On zero stiffness

Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings. This is the accepted version of an article first published in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. The final version is available online at http://pic.sagepub.com/content/early/2013/11/14/0954406213511903.abstract

Review of inflatable booms for deployable space structures: Packing and rigidization

Inflatable structures offer the potential of compactly stowing lightweight structures, which assume a fully deployed state in space. An important category of space inflatables are cylindrical booms, which may form the structural members of trusses or the support structure for solar sails. Two critical and interdependent aspects of designing inflatable cylindrical booms for space applications are i) packaging methods that enable compact stowage and ensure reliable deployment, and ii) rigidization techniques that provide long-term structural ridigity after deployment. The vast literature in these two fields is summarized to establish the state of the art.The work described in this paper forms part of the DeployTech project; the authors gratefully acknowledge the funding from the European Commission Seventh Framework Programme (FP7).This is the accepted, peer-reviewed manuscript of an article originally published in the Journal of Spacecraft and Rockets. The final published version is available at http://arc.aiaa.org/doi/abs/10.2514/1.A32598

Symmetry perspectives on some auxetic body-bar frameworks

Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode.P.W. Fowler acknowledges support from the Royal Society/Leverhulme Trust in the form of a Senior Research Fellowship for 2013. T. Tarnai is grateful for financial support under OKTA grant K81146.This is the final published version distributed under a Creative Commons Attribution License, which can also be found on the publisher's website at: http://www.mdpi.com/2073-8994/6/2/36

On rigid origami I: Piecewise-planar paper with straight-line creases

We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First, we give definitions on important concepts in rigid origami, then focus on how to describe the configuration space of a creased paper. The shape and 0-connectedness of the configuration space are analyzed using algebraic, geometric and numeric methods, where the key results from each method are gathered and reviewed

On rigid origami II: Quadrilateral creased papers

Miura-ori is well-known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations. Here we are considering how to generalize the Miura-ori: what is the collection of rigid-foldable creased papers with a similar quadrilateral crease pattern as the Miura-ori? This paper reports some progress. We find some new variations of Miura-ori with less symmetry than the known rigid-foldable quadrilateral meshes. They are not necessarily developable or flat-foldable, and still only have single degree of freedom in their rigid folding motion. This article presents a classification of the new variations we discovered and explains the methods in detail.George and Lilian Schiff Foundation

Folded orthotropic tape-springs

We consider the large-displacement, elastic folding of orthotropic tape-springs—thin-walled curved strips made from metal and from a woven laminated composite. Bending of the strips leads to a tight localised fold with a characteristic radius, connected on both sides to straight parts by doubly-curved transition, or ploy, regions. We calculate the shapes of these consistent features for a range of orthotropic parameters using geometrically non-linear, compact models. This study is our initial foray into the performance of tape-springs as safety latching mechanisms for aircraft landing gear

Shape of a bistable composite tape-spring in folding

A composite tape-spring structure is a thin-walled, laminated open slit tube. With fibres oriented at ±45˚, it is stable in both the extended and coiled configurations. In this research, we devise a simple ‘free’ bending system with minimal constraints to evaluate the folding nature of composite tape-springs. The shape of the tape-spring is characterised by considering both the shape during folding and the final folded shape. Experiments are carried out on composite tapes with different geometries: a finite element model is established and calibrated using the experimental results; a parametric study on the folded tape shape is performed based on a theoretical model to evaluate the effects of the initial geometry. Torsional buckling is clearly observed, and complemented with details from the FE model. Here, we show good agreement between experiments, simulation and theoretical analysis.Technology Strategy Boar

Relative judgement is relatively difficult: evidence against the role of relative judgement in absolute identification

A variety of processes have been put forward to explain absolute identification performance. One difference between current models of absolute identification is the extent to which the task involves accessing stored representations in long-term memory (e.g. exemplars in memory, Kent & Lamberts, Journal of Experimental Psychology: Learning Memory and Cognition, 31, 289–305, 2005) or relative judgement (comparison of the current stimulus to the stimulus on the previous trial, Stewart, Brown & Chater, Psychological Review, 112, 881–911, 2005). In two experiments we explored this by tapping into these processes. In Experiment 1 participants completed an absolute identification task using eight line lengths whereby a single stimulus was presented on each trial for identification. They also completed a matching task aimed at mirroring exemplar comparison in which eight line lengths were presented in a circular array and the task was to report which of these matched a target presented centrally. Experiment 2 was a relative judgement task and was similar to Experiment 1 except that the task was to report the difference (jump-size) between the current stimulus and that on the previous trial. The absolute identification and matching data showed clear similarities (faster and more accurate responding for stimuli near the edges of the range and similar stimulus-response confusions). In contrast, relative judgment performance was poor suggesting relative judgement is not straightforward. Moreover, performance as a function of jump-size differed considerably between the relative judgement and absolute identification tasks. Similarly, in the relative judgement task, predicting correct stimulus identification based on successful relative judgement yielded the reverse pattern of performance observed in the absolute identification task. Overall, the data suggest that relative judgement does not underlie absolute identification and that the task is more likely reliant on an exemplar comparison process

Bundle folding type III Bricard linkages

The paper presents a set of one-degree-of-freedom overconstrained linkages, which can be folded into a bundle and deployed into a polygon on a plane. The proposed mechanisms are movable Bricard octahedra of type III, characterized by the existence of two configurations where all joints are coplanar. The possible geometries of doubly-collapsible Bricard linkages are parameterized and their kinematics is analyzed. A line-intersection method is proposed to construct a bundle-folding mechanism of this type. Necessary and sufficient conditions are derived for the deployed-configuration polygon to be a square. Simulation and prototype experiment results validate the analysis and design.This research has been supported by the National Natural Science Foundation of China under Grant 51605011, 51635002(Key Program), the Fundamental Research Funds for the Central Universities (YWF-19-BJ-J-336), the State Key Laboratory of Robotics and System (HIT), and the AUTORECON project funded under the Seventh Framework Program of the European Commission (Collaborative Project NMP-FOF-2011-285189). The authors gratefully acknowledge the supporting agencies