Elastic Hinges Research Articles

Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model

We present a numerical framework bringing together a structural and a surface-energy minimization model to compute nano- and microorigami self-folding processes, that are three-dimensional in nature. A liquid drop, initially at rest on the template, triggers the spontaneous folding and deforms dynamically with the template. As application, the self-folding of thin two-dimensional templates into pyramidal microstructures is simulated. Each template is composed of a fixed regular base connected to rigid triangular side panels by two elastic hinges. We presently determine the condition, at which the transition from partial to full drop encapsulation occurs. The present model makes use of phase fields to numerically represent the drop and the template. This allows to: (i) develop an efficient computational method, which incorporates time-derivative terms and (ii) study three-dimensional complex self-folding processes.

Stowage Analysis of a Flat Flexure Elastic Hinge for Deployable Space Structures

This paper introduces a design framework for elastically deformable hinges consisting of two parallel flat flexures, focusing on the case where the hinge is folded by 180 deg in the stowed configuration. The authors first consider architectures in which the flexures are staggered to avoid contact so that they can be modeled independently using Euler’s elastica. They next focus on the nonstaggered case when folding can result in contact between the flexures, which they study through finite element simulations. The paper provides a set of design guidelines by rationalizing the relationship between hinge dimensions and the allowable curvature in the flexure material. For most hinge geometries applicable to deployable structures, the authors find a simple requirement for the minimum flexure length as a function of the allowable curvature in the material, Lh>10.7/κm. Their analysis also provides insight into the reaction forces necessary to keep the hinge in the folded configuration, which is useful in determining the deployment dynamics and the constraints necessary to secure the panel in place during stowage. Experimental prototypes show good agreement with the numerical predictions.

From elastic shallow shells to beams with elastic hinges by Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence

In this paper, we study the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with “smooth” solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam.

The bismar scale and elastic collisions: a geometrical analogy

Throughout history, scales have served as instrumental tools for quantifying the weight of objects, relying on a comparative assessment against a specified reference weight. Scales featuring uneven arms, such as the bismar scale, have proven particularly adept at gauging masses within a specific range relative to a predetermined reference mass. On the other hand, the kinematics of elastic collisions hinge on the inertial masses of the colliding entities. By observing the aftermath of a collision between a known reference mass and an object of unknown mass, one can deduce the latter’s mass. In this contribution, we highlight a fascinating and clear analogy between these two methodologies. We do so by adapting a geometric approach, initially applicable to the bismar scale, to both non-relativistic and relativistic elastic collisions, encompassing phenomena such as Compton scattering.

Modeling method study for transfer matrix of space rigid bodies supported by multiple elastic hinges

When rigid bodies as well as elastic hinges connected are modeled by using a transfer matrix method, they need to be defined as multi-input and multi-output space rigid bodies, resulting in higher dimensions of the whole transfer matrix and complexity of modeling. To reduce the dimensions of the whole matrix and improve computational efficiency and accuracy, the elastic hinges and the rigid bodies are integrated into a unified model in this paper. Then a single 12×12 matrix is obtained through theoretical derivation. The resulting transfer matrix of space rigid bodies supported by multiple elastic hinges not only reduces the dimensions of the whole matrix but also simplifies the configuration of the transfer matrix model by which some tree-like systems can be simplified into chain-like systems. Subsequently, the effectiveness of the matrix is validated through computational comparative analysis of typical systems. The modeling method is an important optimization to the calculation method of the dynamics characteristics of the transfer matrix.

Vehicle suspension based on torsion bar and elastic hinge

The article is devoted to the development of a vehicle suspension with a nonlinear characteristic based on a torsion bar and an elastic hinge with a given characteristic on the example of tracked vehicles for constructing oil and gas pipelines. The characteristic of the elastic hinge is such that when the existing torsion bar suspension and the elastic hinge are connected in parallel, the desired characteristic is obtained. For this non-linear characteristic in the static displacement region, low stiffness was obtained, but the total stored energy at the maximum deflection of the balance bar of the resulting suspension is greater than that of existing torsion suspensions. The smoothness of the tracked vehicles with a low stiffness of the suspension increases significantly. The calculation of vibrations of the proposed suspension under kinematic excitation was carried out. A harmonic function is considered as the trajectory of the profile; a function corresponding to a single obstacle and a function corresponding to an ascent to a ledge of a given height. The elastic hinge is a pneumatic spring moving between the guides of the design form. The force characteristic of the hinge depends on the shape of the guides and on the pressure in the air spring. The calculation of the circular shapes of the guides of the elastic hinge is given. The values of the forces arising between the pneumatic spring and the guides are determined.

Asymmetric flapping of a multi-segmented elastic structure

Motivated by the propulsion of animals using articulated bodies, this study experimentally investigates the deformation and torque generation of a multi-segmented structure undergoing flapping motion. The segmented structure consists of multiple rigid segments connected in a line through elastic sheets functioning as elastic hinges. To enhance the asymmetry in the deflection of the segmented structure between the power and recovery strokes, the elastic hinges are designed to bend only one way from their original position. To characterize the deflection profile of the segmented structure, new definitions are proposed for the effective bending stiffness of the entire structure and the dimensionless speed representing the relative magnitude of the fluid force acting on the structure to its internal bending force. These two quantities are used to determine the tip deflection adjusted by the discrete profile. Two typical deflection responses during the recovery stroke are identified, namely, an in-phase response and a delayed response. The difference in these deflection responses causes substantial changes in torque and thrust generation, particularly during the early stage of the subsequent power stroke. An evaluation of the torque and thrust generation performance, in terms of the net cyclic value and the degree of asymmetry between the two strokes, reveals the optimal model design and operation conditions of the segmented structure.

Micro-CT driven characterization and validation of constituents’ properties used in origami-inspired foldable composites fabricated via different manufacturing processes

High packaging efficient lightweight jointless deployable folding structures are nowadays fabricated from combination of rigid and thin flexible elastic hinges using fiber reinforced polymers composites (FRPCs) for various applications such as space, robotics, flexible electronics, etc. It is of high importance to optimize these structures in the design phase using computer aided analysis tools for which the structural-level elastic constants are challenging to find experimentally. In this work, a generic X-ray computed tomography (micro-CT) driven framework based on voxel modeling approach was developed to virtually characterize the smallest building block of a typical large-scale foldable structure that consists of a rigid region and elastic hinge needed for folding operation. The voxel-based description of a real representative volume element (RVE) was generated using the images obtained from the micro-CT. The homogenized mechanical properties for each of the material systems was then obtained by multi-parameter component segmentation and subsequent directional averaging of the corresponding voxels. Three-dimensional void analyses were also shown using the micro-CT based voxel modeling. The accuracy of the non-destructive framework was demonstrated for four materials systems, based on different combinations of the matrix and fabric architectures in comparison with the mechanical tests. The homogenized mechanical properties obtained using the present framework based on the real RVE showed good agreement with the experimental results providing a foundation for a structural-level computer aided analysis.

Design and experiment of a new double needle type piezoelectric jetting dispenser

To improve the performance of piezoelectric (PZT) jetting dispensers in the electronic packaging industry and address the problems of oversized, easily fatigued elastic hinges and low repetition accuracy of conventional PZT jetting dispensers with a compliant mechanism-based lever, a new double needle PZT jetting dispenser prototype was developed. The advantage of the proposed structure over compliant mechanism-based lever was demonstrated by dynamics analysis. Firstly, the design stroke of the needle and the modal state of the dispenser body were analyzed using ANSYS. Secondly, the theoretical model of adhesive injection was established, the fluid pressure change process inside the nozzle during the working cycle of the jetting dispenser was simulated using Fluent, and the effects of the supply pressure and needle stroke on the injection speed of the droplet were investigated. Finally, a test bench was built to conduct the experiment, and the results showed that the supply pressure and the driving signal duty cycle between 20% and 80% were positively correlated with the size of droplet diameter, whereas the driving signal frequency was negatively correlated with the droplet diameter, thereby validating the proposed adhesive injection model. Under the experimental conditions, the highest operating frequency of the designed PZT jetting dispenser was 400 Hz, which is close to the high-frequency level of existing studies, and the minimum droplet diameter obtained was 0.36 mm, which is 0.1–0.2 mm less than that of the existing PZT jetting dispenser with a compliant mechanism drive, meeting the industry requirements for the working performance of a PZT jetting dispenser.

Deployment analysis of a composite thin-walled toroidal rim with elastic hinges: Application to an umbrella-type reflector of spacecraft antenna

Deployment analysis of a composite thin-walled toroidal rim with elastic hinges: Application to an umbrella-type reflector of spacecraft antenna

The theoretical and experimental basis for calculating and justifying the parameters and regimes of the working areas of the cleaning zone of fibrous materials

In the article, there is the scheme and principle of the work of the cotton cleaner from small litter includes a composite pin drum with elastic elements and a vibrating mesh surface on elastic hinges. Theoretically, the torsional-vibrational motion of a two-mass system of a composite shoe drum has been studied, and the regularities of the dependence of changes in the parameters of the pin drum have been obtained. Based on the approximate analytical solution of the integro-differential equation, the law of angular vibrations of the net surface on the elastic supports of the cotton cleaner is studied. Experimental studies revealed regularities of loading and a change in the speed of rotation of the drum. The results of the full-factor experimental studies of the sample of the composite fluke drum are given. Based on the study of each of the three factors on the changes in the cleansing effect of cotton, the graphical dependencies of the parameters are postrene. The best values of the factors at which a high purifying effect of cotton from small weeds are achieved are recommended. Production tests revealed that the cleaning effect in comparison with the existing version of the drum spindle in the recommended increases by an average of 2.7%.

A Simplified Method to Analyze Dynamic Response of VLFS Based on the Kane Method

Abstract A two-dimensional (2D) simplified model of the very large floating structure (VLFS) is formulated based on Huston's interpretation of the Kane methodology. In this proposed model, the VLFS is considered as a series of discrete floating bodies connected by elastic hinges. The rotation stiffness of elastic hinges has a great influence on the dynamic responses of VLFS and its value is determined based on the vertical displacements equivalent between the simply supported beam model and the elastically hinged multiple bodies model with the same boundary conditions on a concentrated load. Reduced Kane equations are used in the actual dynamic analysis, once initial conditions and mechanical analysis of the system have been formulated. Validation of the Kane-based method and the reliability of the corresponding program developed are established by several comparative studies on a continuous structure and a hinged structure with three parts. The predictions based on the proposed method are essentially identical to the model test data and calculation results provided by related literature.

Development of a two-step stylus with elastic hinge for microstructure measurement to improve sensitivity and vibration characteristics

In recent years, there has been an increasing demand for measuring a small hole with a diameter of 10 μm or less. Many micro coordinate measuring machines (micro CMMs) have been developed so far. However, as the diameters of these probes decrease below 10 μm, the rigidity of the probe decreases, making it difficult to detect contact between the stylus tip and the measured surface. For the same reason, the stylus with large aspect ratios cannot be used. Therefore, we have been developing a measurement system using an optical fiber as a stylus to measure microstructures with low measurement force. In this research, we proposed the two-step plus hinge stylus with a diameter less than a few μm to improve sensitivity and vibration characteristics. The design parameters of the stylus were simulated by the finite element method, and the results of the actual examination are summarized as follows. The simulation results using the finite element method indicate that the contact sensitivity was improved from 17% for the standard stylus to 37% for the two-step plus hinge stylus. The experimental results indicate that the contact sensitivity was improved from 17% for the standard stylus to 35% for the two-step plus hinge stylus. The results of the stylus stability evaluation experiment showed that the maximum fluctuation of the standard stylus is approximately 1 μm, and that of the two-step plus hinge stylus is approximately 0.05 μm, which confirms that the use of a two-step plus hinge stylus can improve vibration characteristics. The performance of this stylus was evaluated by measuring the micro hole with a diameter of 7 μm. The repeatability of each measurement point was approximately 50 nm.

Rolled Dielectric Elastomer Antagonistic Actuators for Biomimetic Underwater Robots.

In this study, an antagonistic actuator using dielectric elastomer actuators (DEAs) is developed to investigate the use of rolled DEAs in underwater robots. The actuator consists of a backbone, an elastic hinge, and two rolled DEAs placed in an antagonistic fashion, allowing for the generation of bidirectional movements of the actuator tip. To prove this concept, an analytical model of the actuator is built. The experimental samples are fabricated based on the specification determined by the model. In the fabricated actuator, each rolled DEA has a diameter of 6 mm and a length of 21 mm. The whole device weighs 1.7 g. In the tested voltage range of 0-1200 V, the actuator exhibits a voltage-controllable angle and torque of up to 2.2° and 11.3 mN∙mm, respectively. The actuator is then implemented into a swimming robot, which shows forward speed of 0.9 mm/s at the applied voltage of 1000 V and the driving frequency of 10 Hz. The results demonstrate the feasibility of using rolled DEAs in underwater robots.

Research on vibration characteristics of aircraft based on MSTMM

The vibration seriously affects the safety and stability of aircraft in flight. With the increase of slenderness ratio of aircraft, the bending stiffness and natural frequency of transverse vibration are gradually decreasing. In this paper, the aircraft dynamics model is established by using MSTMM. The aircraft body is equivalent to Euler-Bernoulli beams with variable cross sections, the rudder system is equivalent to a rigid body, and the connecting part between these is regarded as a space elastic hinge. The overall transfer equation, overall transfer matrix and characteristics equation of the aircraft are derived. The vibration characteristics of aircraft with tail axial thrust in flight are calculated. The correctness of results is verified by the finite element software and show that thrust has a great influence on the vibration characteristics of aircraft. This paper provides an effective method for calculating the vibration characteristics of aircraft.

Free vibrarion characteristics of a ship's power-transmission-propulsion system based on MSTMM

The power-transmission-propulsion system is the core moving component of a ship. In many cases, its vibration is a serious problem, which destroys the stability of the shafting operation and weakens the concealment of the ship. Free vibration characteristics analysis is the basis to investigate the dynamic characteristics of the ship's power-transmission-propulsion system. When the exciting force frequency of the propeller or engine is close to the natural vibration frequency of the systems, resonance will occur and cause catastrophic damage. MSTMM is an unusual modelling strategy for linear multi-body dynamics systems. However, it can deal with large-scale complex rigid-flexible coupling systems but also take into account computational efficiency. Due to the above advantages, the present paper used the automatic derivation theorem to establish the dynamic model, topology, overall transfer equation and characteristic equation for the typical ship power-transmissionpropulsion systems based on MSTMM and ML-MSTMM, respectively. The dynamic model is quite simplified in that the transmission shaft's rotation and the hull's added mass are not considered. The SVs at the boundary contains displacement, angle, moments and forces. The transfer matrices of a plane elastic hinge connecting two plane vibrating rigid bodies are derived. This paper solved the vibration characteristics by the recursive eigenvalue search algorithm. The correctness of the results obtained by MSTMM and ML-MSTMM is verified by comparison with each other.

Design and Prototyping of Biaxial Flexible Support Table for Fine Positioning Through Controlled Magnetic Attraction Forces

High-precision positioning can be obtained by reducing sliding friction and securing support rigidity. A prototype of a biaxial positioning table with non-contact drive by magnetic force and flexible mechanism support was developed to meet these requirements. The magnetic poles of a permanent magnet and an electromagnet were placed opposite to each other with an appropriate gap between them, and the attraction force between the two poles was used as the actuator for fine feed. The table was supported with a flexible mechanism composed of metal (A2017) beams with notches and elastic hinges assembled into a square frame shape. The permanent magnets were commercial neodymium magnets, and the electromagnets were self-made of S45C core bars. Two types of attraction force, maximum and minimum, were set depending on the number of neodymium magnets and the magnetic pole gap. The relationship between the applied current and attraction force for each type was calibrated using an electronic balance. Upon increasing and decreasing the applied current to the electromagnets, a linear relationship was shown between them. The relationship between the attraction force and the X- and Y-axes displacements was simulated by finite element analysis. Based on both results, the relationship between the applied current and displacement was estimated. The fine-feed experiment was conducted in both directions of the X- and Y-axes by applying current to electromagnets in a stepwise sequence. The displacements of total strokes in the long-stroke feed on applying the maximum attraction force were 340 μm and 315 μm for the X-axis and 160 μm and 133 μm for the Y-axis. These values are 2.0–2.8 times larger than the estimated displacement. Additionally, 3%–12% of the other axes interference occurred between the X- and Y-axes. In the high resolution feed applying the minimum attraction force, the displacement per step was 75 nm and 78 nm for the X-axis and 35 nm and 39 nm for the Y-axis. Cooperative feed with a combination of long stroke and high resolution was verified to be feasible.

Effective linear wave motion in periodic origami structures

We establish a dynamic homogenization framework catering for the linear elastic wave motion in periodic origami structures. The latter are modeled via “bar-and-hinge” paradigm where: (i) the folding of the structure and the bending of individual panels are modeled via elastic hinges, and (ii) the in-plane deformation of each panel is modeled with elastic bars. Using the so-formulated discrete model of an origami structure, we pursue finite wavenumber-finite frequency (FW-FF) homogenization of the wave motion in a spectral neighborhood of simple, repeated, and nearby eigenfrequencies at an arbitrary wavenumber within the first Brillouin zone. The lynchpin of the proposed approach is the “projection” of the nodal displacements over each unit cell onto a suitable Bloch eigenvector, evaluated at the “center” of the spectral region of interest. For completeness, we make an account for: (i) the source term acting at the nodes of a discrete structure, and (ii) periodic Dirichlet boundary conditions. We obtain the leading-order (system of) effective equation(s) synthesizing the wave motion in a selected spectral neighborhood, and we describe asymptotically the corresponding dispersion relationship. We illustrate the proposed framework by comparing numerically the Bloch dispersion relationship to its asymptotic approximation for (a) a 2D-periodic Miura-ori structure, and (b) a 1D-periodic Miura tube. The dispersion analysis is complemented by evaluating the effective wave motion (in terms of both “macroscopic” and “microscopic” essentials) in a 2D-periodic Miura-ori structure due to spatially-localized source term acting either inside a band gap or within a passband.

Umbrella meshes

We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.

Исследование устойчивости систем с сосредоточенными параметрами на основе критерия критических уровней энергии

The article analyses the stability of systems with lumped parameters from the standpoint of the criterion of critical energy levels. Until now, there is no consensus both on the reasons for the manifestation of the buckling of the deformation form in building structures, and on the formulation of criteria that determine the critical state. Most often in structural mechanics and the theory of stability of structures, energy criteria are used in the form of Timoshenko and Brian. Despite the simplicity of the formulation of the first criterion and the generality of the second, it is difficult to assert that they can cover the entire spectrum of stability problems that arise in technology. The criterion of critical energy levels allows one to set and solve stability problems without restrictions on the smallness of displacements, the type of impact on the system, and is intended for formulating boundary states. To understand the essence of the mentioned criteria and to illustrate the differences, simple problems are proposed in the form of systems with lumped parameters with several degrees of freedom. The design research technique is illustrated by the example of a system model with lumped parameters in the form of elastic hinges. Energy relations are given that describe the state of the system at critical energy levels. The results obtained for critical internal forces coincide with the values of external critical loads known from the literature, which confirms the well-known fact of the theory of eigenvalue problems that the branch points of the solution coincide in linear and nonlinear formulations. A technique for determining the values of the deviation angles of the system elements in elastic hinges is shown. A comparison is made of the rotation angles of the system elements in the formulation of the problem in a linear (infinitely small deviation angles) and non-linear formulation.