Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniformâ€¦ (More)

A theory of flexibility and rigidity is developed for general infinite bar-joint frameworks (G, p). Determinations of nondeformability through vanishing flexibility are obtained as well as sufficientâ€¦ (More)

We show that planar embeddable 3-connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specificationsâ€¦ (More)

The graphs G = (V,E) with |E| = 2|V | âˆ’ ` that satisfy |Eâ€²| â‰¤ 2|V â€²| âˆ’ ` for any subgraph Gâ€² = (V â€², Eâ€²) (and for ` = 1, 2, 3) are the (2, `)-tight graphs. The Hennebergâ€“Laman theorem characterizesâ€¦ (More)

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in R. A more general theory is developed forâ€¦ (More)

A foundational theorem of Laman provides a counting characterisation of the finite simple graphs whose generic bar-joint frameworks in two dimensions are infinitesimally rigid. Recently a Laman-typeâ€¦ (More)

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of theâ€¦ (More)

A 2-dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical extension of the fieldâ€¦ (More)

We show that planar embeddable 3-connected CAD graphs are generically non-soluble. A CAD graph represents a configuration of points on the Euclidean plane with just enough distance dimensions betweenâ€¦ (More)