IMMOBILIZING HINGED POLYGONS

Immobilizing Hinged Polygons

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility, which are comparable to second and first order immobility for a single object [8, 7, 11, 12] robust immobility differs from immobility in that it additionally requires insensitivity to small perturbations of contacts. We sh...

Fixturing Hinged Polygons

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility—which are comparable to second and first order immobility for a single object—to capture the intuitive requirement for a fixture of a chain of hinged objects; robust immobility differs from immobility in that it additionally...

Hinged Dissection of Polygons is Hard

We show several natural questions about hinged dissections of polygons to be PSPACE-hard. The most basic of these is: Given a hinged set of pieces and two configurations for them, can we swing the pieces on the hinges to transform one configuration to the other? We also consider variants in which the configurations must be convex, the placement of hinges is not specified, or the configurations ...

On a Problem of Immobilizing Polygons

Hinged Dissection of Polypolyhedra

This paper presents a general family of 3D hinged dissections for polypolyhedra, i.e., connected 3D solids formed by joining several rigid copies of the same polyhedron along identical faces. (Such joinings are possible only for reflectionally symmetric faces.) Each hinged dissection consists of a linear number of solid polyhedral pieces hinged along their edges to form a flexible closed chain ...