scholarly journals On the Incompressibility of Cylindrical Origami Patterns

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Friedrich Bös ◽  
Max Wardetzky ◽  
Etienne Vouga ◽  
Omer Gottesman
Keyword(s):  
Finite Number ◽  
Three Dimensional ◽  
Deployable Structures ◽  
Art And Science ◽  
Cylindrical Structures ◽  
Mechanical Metamaterials

The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials. Here we investigate the axial compressibility of origami cylinders, i.e., cylindrical structures folded from rectangular sheets of paper. We prove, using geometric arguments, that a general fold pattern only allows for a finite number of isometric cylindrical embeddings. Therefore, compressibility of such structures requires either stretching the material or deforming the folds. Our result considerably restricts the space of constructions that must be searched when designing new types of origami-based rigid-foldable deployable structures and metamaterials.

Development and Analysis of a Three-Dimensional Printed Miniature Walking Robot With Soft Joints and Links

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Anthony DeMario ◽  
Jianguo Zhao
Keyword(s):  
Numerical Method ◽  
Three Dimensional ◽  
Soft Materials ◽  
Walking Robot ◽  
Deployable Structures ◽  
Miniature Robots ◽  
Revolute Joints ◽  
Mechanical Metamaterials ◽  
Wide Range ◽  
Locomotion Speed

Miniature robots have many applications ranging from military surveillance to search and rescue in disaster areas. Nevertheless, the fabrication of such robots has traditionally been labor-intensive and time-consuming. This paper proposes to directly leverage multimaterial 3D printing (MM3P) to fabricate centimeter-scale robots by utilizing soft materials to create not only soft joints to replace revolute joints but also soft links to replace rigid links. We demonstrate the capability of MM3P by creating a miniature, four-legged walking robot. Moreover, we leverage a three-spring rotational-prismatic-rotational (RPR) model to approximate the motion of soft joints or links, which is further utilized to numerically predict the motion of the leg mechanism with multiple soft joints and links. The accuracy of the proposed numerical method is validated with experimental results, and outperforms the results from using a psuedorigid-body (PRB) 1R model to approximate the motion of soft joints/links of the same mechanism. Meanwhile, a functional walking robot actuated by a single DC motor is demonstrated with a locomotion speed of 5.7 cm/s. We envision that the concept of employing both soft joints and links will inspire the design and realization of novel miniature mechanisms for a wide range of applications including robotics, deployable structures, or mechanical metamaterials. The proposed numerical method can also be readily applied to analyze other mechanisms with soft joints and links.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

scholarly journals Divergent Design of Mechanical Metamaterials Clan Deducted from Arc-serpentine Curve

2021 ◽  
Author(s):  
Shengli Mi ◽  
Hongyi Yao ◽  
Xiaoyu Zhao ◽  
Wei Sun
Keyword(s):  
Thick Plate ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Design Strategies ◽  
Shape Morphing ◽  
Mechanical Metamaterials ◽  
Unit Cells ◽  
Combinatorial Principles ◽  
Composite Curve ◽  
Typical Design

Abstract The exotic properties of mechanical metamaterials are determined by their unit-cells' structure and spatial arrangement, in analogy with the atoms of conventional materials. Companioned with the mechanism of structural or cellular materials1–5, the ancient wisdom of origami6–11 and kirigami12–16 and the involvement of multiphysics interaction2,17,18 enrich the programable mechanical behaviors of metamaterials, including shape-morphing8,12,14,16,19, compliance4,5,8,17,20, texture2,18,21, and topology11,18,22−25. However, typical design strategies are mainly convergent, which transfers various structures into one family of metamaterials that are relatively incompatible with the others and do not fully bring combinatorial principles3,10,26 into play. Here, we report a divergent strategy that designs a clan of mechanical metamaterials with diverse properties derived from a symmetric curve consisting of serpentines and arcs. We derived this composite curve into planar and cubic unit-cells and modularized them by attaching magnetics. Moreover, stacking each of them yields two- and three-dimensional auxetic metamaterials, respectively. Assembling with both modules, we achieved three thick plate-like metamaterials separately with flexibility, in-plane buckling, and foldability. Furthermore, we demonstrated that the hybrid of paradox properties is possible by combining two of the above assembles. We anticipate that this divergent strategy paves the path of building a hierarchical library of diverse combinable mechanical metamaterials and making conventional convergent strategies more efficient to various requests. Main

scholarly journals A 3D-printed molecular ferroelectric metamaterial

2020 ◽  
Vol 117 (44) ◽  
pp. 27204-27210 ◽  
Author(s):  
Yong Hu ◽  
Zipeng Guo ◽  
Andrew Ragonese ◽  
Taishan Zhu ◽  
Saurabh Khuje ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Water Soluble ◽  
Crystalline Lattice ◽  
Self Healing ◽  
Dynamic Tuning ◽  
Mechanical Metamaterials ◽  
Electric Polarizabilities ◽  
3D Geometry

Molecular ferroelectrics combine electromechanical coupling and electric polarizabilities, offering immense promise in stimuli-dependent metamaterials. Despite such promise, current physical realizations of mechanical metamaterials remain hindered by the lack of rapid-prototyping ferroelectric metamaterial structures. Here, we present a continuous rapid printing strategy for the volumetric deposition of water-soluble molecular ferroelectric metamaterials with precise spatial control in virtually any three-dimensional (3D) geometry by means of an electric-field–assisted additive manufacturing. We demonstrate a scaffold-supported ferroelectric crystalline lattice that enables self-healing and a reprogrammable stiffness for dynamic tuning of mechanical metamaterials with a long lifetime and sustainability. A molecular ferroelectric architecture with resonant inclusions then exhibits adaptive mitigation of incident vibroacoustic dynamic loads via an electrically tunable subwavelength-frequency band gap. The findings shown here pave the way for the versatile additive manufacturing of molecular ferroelectric metamaterials.

scholarly journals The Rise of (Chiral) 3D Mechanical Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3527 ◽  
Author(s):  
Janet Reinbold ◽  
Tobias Frenzel ◽  
Alexander Münchinger ◽  
Martin Wegener
Keyword(s):  
Crystal Lattice ◽  
Lattice Constant ◽  
Linear Polarization ◽  
Three Dimensional ◽  
Future Perspectives ◽  
Special Issue ◽  
Polarization Rotation ◽  
Mechanical Metamaterials ◽  
The One ◽  
Crystal Lattice Constant

On the occasion of this special issue, we start by briefly outlining some of the history and future perspectives of the field of 3D metamaterials in general and 3D mechanical metamaterials in particular. Next, in the spirit of a specific example, we present our original numerical as well as experimental results on the phenomenon of acoustical activity, the mechanical counterpart of optical activity. We consider a three-dimensional chiral cubic mechanical metamaterial architecture that is different from the one that we have investigated in recent early experiments. We find even larger linear-polarization rotation angles per metamaterial crystal lattice constant than previously and a slower decrease of the effects towards the bulk limit.

scholarly journals Non-Auxetic Mechanical Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 635 ◽  
Author(s):  
Christa de Jonge ◽  
Helena Kolken ◽  
Amir Zadpoor
Keyword(s):  
Mechanical Properties ◽  
Yield Stress ◽  
Fatigue Behavior ◽  
Analytical Data ◽  
Three Dimensional ◽  
Mechanical Metamaterials ◽  
Macro Scale ◽  
Unit Cells ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The concept of “mechanical metamaterials” has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson’s ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson’s ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12–36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.

CHARLES BOURGEOIS (1759-1832), HIS ANTINEWTONIAN COLOUR THEORY AND THE RECONCILEMENT OF ART AND SCIENCE

Nuncius ◽  
2007 ◽  
Vol 22 (1) ◽  
pp. 15-48
Author(s):  
JOOST MERTENS
Keyword(s):  
White Light ◽  
Royal Academy ◽  
Three Dimensional ◽  
Colour Space ◽  
Art And Science ◽  
The Arts ◽  
General Rules ◽  
Colour Theory ◽  
Composite Nature ◽  
Academy Of Sciences

Abstracttitle ABSTRACT /title Between 1810 and 1825, Charles Bourgeois (1759-1832), miniaturist, pigment manufacturer and physicist, developed a colour optics that defied both the Newtonian view of the composite nature of white light and the widely accepted strict separation between science and the arts. In this paper four themes are discussed: the general rules of colour mixing and the resulting three-dimensional colour space CEI (Couleur, Excdent, Intensit); Bourgeois' theory of light as a vehicle for non-luminous colours; His attempt at disproving Newton's central principle of the unequal refrangibility of different colours; and his relation, or rather non-relation, with the Royal Academy of Sciences which considered Bourgeois' theory of light a piece of nonsense.

scholarly journals Experiments on cloaking in optics, thermodynamics and mechanics

2015 ◽  
Vol 373 (2049) ◽  
pp. 20140357 ◽  
Author(s):  
Muamer Kadic ◽  
Tiemo Bückmann ◽  
Robert Schittny ◽  
Martin Wegener
Keyword(s):  
Three Dimensional ◽  
Thin Plates ◽  
Visible Range ◽  
Flexural Waves ◽  
Discrete Lattices ◽  
Mechanical Metamaterials ◽  
Visible Frequency ◽  
Transient Thermal ◽  
Thermal Cloaking ◽  
Static Core

Spatial coordinate transformations can be used to transform boundaries, material parameters or discrete lattices. We discuss fundamental constraints in regard to cloaking and review our corresponding experiments in optics, thermodynamics and mechanics. For example, we emphasize three-dimensional broadband visible-frequency carpet cloaking, transient thermal cloaking, three-dimensional omnidirectional macroscopic broadband cloaking for diffuse light throughout the entire visible range, cloaking for flexural waves in thin plates and three-dimensional elasto-static core–shell cloaking using pentamode mechanical metamaterials.

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