Rigid Cylindrical Frameworks with Two Coincident Points

Rigid Two-Dimensional Frameworks with Two Coincident Points

Let G = (V,E) be a graph and u, v ∈ V be two distinct vertices. We give a necessary and sufficient condition for the existence of an infinitesimally rigid two-dimensional bar-and-joint framework (G, p), in which the positions of u and v coincide. We also determine the rank function of the corresponding modified generic rigidity matroid on ground-set E. The results lead to efficient algorithms f...

Rigid Two-Dimensional Frameworks with Three Collinear Points

Let G = (V,E) be a graph and x, y, z ∈ V be three designated vertices. We give a necessary and sufficient condition for the existence of a rigid twodimensional framework (G, p), in which x, y, z are collinear. This result extends a classical result of Laman on the existence of a rigid framework on G. Our proof leads to an efficient algorithm which can test whether G satisfies the condition.

Combining Globally Rigid Frameworks

Here it is shown how to combine two generically globally rigid bar frameworks in d-space to get another generically globally rigid framework. The construction is to identify d+1 vertices from each of the frameworks and erase one of the edges that they have in common.

One-DOF Cylindrical Deployable Structures with Rigid Quadrilateral Panels

In this paper, we present a novel cylindrical deployable structure and variations of its design with the following characteristics: 1. Flat-foldable: The shape flattens into a compact 2D configuration. 2. Rigid-foldable: Each element does not deform throughout the transformation. 3. One-DOF: The mechanism has exactly one degree of freedom. 4. Thick: Facets can be substituted with thick or multi...

Globally rigid frameworks and rigid tensegrity graphs in the plane