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Invariant dual mechanics of tensegrity and origami.

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Title: Invariant dual mechanics of tensegrity and origami.
Authors: Dang, Xiangxin1, Paulino, Glaucio H.1,2 gpaulino@princeton.edu
Source: Proceedings of the National Academy of Sciences of the United States of America. 3/24/2026, Vol. 123 Issue 12, p1-10. 39p.
Subjects: Tensegrity (Engineering), Kinematics, Dynamic stability, Statics, Structural engineering, Mechanics (Physics)
Abstract: Statics and kinematics are often viewed as intertwined branches of mechanics. The principle of virtual work indicates this interconnection: For a system in static equilibrium, the total work performed by all forces during any virtual displacement must equal zero. In this work, we make the interplay between statics and kinematics more explicit by focusing on two engineering structures--tensegrity and origami. Specifically, we demonstrate a quantitative duality relationship between the states of self-stress of tensegrity and the infinitesimal mechanisms of origami. More importantly, we show that this duality remains invariant under nondegenerate linear transformations applied to the tensegrity and origami configurations. Furthermore, we establish that the stability property of tensegrity, particularly superstability, is preserved under such transformations. We apply the invariant duality theory to tensegrity and origami structures with prismatic and polyhedral geometries, illustrating its broad applicability. Such duality is also applicable to the fast generation of irregular, three-dimensional architected materials and structures. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Invariant dual mechanics of tensegrity and origami.
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  Data: <searchLink fieldCode="DE" term="%22Tensegrity+%28Engineering%29%22">Tensegrity (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Kinematics%22">Kinematics</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+stability%22">Dynamic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Statics%22">Statics</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+engineering%22">Structural engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanics+%28Physics%29%22">Mechanics (Physics)</searchLink>
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  Data: Statics and kinematics are often viewed as intertwined branches of mechanics. The principle of virtual work indicates this interconnection: For a system in static equilibrium, the total work performed by all forces during any virtual displacement must equal zero. In this work, we make the interplay between statics and kinematics more explicit by focusing on two engineering structures--tensegrity and origami. Specifically, we demonstrate a quantitative duality relationship between the states of self-stress of tensegrity and the infinitesimal mechanisms of origami. More importantly, we show that this duality remains invariant under nondegenerate linear transformations applied to the tensegrity and origami configurations. Furthermore, we establish that the stability property of tensegrity, particularly superstability, is preserved under such transformations. We apply the invariant duality theory to tensegrity and origami structures with prismatic and polyhedral geometries, illustrating its broad applicability. Such duality is also applicable to the fast generation of irregular, three-dimensional architected materials and structures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: 3/24/2026
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              Y: 2026
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