Generic Rigidity Matroids with Dilworth Truncations

We prove that the linear matroid that defines the generic rigidity of d-dimensional bodyrod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of ( d+1 2 ) copies of a graphic matroid by applying variants of Dilworth truncation operations nr times, where nr denotes the number of rods. This result leads to an alternative proof of Tay’s combinatorial characterizations of the generic rigidity of rod-bar frameworks and that of identified body-hinge frameworks.