Self-stress and the Nonlinear Response of the Kresling Origami and Tensegrity Frustums: a Unified Outlook

Kresling origami and tensegrity frustums have been studied extensively in two related but separate lines of research, ranging in the fields of mechanics, physics, robotics and materials science. Although these two systems share the same geometry and connectivity of vertices and edges, the analogies between their mechanical properties have not yet been fully highlighted in the literature. Here, a unified description of Kresling origami and tensegrity frustums is presented. Starting with the form-finding analysis, a new geometric compatibility condition for the realization of load-free and stress-free configurations is derived, and it is proved that the Kresling origami can also exist in self-stressed configurations. The self-stress state of rigid Kresling origami with frictionless hinges at folds is obtained analytically, and its relationship with the self-stress of tensegrity frustums is elucidated. Next, two regimes of mechanical response are distinguished in terms of a frustration parameter, which is associated with a prestress-tunable stiffening response when it is positive and with a bistable response when it is negative. Finally, comparative and parametric analyses, including those regarding flat-foldable Kresling origami, are performed to gain insight and a comprehensive understanding of the design possibilities of these structures.