Funicular Polyhedra

Abstract

The funicular polyhedron, the three-dimensional figure bounded by the links of a net supported at some of its knots (nodes), is treated theoretically by a new method in two stages. A geometrically allowable figure, with assumed coordinates of all supported nodes and of some others, is first computed consistently with the postulate that all the links are inextensible. The necessary vertical supporting forces at all nodes and horizontal forces at the supported nodes first specified, are then computed consistently with the postulate that the links are rigid and that their weights are supported equally at both ends without friction. Here additional vertical forces at nodes may be assumed at pleasure to simulate net-supported loads. Finally, vertical forces at nodes not meant to be supported are reduced in absolute magnitude, eventually to negligible values, by repeated small changes in their coordinates as assumed or computed in the first stage. There is some discussion of simple net types, and numerical examples of symmetrical funicular polyhedra of relatively few meshes are worked out precisely.