Statics of integrated origami and tensegrity systems

Abstract

This study presents an explicit form of the static equilibrium equations of integrated origami and tensegrity systems. The analytical approach allows one to model and analyze the isolated origami and tensegrity paradigms as a whole system. The tensegrity and origami members are described by the nodal coordinates and hinge angels between the origami panels. The nonlinear static equations of the integrated system are derived by the Lagrangian method. By Taylor’s expansion theory, we also presented its linearized form. The developed approach is capable of conducting the following comprehensive statics studies for any integrated origami and tensegrity systems: (1) Performing loading analysis, where bars and strings can have elastic or plastic deformations. (2) Conducting infinitesimal and large deformation analysis, which is helpful in understanding the stress in structural members and actuation strategies. (3) Dealing with various kinds of boundary conditions, for example, fixing or applying static loads at any nodes in any direction (i.e., gravitational force, some specified forces, or moments). (4) Conducting stiffness analysis, including eigenvalues and their modes. Three examples, a Miura origami unit, an integrated tensegrity origami shelter, and a cable-driven Kresling structure, are carefully selected and studied. This study provides a deep insight into structures, materials, as well as performances. The integration idea also promotes our ability to design and build deployable structures at large.