Rigidity of Frameworks Supported on Surfaces
Rigidity of Frameworks Supported on Surfaces
A theorem of Laman gives a combinatorial characterization of the graphs that admit a realization as a minimally rigid generic bar-joint framework in $\mathbb{R}^2$. A more general theory is developed for frameworks in $\mathbb{R}^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\mathcal{M}$. Furthermore, when $\mathcal{M}$ is …