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Designing novel structures with hierarchically synchronized deformations

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Abstract

In this paper, we propose a general mechanism to realize a uniform global motion of an n-level hierarchical structure constructed by base components of various shapes, which has only n degrees of freedom. The uniform global motion of the components at the same level of hierarchy is synchronized and independent of movements at other levels. The significantly reduced number of degrees of freedom is achieved by introducing a parallelogram linkage loop to the structure while the hierarchy is obtained from the similarity between the structure and its representative components at different levels. Theoretical analysis reveals the kinematic equations that govern the expansion and retraction of the deployable devices. Numerical simulation and physical prototyping verify the theoretical prediction. This study paves a way towards designing deployable and easily controllable devices and structures for many applications in aeronautics, electronics, optics, and MEMS.

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... Several recent developments of Resch's interconnected assemblies considered 'hierarchical' generalisations of these structures 45,75,80,[82][83][84][85][86][87][88] . In hierarchical structures/materials, a distinct structural pattern repeats in different scales 89 , that is why they are also called 'multiscale' structures/materials 7 . ...
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... In this paper, we show that rigid origami can construct this structure. Parallelogram linkages are planar 4-bar linkages in the shape of a parallelogram [4]. Extending the links outwards creates a structure, as shown in Figure 2, that is similar to a scissor-like structure. ...
Conference Paper
Scissor-like structures are commonly composed of two straight rigid supports in a crisscross pattern connected by a pivot at its point of intersection [1]. Opposite angles formed by the supports are equal regardless of the structure’s folded state. Parallelogram linkages have a similar property. Rigid origami can be used to create these structures by combining two identical copies of a 4-crease single-vertex flat-foldable rigid origami, a single 4C, to form a flat-foldable composite structure, a double 4C. In this paper, we prove mathematically that regardless of the folded state of a single-4C, its even dihedral angles are equal, and odd dihedral angles are equal. As a result, the double 4C consists of 2 scissor-like structures. A past method to prove these dihedral angle equalities requires a more complex approach involving rotation matrices using Denavit and Hartenberg parameters [2,3]. This paper will provide a more intuitive method that proves the same equalities. We will also show that a similar construction of the double 4C using thick-panel versions of the single 4C satisfies the same dihedral angle equalities necessary for the formation of parallelogram linkages. The construction of the double 4C can help design self-folding mechanisms and useful metamaterials.
... kirigami-based structures [7,19,23], fractal hierarchical structures [54,55], and dimpled elastic sheets [52], have been implemented in designing multifunctional materials. However, microstructures with corrugated configuration have been overlooked, which may improve mechanical performance such as stretchability of associated metamaterials [56][57][58]. ...
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Metamaterials, rationally designed multiscale composite systems, have attracted extensive interest for their potential applications in a broad range of applications due to their unique properties such as negative Poisson’s ratio,...
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A new mechanism to achieve a negative Poisson's ratio is presented. An arrangement is made which involves rigid squares connected together at their vertices by hinges. The off-axis mechanical properties obtained from the standard transformation equations show that the idealized system is isotropic. The Poisson's ratio has a value of -1 irrespective of the direction of loading. The geometry modelled is the projection of a plane in inorganic crystalline materials and involves octahedrally co-ordinated atoms.
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Materials with negative Poisson's ratios (auxetic) get fatter when stretched and thinner when compressed. This paper discusses a new explanation for achieving auxetic behaviour in foam cellular materials, namely a ‘rotation of rigid units’ mechanism. Such auxetic cellular materials can be produced from conventional open-cell cellular materials if the ribs of cell are slightly thicker in the proximity of the joints when compared to the centre of the ribs with the consequence that if the conventional cellular material is volumetrically compressed (and then ‘frozen’ in the compressed conformation), the cellular structure will deform in such a way which conserves the geometry at the joints (i.e. behave like ‘rigid units’) whilst the major deformations will occur along the length of the more flexible ribs which form ‘kinks’ at their centres as a result of the extensive buckling. It is proposed that uniaxial tensile loading of such cellular systems will result auxetic behaviour due to re-unfolding of these ‘kinks’ and re-rotation of the ‘rigid joints’.
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Two-dimensional (2D) hierarchical cellular materials made up of sandwich walls are predicted to have superior mechanical properties compared with solid-wall cellular materials. Equations of the stiffness, the buckling strength, the plastic collapse strength, the brittle failure strength and the fracture toughness were deduced. The enhancement of the mechanical properties of 2nd order hierarchical honeycombs is substantial (even an order of magnitude). The hierarchical honeycomb is much more damage tolerant and insensitive to wavy imperfections of the cell wall. Sandwich struts also enhance the buckling strength of the stretching-dominated 2nd order lattice grid material. Made up of sandwich struts, the hierarchical honeycomb has comparable mechanical properties with the stretching-dominated lattice grid material.
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