Origami building blocks: generic and special 4-vertices

Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their folding behavior. For generic vertices, we distinguish three vertex types and two subtypes. We establish relationships based on the relative sizes of the sector angles to determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special 4-vertices and serves as a roadmap for designing origami metamaterials.Comment: 8 pages, 9 figure

Asymmetries in triboelectric charging: generalizing mosaic models to different-material samples and sliding contacts

Nominally identical materials exchange net electric charge during contact through a mechanism that is still debated. `Mosaic models', in which surfaces are presumed to consist of a random patchwork of microscopic donor/acceptor sites, offer an appealing explanation for this phenomenon. However, recent experiments have shown that global differences persist even between same-material samples, which the standard mosaic framework does not account for. Here, we expand the mosaic framework by incorporating global differences in the densities of donor/acceptor sites. We develop an analytical model, backed by numerical simulations, that smoothly connects the global and deterministic charge transfer of different materials to the local and stochastic mosaic picture normally associated with identical materials. Going further, we extend our model to explain the effect of contact asymmetries during sliding, providing a plausible explanation for reversal of charging sign that has been observed experimentally.Comment: 8 pages, 6 figure

Single-collision statistics reveal a global, water-driven mechanism for contact electrification in granular media

Models for same-material contact electrification in granular media often rely on a local charge-driving parameter whose spatial variations lead to a stochastic origin for charge exchange. Measuring the charge transfer from individual granular spheres after contacts with substrates of the same material, we find that the charge-driving parameter is global, not local. Cleaning and baking samples fully resets their charging behavior, which indicates the underlying global parameter is not intrinsic to the material, but acquired from its history. Charging behavior is randomly and irreversibly affected by changes in relative humidity, pointing to a mechanism where adsorbates, in particular water, are fundamental to the charge-transfer process.Comment: 6 pages, 5 figure

Designing the energy landscape of folded structures

We show that multistability is an inherent feature of planar folded objects. By systematically exploring the energy landscape of the simplest such system, i.e., a single vertex fold connecting four rigid plates where all elastic energy is stored in the folds, we show that bistability is generally expected. With simple design rules we can add a third or even a fourth-stable state. Under exceptional circumstances, we can “remove” one minima to create effectively monostable systems. Tiling such structures allows us to design metamaterials with functional stability landscapes

Origami Multistabilty: From Single Vertices to Metasheets

We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two distinct branches meeting at the flat state. This suggests that generic vertices are at least bistable, but we find that the nonlinear nature of these branches allows for vertices with as many as five distinct stable states. In vertices with collinear folds and/or symmetry, more branches emerge leading to up to six stable states. Finally, we introduce a procedure to tile arbitrary 4-vertices while preserving their stable states, thus allowing the design and creation of multistable origami metasheets.Comment: For supplemental movies please visit http://www.lorentz.leidenuniv.nl/~chen/multisheet

Non-Euclidean Origami

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex

Quantitatively consistent, scale-spanning model for same-material tribocharging

By rigorously accounting for mesoscale spatial correlations in donor/acceptor surface properties, we develop a scale-spanning model for same-material tribocharging. We find that mesoscale correlations affect not only the magnitude of charge transfer but also the fluctuations-suppressing otherwise overwhelming charge-transfer variability that is not observed experimentally. We furthermore propose a generic theoretical mechanism by which the mesoscale features might emerge, which is qualitatively consistent with other proposals in the literature.Comment: 5 pages, 4 figures. Supplemental Material: 13 pages, 10 figures, 1 movi

Cover slip external cavity diode laser

The design of a 671 nm diode laser with a mode-hop-free tuning range of 40 GHz is described. This long tuning range is achieved by simultaneously ramping the external cavity length with the laser injection current. The external cavity consists of a microscope cover slip mounted on piezoelectric actuators. In such a configuration the laser output pointing remains fixed, independent of its frequency. Using a diode with an output power of 5-7 mW, the laser linewidth was found to be smaller than 30 MHz. This cover slip cavity and feedforward laser current control system is simple, economical, robust, and easy to use for spectroscopy, as we demonstrate with lithium vapor and lithium atom beam experiments.Comment: 7 pages, 6 figures, submitted to Review of Scientific Instruments 7/29/0