Low Flexural Rigidity Research Articles

Controllable Multimodal Actuation in Fully Printed Ultrathin Micro-Patterned Electrochemical Actuators.

Submillimeter or micrometer scale electrically controlled soft actuators have immense potential in microrobotics, haptics, and biomedical applications. However, the fabrication of miniaturized and micropatterned open-air soft actuators has remained challenging. In this study, we demonstrate the microfabrication of trilayer electrochemical actuators (ECAs) through aerosol jet printing (AJP), a rapid prototyping method with a 10 μm lateral resolution. We make fully printed 1000 × 5000 × 12 μm3 ultrathin ECAs, each of which comprises a Nafion electrolyte layer sandwiched between two poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) electrode layers. The ECAs actuate due to the electric-field-driven migration of hydrated protons. Due to the thinness that gives rise to a low proton transport length and a low flexural rigidity, the printed ECAs can operate under low voltages (∼0.5 V) and have a relatively fast response (∼seconds). We print all the components of an actuator that consists of two individually controlled submillimeter segments and demonstrate its multimodal actuation. The convenience, versatility, rapidity, and low cost of our microfabrication strategy promise future developments in integrating arrays of intricately patterned individually controlled soft microactuators on compact stretchable electronic circuits.

Finite Element Analysis of the Effect for Different Thicknesses and Stitching Densities under the Low-Velocity Impact of Stitched Composite Laminates.

In this study, a progressive damage model was developed for the mechanical response and damage evolution of carbon fiber stitched composite laminates under low-velocity impact (LVI). The three-dimensional Hashin and Hou failure criteria were used to identify fiber and matrix damage. The cohesive zone model was adopted to simulate the delamination damage, combined with the linear degradation discounting of the equivalent displacement method to characterize the stiffness degradation of the material, and the corresponding user material subroutine VUMAT was coded. The finite element analysis of the LVI of stitched composite laminates under different energies was finished in Abaqus/Explicit. Furthermore, the simulation predictions matched well with the results of the experimental tests. Based on this, composite laminates' mechanical response and damage forms with different thicknesses and stitch densities were analyzed. The findings show that the main damages of composite laminates were matrix tensile damage and delamination. The stitching process could improve the impact tolerance of composite laminates, inhibiting delamination and reducing the area of the delamination damage. The higher the density of the stitching, the more noticeable its inhibition would be. The thickness of the laminate also had a more significant effect on the damage to the laminate. Thin plates were more prone to matrix tensile damage due to their lower flexural rigidity, whereas thick plates were more susceptible to delamination because of their higher flexural rigidity.

A high-eigenfrequency differential stiffness probe for high-speed scanning probe microscopy

Microcantilever probes used for high-speed scanning probe microscopy are typically required to satisfy two mutually contradicting objectives: high eigenfrequency ( ω n ) and low flexural rigidity ( k b ). The conventional design approach shortens the microcantilever’s length to increase the eigenfrequencies (as ω n ∝ 1 / L 2 ); however, this also increases the probe’s rigidity (as k b ∝ 1 / L 3 ). This paper demonstrates—through experiments and physical modelling—the design of a novel high-eigenfrequency probe by redistributing the microcantilever’s mass along its length. A 100% increase in the probe’s eigenfrequency is achieved with this modified design, even while reducing its stiffness by 50%. Through experiments, this reduced stiffness has been found to enhance the probe’s force sensitivity . Also, the probe’s design facilitates redistributing the fluid pressure between its underside surface and the sample, thereby improving the quality factor by more than 100%. Significant reduction in ‘overshoot’ and ‘parachute’ is observed in contact mode scanning at the video rate. The improvements in the image resolution are proven for a variety of sample surfaces at very high scan rates up to 40 Hz (corresponding to a linear speed of 3.20 mm s − 1 ) upon scanning over an area of 40 × 40 μ m and are successfully demonstrated to map topographies with negligible image artefacts.

Ultra-flexible semitransparent organic photovoltaics

Ultra-flexible organic photovoltaics (OPVs) are promising candidates for next-generation power sources owing to their low weight, transparency, and flexibility. However, obtaining ultra-flexibility under extreme repetitive mechanical stress while maintaining optical transparency remains challenging because of the intrinsic brittleness of transparent electrodes. Here, we introduce strain-durable ultra-flexible semitransparent OPVs with a thickness below 2 μm. The conformal surface coverage of nanoscale thin metal electrodes (< 10 nm) is achieved, resulting in extremely low flexural rigidity and high strain durability. In-depth optical and electrical analyses on ultrathin metal electrodes showed that the devices maintain over 73% of their initial efficiency after 1000 cycles of repetitive compression and release at 66% compressive strain, and the average visible light transmittances remain higher than 30%. To our knowledge, this is the first systematical study on mechanical behaviors of strain-durable ultra-flexible ST-OPVs through precise adjustment of each ultrathin electrode thickness toward the emergence of next-generation flexible power sources.

Influence of Printed Encapsulation Layer on the Mechanical Reliability and Performance of V₂O₅ Nanowires-Based Flexible Temperature Sensors

Nanowires (NWs) based sensors have been studied extensively to measure various physical, chemical, and biological parameters as their large surface-to-volume ratio leads to sensitive devices. Further, due to the low flexural rigidity of NWs, these sensors can be developed on ultra-flexible substrates. However, their performance often degrades after repeated mechanical deformations or when they are exposed to the different ambient environment. A well-thought-out device engineering step could resolve these issues. As a potential solution, the soft material-based encapsulation layers have been explored. These are suitable for most sensor types except the temperature sensors, where they reduce the efficiency of heat transfer. Addressing this issue, we present here vanadium pentoxide (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> ) NWs based temperature sensors with nanosilica/epoxy (NS/epoxy) based encapsulation layer. The encapsulation layer is selectively deposited with high resolution electrohydrodynamic printing. The comparison of non-encapsulated (N-ES) and encapsulated (ES) devices, after applied mechanical loadings (bending and twisting), shows a robust and reliable temperature sensing performance of the latter. This study shows how the sensing performance can be preserved and the lifetime of flexible temperature sensors elongated by using an encapsulation layer.

Optical Nanofiber Skins for Multifunctional Humanoid Tactility

Humanoid tactility has been boosting robotic intelligence in object recognition, dexterous manipulation, and human–robot interaction. For many artificial tactile sensors, especially those based on optical principles, inflexibility, bulkiness, and monomodality limit their potential to function as humanoid skins. Herein, by embedding lab‐made optical nanofibers (ONFs) into elastomeric films, soft, flexible, thin (around 500 μm, similar to human skin), and multimodal (force and thermosensitive) robotic skins are achieved. These superior characteristics arise from the low flexural rigidity and large evanescent field of ONFs, due to their subwavelength diameters (down to 450 nm). By tuning light wavelength, ONF diameter, and skin thickness, variable sensitivities and sensing ranges for both force and temperature are reported. Depending on different sensing requirements, special modules can be further assembled on the ONF skins for various surface properties, including hardness, texture, and thermal conductivity. The ONF skins can enable a commercial robot to emulate human behaviors, including adaptive grasping of flimsy objects, contactless temperature measurement, and even the perception of leaf veins. It is anticipated that these ONF skins could offer a unique solution in multiple intelligent systems such as robotics, prosthetics, human–machine interface and wearable devices.

Shear-coupling of graphene grain boundaries: Elementary mechanisms, effects of topology, and role of buckling

Engineering grain boundary structure is a promising method for rational control of the microstructure and mechanical properties of two-dimensional materials. In bulk materials, shear stresses can drive grain boundary migration through the dislocations in grain boundaries. However, while shear coupling of grain boundaries has been studied in bulk materials like nanocrystalline copper, its translation to two-dimensional materials where out-of-plane deformation can relieve in-plane shear is not yet established. We investigate how the low flexural rigidity of graphene effects shear coupled grain boundary motion using atomic scale simulations of flat and buckled grain boundaries. We define the coupling shear strain as the strain at which a grain boundary has advanced by one Burgers vector and is at equilibrium and the critical shear strain as the strain at which migration of the first dislocation in the grain boundary becomes thermodynamically favorable. We show that the out-of-plane deformation does not influence the coupling shear strain and is governed only by the grain boundary topology. While the critical shear strain is altered somewhat by the low flexural rigidity due to buckling induced softening, it is also still dominated by the grain boundary topology. Our atomic scale results are synthesized into two models that predict the coupling and critical shears.

Machined Surface Image Analysis for Process Instability Identification in Micromilling of Ti6Al4V

The low flexural rigidity of micro-end mill used in micromilling process undergoes catastrophic failure at low amplitude chatter and hence it is critical to identify the low amplitude chatter to produce the chatter free machined surfaces. An unfixing of the workpiece to identify the chatter by analyzing the power spectral density of machined surface topography alters the process set-up and even a minute change in workpiece surface flatness during re-fixing the workpiece lead to variation in depth of cut, which changes the precision of machined surface in micromilling process. Consequently, in the present work, an image analysis method has been proposed for machined surface analysis in micromilling of Ti6Al4V. Different statistical parameters like arithmetic gray level average value of the distribution of pixel intensities and optical parameter have been analyzed to detect the process instability. The estimated statistical parameters of the machined surface images for different process parameters has been compared with the measured surface roughness of the machined surfaces. The frequency spectrum analysis of the machined surface image analysis has also been carried out, which shows the distribution of pixel intensities at different frequencies. Arithmetic gray level average of pixel intensity of the machined surface image has been found to be decreasing with an increases of the roughness of the machined surface. The optical parameter of the machined surface increases with the increases of the roughness. The critical value of arithmetic gray level average of pixel intensity and optical parameter was found to be 148 and 0.36, respectively for chatter onset. The distribution of pixel intensity at different frequencies shows the diffused pattern of brightness of the pixel away from the center location in chatter dominant machining while the distribution of brightness of pixel was found to be circular in nature around the central spot in stable machining. The chatter and stable machining condition has also been verified with the vibration spectrum of the workpiece, where the vibration of the workpiece has been captured using accelerometer. The proposed image analysis method can further be used for online monitoring of machining process.

The effect of combined loading on the behavior of micropiled rafts installed with inclined condition

One of the major disadvantages of micropiles is their low lateral stiffness and flexural rigidity due to the small diameter. This limitation can be handled in current practice, by installing the micropile with inclined condition or providing a steel casing. Additional steel casings will increase the lateral load capacity of micropiles but increase the project cost as well. Thus, inclination of micropile which is relatively simple and cheap is recommended. In this paper, a comprehensive numerical analysis is conducted on the behavior of micropiled rafts installed with inclined condition under combined vertical and lateral loading. A FEM calibrated against full-scale axial and lateral field tests is used to conduct the analysis. The soil profile is soft clay soil underlain by a layer of dense sand. The study investigates the impact of several parameters which are as follows: magnitude of vertical loading, reinforcement type, inclination angle of micropiles, and number of inclined micropiles. The study reveals that increasing vertical loads causes continuous decrease in the lateral load capacity of micropiled rafts. When all micropiles installed are inclined, the positively inclined micropiles carry 79–86% of the total lateral load carried by micropiles, whereas the negatively inclined ones carry 14–21%. Inclined micropiles offer greater lateral load sharing ratio (αh) than that of vertical ones, largest at θ = 45°. The effect of micropile reinforcement on improving the lateral performance is low compared to the effect of micropile inclination angle.

Elasto‐Capillary Manipulation of Freestanding Inorganic Nanosheets: An Implication for Nano‐Manufacturing of Low‐Dimensional Structures

AbstractUltrathin inorganic nanosheets (e.g., 2D nanomaterials, thin films, etc.) have attracted tremendous research interest because of their unique properties and promising applications. However, because of their ultrathin thickness (&lt;100 nm) and low flexural rigidity, it is difficult to manufacture low‐dimensional structures using these nanosheets. In this work, the observation of an intriguing elasto‐capillary unfolding phenomenon is first reported which occurs on a variety of freestanding inorganic nanosheets floating on a liquid surface. Through theoretical modeling and experiments, it is demonstrated that one can easily unfold, re‐roll, and transport different kinds of nanosheets by tuning the interfacial properties of the liquid. As a result, one can assemble nanosheets on the liquid surface into small structures (e.g., heterogeneous scrolls, optical resonators) and/or transfer them out of the liquid surface onto other surfaces for the manufacturing of flexible devices. The outcome of this research paves the way for nano‐manufacturing of low‐dimensional structures with ultrathin inorganic nanosheets.

Ultra‐Thin and Conformable Electrodes Composed of Single‐Walled Carbon Nanotube Networks for Skin‐Contact Dielectric Elastomer Actuators

AbstractSkin‐contact dielectric elastomer actuators (DEAs) consisting of skin‐conformable, stretchable electrodes are fabricated using a roll‐to‐roll‐based gravure coating method. In this method, single‐walled carbon nanotubes (SWCNTs) are continuously applied on a free‐standing ultra‐thin film (nanosheet) of poly(styrene‐b‐butadiene‐b‐styrene) (SBS) to produce an SWCNT‐SBS nanosheet of 101‐nm thickness. After the first SWCNT coating, the SWCNT‐SBS nanosheet shows a Young's modulus (i.e., 80.9 MPa) comparable to that of the SBS film and a sheet resistance of 4.6 kΩ sq−1. Using the free‐standing SWCNT‐SBS nanosheets as electrodes, a ten‐layered DEA is fabricated without glue or dielectric elastomer precursors on three substrates with different stiffness, namely glass, Ecoflex 00–30, and a urethane elastomer model skin. The low flexural rigidity of the ten‐layered DEA (105 nN m) ensures conformability to the shape of an index finger. Application of an actuation voltage of 2100 V produces a two‐fold larger displacement of the DEA on the Ecoflex 00–30 substrate compared with that on the glass substrate. The ability of the DEA to conform to the surface of skin will enable its application in skin‐contact haptic devices.

Design and Analysis of Ultra-Precise Large Range Linear Motion Platforms Using Compliant Mechanism

Double parallelogram compliant mechanism (DPCM) is extensively used to obtain precise straight-line motion. Symmetric DPCMs, used previously, traverse a straight-line path without parasitic error when gravity vector is perpendicular to the plane of bending of beams. However, when gravity vector is either in line with beams (orientation B) or in the plane of bending of beams (orientation C), asymmetry in the loading causes undesired deviation from a straight-line path. This undesired deviation called parasitic error increases, especially in beams with relatively low flexural rigidity required to obtain larger displacements with low power actuators. This paper first characterizes parasitic error, in such cases, using large deformation analysis and further proposes novel ways to minimize it. A recently developed, chained beam constraint method is used to model, characterize, and optimize DPCMs. Optimized parameters are further validated by FEA and experiments. In orientation B, after implementing the proposed method, numerical analysis and experimental results show that the undesired parasitic error of 123 &#x03BC;m is drastically reduced to 2 &#x03BC;m and 6 &#x03BC;m, respectively. Moreover, systematic design procedure with corresponding graphs is presented to avoid modeling and optimization steps for a user-specific case. The proposed methods pave pathways to reducing the parasitic error during large-range motion using multiple orientations of DPCMs and thus make DPCMs more employable in several precision motion applications such as 3D optical scanners, 3D micro-printers, CMM probes, and microscopy stages.

Estimation of the critical buckling load of pile foundations during soil liquefaction

Buckling instability of slender piles may occur based on the effect of excessive axial loads acting on a pile with diminishing effective stress and shear strength owing to surrounding soil liquefaction. However, several guidelines for pile design often provide insufficient consideration of buckling failure, and it is significant to study the buckling failure of piles in liquefiable sites for the design and inspection of piles. In this paper, an efficient method of determining the critical buckling load of piles considering the material and geometric nonlinearities of piles based on the excess pore pressure distribution is proposed based on the beam-on nonlinear Winkler foundation (BNWF) model. Then, the method is verified and validated using results from centrifuge tests. Next, plots of the main effects and analysis of variance (ANOVA) were used for the sensitivity analysis of pile failure modes under axial loading. The initial imperfections and flexural rigidity of the pile have significant effects on the pile failure modes, and the pile is susceptible to buckling failure with low initial imperfections and flexural rigidity. Furthermore, the effects of the flexural rigidity of the pile, unsupported length ratio, initial imperfections, and degree of soil layer liquefaction on the critical buckling load of the pile in liquefiable soil are examined. The axial load-carrying capacity of the pile decreases with increasing initial imperfection amplitude, decreasing flexural rigidity of the pile, decreasing unsupported length ratio and severer degree of soil layer liquefaction. Finally, an estimating formula for predicting the critical buckling load of piles in liquefiable soil and an application example are presented.

Mechanical characteristics and comfort evaluation under pedestrian vertical excitation of a thin-walled cold-formed steel footbridge

Thin-walled cold-formed steel (TWCFS) structures have a great application prospect and are widely adopted in low-rise residential constructions due to great mechanical and economical properties. Since TWCFS member has low flexural rigidity and is hard to weld, it is rarely used in bridge engineering. In Poyang Lake Wetland of Jiangxi Province, China, a TWCFS footbridge was built. In this paper, Serial tests including static loading test, natural frequency test and pedestrian comfort test were conducted. At the same time, finite element analysis (FEA) models were built with Midas/Civil software. The data shows that although natural frequency is far greater than the range of pedestrian walking frequency and will not lead to the resonance of bridge, the peak acceleration under crowd load reflects poor pedestrian comfort. The structure was modified for improving pedestrian comfort and the results after modification verify that the comfort can be ensured.

Realizing Optoelectronic Devices from Crumpled Two-Dimensional Material Heterostructures.

Due to their high in-plane stiffness and low flexural rigidity, two-dimensional (2D) materials are excellent candidates for engineering three-dimensional (3D) nanostructures using crumpling. An important new direction is to integrate 2D materials into crumpled heterostructures, which can have much more complex device geometries. Here, we demonstrate phototransistors from crumpled 2D heterostructures formed from graphene contacts to a monolayer transition-metal dichalcogenide (MoS2, WSe2) channel and quantify the membrane morphology and optoelectronic performance. First, we examined the morphology of folds in the heterostructure and constituent monolayers under uniaxial compression. The 2D membranes relieve the stress by delaminating from the substrate and creating nearly periodic folds whose spacing depends on the membrane type. The matched mechanical stiffness of the constituting layers allows the 2D heterostructure to maintain a conformal interface through large deformations. Next, we examined the optoelectronic performance of a biaxially crumpled graphene-WSe2 phototransistor. Photoluminescence (PL) spectroscopy shows that the optical band gap of WSe2 shifts by less than 2 meV between flat and 15% biaxial crumpling, corresponding to a change in strain of less than 0.05%. The photoresponsivity scaled as P-0.38 and reached 20 A/W under an illumination power density of 4 μW/cm2 at 20 V bias, a performance comparable to flat photosensors. Using photocurrent microscopy, we observe that the photoresponsivity increases by only 20% after crumpling. Both the PL and photoresponse confirm that crumpling and delamination prevent the buildup of compressive strain leading to highly deformed materials and devices with similar performance to their flat analogs. These results set a foundation for crumpled all-2D heterostructure devices and circuitry for flexible and stretchable electronic applications.

Process Mechanics Based Uncertainty Modeling for Cutting Force Prediction in High Speed Micromilling of Ti6Al4V

High speed machining is essential to counter the low flexural rigidity of micro-end mill in micromilling process. High speed machining can excite the higher frequency modes and in addition, run-out is also amplified. These effects in high speed micromachining induces the uncertainty in cutting forces. The estimation of cutting coefficients without inclusion of uncertainty cannot give accurate values and hence, the predicted cutting force and machining stability using these cutting coefficient may not be accurate. In the present work, cutting coefficients have been determined using the Bayesian inference which includes the uncertainty in estimated cutting coefficients. Note that, estimated cutting coefficient independent of chip load and cutting velocity does not include the high speed micromachining mechanics like size effect. The cutting coefficients have been estimated as a function of cutting velocity and chip load in the present work. The segmented cutting coefficients for different ranges of cutting speed varying from 10000 rpm to 110000 rpm has been obtained as a non-liner function of chip load. Bayesian inference modelling for cutting coefficients has been carried out using the Metropolis-Hastings (MH) algorithm Markov Chain Monte Carlo (MCMC) method. The convergence of prior and posterior distribution has been verified using correlation and trace of samples used for sampling. The posterior distribution shows that there is a good fitting, which accurately predicts the mean of the cutting coefficients. Finally, predicted cutting coefficients have been compared with cutting coefficients obtained from the deterministic approach using least square method. The experimentally estimated cutting coefficients are found to be lying within the upper and lower limit of predicted cutting coefficients with Bayesian inference approach. The predicted cutting coefficients using Bayesian inference shows the deviation of 0.89% and 8.4% at 40000 rpm from experimentally obtained cutting coefficients for tangential and radial cutting coefficients, respectively. The experimental cutting force is found to be lying within the upper and lower limit of predicted cutting force with Bayesian inference based cutting coefficients fitting at 105000 rpm.

Cyclic Reversed Loading Test of Different Structural Beam-To-Column Connections in Assembled Steel Structure

Three new assembled connections between an I-section beam and I-section column were proposed in this paper. To investigate the aseismic behaviour of these assembled connections, four specimens under cyclic loading were tested. The test process of the specimens was recorded and analyzed. The hysteretic properties, failure mode, ultimate load, and ductility were studied. The test results show that the specimens with assembled connections have better ductility and bearing capacity than the specimen with a welding type connection. The specimen with an “L” shaped steel plate has a strong energy dissipation capacity but low flexural rigidity. If triangular stiffeners were added to the “L” shaped steel plate, the mechanical properties of the assembled connection would be substantially improved.

Highly Localized and Efficient Energy Harvesting in a Phononic Crystal Beam: Defect Placement and Experimental Validation

We study energy harvesting in a binary phononic crystal (PC) beam at the defect mode. Specifically, we consider the placement of a mismatched unit cell related to the excitation point. The mismatched unit cell contains a perfect segment and a geometrically mismatched one with a lower flexural rigidity which serves as a point defect. We show that the strain in the defect PC beam is much larger than those in homogeneous beams with a defect segment. We suggest that the defect segment should be arranged in the first unit cell, but not directly connected to the excitation source, to achieve efficient less-attenuated localized energy harvesting. To harvest the energy, a polyvinylidene fluoride (PVDF) film is attached on top of the mismatched segment. Our numerical and experimental results indicate that the placement of the mismatched segment, which has not been addressed for PC beams under mechanical excitation, plays an important role in efficient energy harvesting based on the defect mode.

Vibration control of bridges under simultaneous effects of earthquake and moving loads using steel pipe dampers

This study aims to develop a practical methodology based on the eigenfunction expansion method to assess the effects of simultaneous action of vertical earthquake excitation and moving vehicle loads in single-span and multi-span simply-supported bridges. While the effects of vertical earthquake ground motions are generally ignored in common design practice, it is shown that the influence of simultaneous vertical earthquake excitation and vehicle loads can considerably affect the structural response of the bridge, especially in near-field earthquakes with high amplitude vertical components. To address this issue, a novel vibration suppression system is proposed using steel pipe dampers and its reliability is investigated for a wide range of bridge flexural rigidity under seven different earthquake records. The results indicate that the proposed system can significantly (up to 75%) suppress the vertical vibrations generated in the bridge, especially for the systems with lower flexural rigidity. For the same maximum deflection limits, application of pipe dampers could reduce the required flexural rigidity of the bridge (up to 50%), and therefore, lead to more economic design solutions with lower structural weight.

Biohybrid Actuators Based on Skeletal Muscle-Powered Microgrooved Ultrathin Films Consisting of Poly(styrene-block-butadiene-block-styrene)

This paper describes a biohybrid actuator consisting of a microgrooved thin film, powered by contractile, aligned skeletal muscle cells. The system was made of a thermoplastic elastomer [SBS, poly(styrene-block-butadiene-block-styrene)]. We prepared SBS thin films with different thicknesses (0.5-11.7 μm) and Young's moduli (46.7-68.6 MPa) to vary their flexural rigidity. The microgrooves on the SBS thin film resembled the microstructure of the extracellular matrix of muscle and facilitated the alignment and differentiation of skeletal muscle cells. Electrical stimulation was applied to self-standing biohybrid thin films to trigger their contraction, enabled by the low flexural rigidity of the SBS thin film. Finite element model simulations were also examined to predict their contractile behavior. We achieved the prediction of displacements, which were rather close to the actual values of the SBS thin film: the discrepancy was <5% on the X axis. These results pave the way for in silico prediction of the contractile capabilities of elastomeric thin films. This study highlights the potential of microgrooved SBS thin films as ultraflexible platforms for biohybrid machines.