# Tensegrity topology optimization by force maximization on arbitrary ground structures

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## Abstract

This paper presents an optimization approach for design of tensegrity structures based on graph theory. The formulation obtains tensegrities from ground structures, through force maximization using mixed integer linear programming. The method seeks a topology of the tensegrity that is within a given geometry, which provides insight into the tensegrity design from a geometric point of view. Although not explicitly enforced, the tensegrities obtained using this approach tend to be both stable and symmetric. Borrowing ideas from computer graphics, we allow “restriction zones” (i.e., passive regions in which no geometric entity should intersect) to be specified in the underlying ground structure. Such feature allows the design of tensegrities for actual engineering applications, such as robotics, in which the volume of the payload needs to be protected. To demonstrate the effectiveness of our proposed design method, we show that it is effective at extracting both well-known tensegrities and new tensegrities from the ground structure network, some of which are prototyped with the aid of additive manufacturing.

## Keywords

Tensegrity Form-finding Ground structure Topology optimization Graph theory Additive manufacturing## Notes

### Acknowledgements

The authors would like to extend their appreciation to Dr. Tomas Zegard and Ms. Emily D. Sanders for helpful discussions which contributed to improve the present work and to Mr. Rob Felt for taking photos of the physical models.

### Funding information

This study received support from the US NSF (National Science Foundation) through Grants 1538830 and 1321661. In addition, Ke Liu received support from the China Scholarship Council (CSC). We are grateful to the support provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology.

### Compliance with ethical standards

### Disclaimer

The information presented in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies.

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