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 show that (p + 2) frictionless point contacts can immobilize any chain of p = 3 polygons without parallel edges; it is unclear that five contacts can immobilize any three polygons in general, Any chain of p arbitrary polygons can be immobilized with at most (p + 3) contacts. We also show that 6 5 (p+2) contacts suffice to robustly immobilize p polygons without parallel edges, and that 5 4 (p + 2) contacts can robustly immobilize p arbitrary polygons.

• Type: Journal
• Year: 2007
• Where: IJCGA
• Authors: Jae-Sook Cheong, A. Frank van der Stappen, Kenneth Y. Goldberg, Mark H. Overmars, Elon Rimon
• Keywords: Frictionless Point Contacts, IJCGA 2007, Polygons, Robust Immobility