Mathematics of stable tensegrity structures

TL;DR

This paper develops a mathematical approach to design stable tensegrity structures by relating the number of rods and strings, demonstrating the feasibility of engineering-suitable stable tensegrities.

Contribution

It introduces a relationship between rods and strings to ensure full-rank convexity, enabling the design of stable tensegrity structures.

Findings

Proposes a form-finding method satisfying convexity criteria.

Designs a stable three-rod ten-string tensegrity.

Shows stable tensegrities are feasible for engineering applications.

Abstract

Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods proposed continue to produce structures with one or more soft/swinging modes. These modes have been vividly highlighted and outlined as the grounds for these structures to be unsuitable as engineering structures. This work proposes a relationship between the number of rods and strings to satisfy the full-rank convexity criterion as a part of the form-finding process. Using the proposed form-finding process for the famous three-rod tensegrity, the work proposes an alternative three-rod ten-string that is stable. The work demonstrates that the stable tensegrities suitable for engineering are feasible and can be designed.