Flexible geometric surfaces classified and new structures discovered
Flexible discrete translational surfaces
Computational Geometry
Summary
The paper studies shapes made by combining two sets of lines, called translational surfaces, to find all that can bend flexibly without breaking. The authors link this to a known problem about certain structures on a sphere, which helped them find two new types of flexible shapes. They also created a way to build all flexible shapes of this kind and explored flexible shapes shaped like tubes and donuts. The work reveals new properties of these flexible structures based on something called Bottema's spherical 16-bar mechanisms.
What this means in practice
- •For architectural engineers: Design flexible surface structures for deployable or shape-changing architectural elements by using the classification and construction methods for discrete translational nets.
- •For mechanical designers: Create novel linkage mechanisms inspired by Bottema's spherical 16-bar systems to build flexible mechanical frameworks with specific movement properties.
Authors
Georg Nawratil
Abstract
We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.