On the symmetries of the origami waterbomb pattern: kinematics and mechanical investigations

Abstract

Origamis are becoming the inspiration of new adaptive structures applied for several purposes. One of the challenges of the design of the origami inspired structures is to deal with the large number of variables and degrees of freedom (DoFs) associated with such complex structures. Closed tessellations have a reduced number of DoF when compared to the opened ones. Besides, the coupling due to the closure of the tessellation promotes some periodicity along the structure. Symmetric behaviors allow the description of the structure from a unit cell behavior, establishing reduced-order models. This paper investigates the origami waterbomb pattern, exploring the unit cell behavior and its symmetries. Initially, kinematics analysis based on an equivalent mechanism approach establishes a reduced-order model associated with symmetry hypotheses. Afterward, mechanical analysis is investigated using a nonlinear finite element analysis through bar-and-hinge formulation. A comparison between both formulations is performed showing the range of validity of the reduced-order model description. The general conclusions are applied to a cylindrical tessellation under symmetric actuation showing the capability of the reduced-order model for the origami description. Results show that the rigid foldability hypothesis is the essential point for the equivalence between the two descriptions.

Multimodal motion of soft origami tripod using electrohydraulic actuator

“…Self-unfolding of the leg allows the top plate movements, as shown in Figure 3. On the legs, the origami waterbomb pattern provides one translation and two rotational deformations 27 . When all actuators are operated, the three legs are unfolded identically, causing the top plate to move linearly.…”

“…In this paper, we propose multimodal motions of structures with a minimal number of electrohydraulic actuators. For this purpose, an origami method called a waterbomb pattern is adopted for three links that are arranged in parallel 27,28 . Electrohydraulic actuator can control each link to achieve multimodal motions with linear and tilting motions.…”

Oribron: An Origami-Inspired Deformable Rigid Bronchoscope for Radial Support

“…If θRefl is used to represent the angle between adjacent reflection axes, θRefl = π/n, and the central angle occupied by each column in the circumferential direction was equal to 2θRefl, as shown by (i) in Figure 3c. If the facet and crease are regarded as rigid linkage and rotary joint respectively, then six-crease origami can be equivalent to a spherical 6R linkage with three degrees of freedom (DOF) [60,61]. Therefore, the Waterbomb formed by connecting multiple groups of sixcrease vertices belongs to the multi-DOF system.…”

Geometry and Kinematics of Cylindrical Waterbomb Tessellation

“…The dynamics of the stent graft and the wheel inspired by waterbomb tube has been analyzed [10,11]. Also, the kinematics and structural deformation of waterbomb tube has been studied [12][13][14]. One of the most interesting phenomena reported on waterbomb tube is that it can form wave-like surfaces [15,16] like in Fig.…”