Bistable Behavior of the Cylindrical Origami Structure With Kresling Pattern

Abstract

The deployment of a cylinder based on origami with Kresling pattern, whose basic mechanisms are formed by the buckling of a thin cylindrical shell under torsional loading, is studied in this paper. The model consists of identical triangular panels with cyclic symmetry and has a small displacement internal inextensional mechanism. First, geometric formulation of the design problem is presented. Then, assuming that the deployment and folding process is uniform, the bistable behavior of the cylinder is discussed. It can be found that, during the deployment, the dimensionless strain energy increases first and then reduces to zero but followed by another sharp increase. Moreover, the limit condition of geometry parameters for the bistable phenomenon is also discussed. Finally, the bistable behavior is also studied by using numerical simulations for simple and more complex case of the cylinder with multistory. The numerical results agree well with the analytical predictions. Therefore, comparisons with finite element predictions have shown that the analytical solutions given in this paper are accurate and have validated the assumptions made in the derivations.

Peristaltic locomotion without digital controllers: Exploiting multi-stability in origami to coordinate robotic motion

“…The inserted picture on the right shows the experimental setup. [41,43]. In this way, the triangular facet deformations induced by folding between the two stable states can be approximated as the stretching and compression of the truss elements along mountain creases.…”

Geometry and design of origami bellows with tunable response

“…As shown in table 2, the tessellations of several types of rotationally symmetric bellows can be derived from variations on this unit cell. Planar tilings of these unit cells have been studied extensively, but relatively few works have studied cylindrical configurations [18,20]. Some developable patterns on the cylinder lack rotational symmetry [17], but here we will focus on regular cylindrical tilings of the above aforementioned cells, whose regularity will be formally introduced as uniform rotational symmetry.…”

“…It was later proved that a cylinder constructed of radially arranged Miura corrugations is incapable of rigid foldability [18]. Recent developments have explored the bistability of bellows patterned with Miura-ori folds [19] as well as a Kresling pattern [20]. These works utilize an elastic rod framework to explore the dynamic response of a folded bellows.…”

Twist-coupled Kirigami cells and mechanisms

“…These include tessellations of identical triangular panels arranged on helical strips ([9],[10]), as well as variations of Miura-Ori sheets wrapped into tubes and assembled into cellular structures with perpendicular load bearing capabilities ([ 8]). Another cylindrical topology, the Kresling pattern, has a series of parallel diagonal creases approximating the pattern that arises during twist-buckling of a thin-walled cylinder ([21], [12], [13]). However, for some geometries compression of these seamless folded cylinders results in permanent structural failure due to formation of kinks and creases in the triangular panels due to tensile strains that develop in the initial stages of compression.We study the mechanics of cut-relieved folded cylindrical cells which we call flexigami.The addition of diagonal cuts imparts flat foldability of cylindrical topologies without incurring kinking and also mechanical behavior that spans from smooth mono-stability to sharp bi-stability.…”