A rapid-response soft end effector inspired by the hummingbird beak.

Biology is a wellspring of inspiration in engineering design. This paper delves into the application of elastic instabilities-commonly used in biological systems to facilitate swift movement-as a power-amplification mechanism for soft robots. Specifically, inspired by the nonlinear mechanics of the hummingbird beak-and shedding further light on it-we design, build and test a novel, rapid-response, soft end effector. The hummingbird beak embodies the capacity for swift movement, achieving closure in less than [Formula: see text]. Previous work demonstrated that rapid movement is achieved through snap-through deformations, induced by muscular actuation of the beak's root. Using nonlinear finite element simulations coupled with continuation algorithms, we unveil a representative portion of the equilibrium manifold of the beak-inspired structure. The exploration involves the application of a sequence of rotations as exerted by the hummingbird muscles. Specific emphasis is placed on pinpointing and tailoring the position along the manifold of the saddle-node bifurcation at which the onset of elastic instability triggers dynamic snap-through. We show the critical importance of the intermediate rotation input in the sequence, as it results in the accumulation of elastic energy that is then explosively released as kinetic energy upon snap-through. Informed by our numerical studies, we conduct experimental testing on a prototype end effector fabricated using a compliant material (thermoplastic polyurethane). The experimental results support the trends observed in the numerical simulations and demonstrate the effectiveness of the bio-inspired design. Specifically, we measure the energy transferred by the soft end effector to a pendulum, varying the input levels in the sequence of prescribed rotations. Additionally, we demonstrate a potential robotic application in scenarios demanding explosive action. From a mechanics perspective, our work sheds light on how pre-stress fields can enable swift movement in soft robotic systems with the potential to facilitate high input-to-output energy efficiency.

Dataset for computational and experimental buckling analysis of constant-stiffness and variable-stiffness composite cylinders.

This dataset encapsulates comprehensive information and experimental outcomes derived from the buckling test of variable-stiffness composite cylinders subjected to axial compression. It is the first dataset about the correlation between experimental and computational analysis for a Rapid-Tow Sheared composite cylinder, a recently developed advanced composite manufacturing technique. The data gathered during the test contains: raw test data for force, end-compression and strain gauges; and digital image correlation. The data for finite element validation is for a quasi-isotropic shell and variable-stiffness rapid tow-sheared shell. The data also contain imperfection signatures from a coordinate-measurement machine (CMM) of both cylinders. This compilation of documented data stands as a robust resource for future investigations, enabling comparative analyses, validation of theoretical models, and advancements in the domain of designing and testing composite structures, particularly those employing variable-stiffness manufacturing techniques.

Buckling-induced sound production in the aeroelastic tymbals of Yponomeuta.

The loss of elastic stability (buckling) can lead to catastrophic failure in the context of traditional engineering structures. Conversely, in nature, buckling often serves a desirable function, such as in the prey-trapping mechanism of the Venus fly trap (Dionaea muscipula). This paper investigates the buckling-enabled sound production in the wingbeat-powered (aeroelastic) tymbals of Yponomeuta moths. The hindwings of Yponomeuta possess a striated band of ridges that snap through sequentially during the up- and downstroke of the wingbeat cycle-a process reminiscent of cellular buckling in compressed slender shells. As a result, bursts of ultrasonic clicks are produced that deter predators (i.e. bats). Using various biological and mechanical characterization techniques, we show that wing camber changes during the wingbeat cycle act as the single actuation mechanism that causes buckling to propagate sequentially through each stria on the tymbal. The snap-through of each stria excites a bald patch of the wing's membrane, thereby amplifying sound pressure levels and radiating sound at the resonant frequencies of the patch. In addition, the interaction of phased tymbal clicks from the two wings enhances the directivity of the acoustic signal strength, suggesting an improvement in acoustic protection. These findings unveil the acousto-mechanics of Yponomeuta tymbals and uncover their buckling-driven evolutionary origin. We anticipate that through bioinspiration, aeroelastic tymbals will encourage novel developments in the context of multi-stable morphing structures, acoustic structural monitoring, and soft robotics.

Probing in situ capacities of prestressed stayed columns: towards a novel structural health monitoring technique.

Prestressed stayed columns (PSCs) are structural systems whose compressive load-carrying capacity is enhanced through pre-tensioned cable stays. Much research has demonstrated that PSCs buckle subcritically when their prestressing levels maximize the critical buckling load of the theoretically perfect arrangement. Erosion of the pre-tensioned cables' effectiveness (e.g. through creep or corrosion) can thus lead to sudden collapse. The present goal is to develop a structural health monitoring (SHM) technique for in-service PSCs that returns the current structural utilization factor based on selected probing measurements. Hence, PSCs with different cable erosion and varying compression levels are probed in the pre-buckling range within the numerical setting through a nonlinear finite element (FE) model. In contrast to the previous work, it is found presently that the initial lateral stiffness from probing a PSC provides a suitable health index for in-service structures. A machine learning-based surrogate is trained on simulated data of the loading factor, cable erosion and probing indices; it is then used as a predictive tool to return the current utilization factor for PSCs alongside the level of cable erosion given probing measurements, showing excellent accuracy and thus provides confidence that an SHM technique based on probing is indeed feasible. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Beyond the fold: experimentally traversing limit points in nonlinear structures.

Recent years have seen a paradigm shift regarding the role of nonlinearities and elastic instabilities in engineering science and applied physics. Traditionally viewed as unwanted aberrations, when controlled to be reversible and well behaved, nonlinearity can enable novel functionalities, such as shape adaptation and energy harvesting. The analysis and design of novel structures that exploit nonlinearities and instabilities have, in part, been facilitated by advances in numerical continuation techniques. An experimental analogue of numerical continuation, on the other hand, has remained elusive. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points over the test specimen. This approach fails at limit points in the control parameter, as the immediate equilibrium beyond limit points is statically unstable, causing the structure to snap to a different equilibrium. Here, we propose a quasi-static experimental path-following method that can continue along stable and unstable equilibria, and traverse limit points. In addition to controlling the displacement at the main load-introduction point, the technique relies on overall shape control of the structure using additional actuators and sensors. The proposed experimental method enables extended testing of the emerging class of structures that exploit nonlinearities and instabilities for novel functionality.

Spatial chaos as a governing factor for imperfection sensitivity in shell buckling.

Shell buckling is known for its extreme sensitivity to initial imperfections. It is generally understood that this sensitivity is caused by subcritical (unstable) buckling, whereby initial geometric imperfections rapidly erode the idealized buckling load of the perfect shell. However, it is less appreciated that subcriticality also creates a strong proclivity for spatially localized buckling modes. The spatial multiplicity of localizations implies a large set of possible trajectories to instability-also known as spatial chaos-with each trajectory affine to a particular imperfection. Using a toy model, namely a link system on a softening elastic foundation, we show that spatial chaos leads to a large spread in buckling loads even for seemingly indistinguishable random imperfections of equal amplitude. By imposing a dominant imperfection, the strong sensitivity to random imperfections is ameliorated. The ability to control the equilibrium trajectory to buckling via dominant imperfections or elastic tailoring creates interesting possibilities for designing imperfection-insensitive shells.

Bespoke extensional elasticity through helical lattice systems.

Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ϵ > 0, we construct a system whose energy is approximately E up to an additive constant, with L∞-error no more that ϵ. The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability.

Shape Control for Experimental Continuation.

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasistatically. The technique involves loading a structure by the application of either a force or a displacement at a main actuation point while simultaneously controlling the overall shape using additional bidirectional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental-as opposed to numerical-continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.

Adaptive compliant structures for flow regulation.

This paper introduces conceptual design principles for a novel class of adaptive structures that provide both flow regulation and control. While of general applicability, these design principles, which revolve around the idea of using the instabilities and elastically nonlinear behaviour of post-buckled panels, are exemplified through a case study: the design of a shape-adaptive air inlet. The inlet comprises a deformable post-buckled member that changes shape depending on the pressure field applied by the surrounding fluid, thereby regulating the inlet aperture. By tailoring the stress field in the post-buckled state and the geometry of the initial, stress-free configuration, the deformable section can snap through to close or open the inlet completely. Owing to its inherent ability to change shape in response to external stimuli-i.e. the aerodynamic loads imposed by different operating conditions-the inlet does not have to rely on linkages and mechanisms for actuation, unlike conventional flow-controlling devices.

Shape morphing Kirigami mechanical metamaterials.

Mechanical metamaterials exhibit unusual properties through the shape and movement of their engineered subunits. This work presents a new investigation of the Poisson's ratios of a family of cellular metamaterials based on Kirigami design principles. Kirigami is the art of cutting and folding paper to obtain 3D shapes. This technique allows us to create cellular structures with engineered cuts and folds that produce large shape and volume changes, and with extremely directional, tuneable mechanical properties. We demonstrate how to produce these structures from flat sheets of composite materials. By a combination of analytical models and numerical simulations we show how these Kirigami cellular metamaterials can change their deformation characteristics. We also demonstrate the potential of using these classes of mechanical metamaterials for shape change applications like morphing structures.

CARAPACE: a novel composite advanced robotic actuator powering assistive compliant exoskeleton: preliminary design.

A novel actuator is introduced that combines an elastically compliant composite structure with conventional electromechanical elements. The proposed design is analogous to that used in Series Elastic Actuators, its distinctive feature being that the compliant composite part offers different stable configurations. In other words, its elastic potential presents points of local minima that correspond to robust stable positions (multistability). This potential is known a priori as a function of the structural geometry, thus providing tremendous benefits in terms of control implementation. Such knowledge enables the complexities arising from the additional degrees of freedom associated with link deformations to be overcome and uncover challenges that extends beyond those posed by standard rigidlink robot dynamics. It is thought that integrating a multistable elastic element in a robotic transmission can provide new scenarios in the field of assistive robotics, as the system may help a subject to stand or carry a load without the need for an active control effort by the actuators.