Generic Rigidity Matroids with Dilworth Truncations

Abstract

We prove that the linear matroid that defines generic rigidity of $d$-dimensional body-rod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of $\left(\genfrac{}{}{0ex}{}{d+1}{2}\right)$ graphic matroids by applying variants of Dilworth truncation $n_r$ times, where $n_r$ denotes the number of rods. This leads to an alternative proof of Tay's combinatorial characterizations of generic rigidity of rod-bar frameworks and that of identified body-hinge frameworks.

Cited by in corpus (2)

• Periodic body-and-bar frameworks
• Rooted-tree Decompositions with Matroid Constraints and the Infinitesimal Rigidity of Frameworks with Boundaries