Statics and Geometry of Underconstrained Axisymmetric 3-Nets

Abstract

A 3-net is a system formed by three intersecting arrays of linear flexible members such that every intersection involves one member of each array. The subject of this study is an axisymmetric 3-net where the first array is meridional and the other two are inclined to a meridian at equal but opposite angles. If the net intersections are not fixed the system is underconstrained and, generally, does not possess a unique configuration. However, such systems allow exceptional configurations in which they lack kinematic mobility and admit prestress. Pertinent equations governing the intricately interrelated statics and geometry of axisymmetric 3-nets are developed and some closed-form solutions are obtained. On this basis, two particular classes of immobile (static) 3-nets are synthesized and two corresponding sets of feasible geometric shapes are investigated.