finite set of edges. Many things can be considered as frameworks, from little things such as a cube or a triangle to larger constructions such as skycrapers and transmission line towers etc. One important characteristic of a framework which the author would like to discuss is rigidity. Consider one simple framework, that is a triangle. It is said to be rigid in R2 since we cannot change the relative position of its vertices. For a square, it is definitely not rigid, or we call it flexible since it can be transformed into a rhombus (refer Fig. 1) with the edge lengths remaining constant.