Curvature Model Research Articles

A 4D-Printing Inverse Design Strategy for Micromachines with Customized Shape-Morphing.

An active heterostructure with smart-response material used as "muscle" and inactive material as "skeleton" can deform over time to respond to external stimuli. 4D printing integrated with two-photon polymerization technology and smart material allows the material or characteristic distribution of active heterostructures to be defined directly at the microscale, providing a huge programmable space. However, the high degree of design freedom and the microscale pose a challenge to the construction of micromachines with customized shape morphing. Here, a reverse design strategy based on multi-material stepwise 4D printing is proposed to guide the structural design of biomimetic micromachines. Inspired by the piecewise constant curvature model of soft robot, a reverse design algorithm based on the Timoshenko model isdeveloped. The algorithm can approximate 2D features to a constant-curvature model and determine an acceptable material distribution within the explored printing range. Three Chinese "Long" (Chinese dragon heralds of good fortune) designed by the strategy candeform to the customized shape. In addition, a microcrawler printed using this method canimitate a real inchworm gait. These results demonstrate that this method can be an efficient tool for the action or shape design of bionic soft microrobots or micromachines with predetermined functions.

Bio-inspired skeletal model and kinematics of humanoid spine and ribs

Development of humanoids with human like range of motion for spine and torso is of great research interest. Present article covers the construction of the humanoid spine and ribs by considering spine as a hyper redundant mechanism with ribs attached in the thoracic region. To demonstrate the joints and motion characteristics, a thorough discussion of the biomechanical aspects of the spine is provided. A three-segment hyper redundant mechanism is utilised to imitate the human mimetic spine. The study considers flexion-extension and lateral bending motions of the spine. In the proposed formulation, a piecewise constant curvature approximation could simulate spine motion during flexion-extension movement. A simplified configuration with each section of spine controlled by two cables for flexion-extension and two cables for lateral bending is adopted. Additionally, a three dimensional CAD model of proposed system is developed and simulated using ADAMS. The constant curvature model and ADAMS simulation results closely match the human range of motion.

Development of a Novel 4-DOF Flexible Endoscopic Robot Using Cable-Driven Multisegment Continuum Mechanisms

Abstract This paper presents the design, analysis, and development of a novel four degrees of freedom (4-DOF) endoscopic robot with cable-driven multisegment flexible continuum mechanisms. The endoscopic robot is mainly composed of the passive positioning arm, cable-pulley system, and 3-DOF flexible continuum mechanism. The forward and inverse kinematics of the endoscopic robot are derived based on the constant curvature assumption, and its working space, flexibility, and preoperative incision determination method are analyzed as well. Based on the hardware structure of the robot system, a control strategy and a control software are developed, and the continuum mechanism is kinematically calibrated to carry out the trajectory planning experiment and simulated surgery experiment. The experimental results show that the calibrated constant curvature model can be used for the motion control of the continuum mechanism, and the 4-DOF endoscopic robot can meet the visual field requirements of minimally invasive surgery.

Atmospheric-pressure shock-tube measurements of high-temperature propane laminar flame speed across multiple equivalence ratios

Laminar flame speeds of premixed propane in 21%O2-79% Ar (so-called ”airgon”) were experimentally measured in a shock tube at atmospheric pressure (1 atm±2%) for a range of equivalence ratios (0.5, 0.75, 1, and 1.2) and unburned-gas temperatures (644–1,044 K). Simultaneous side-wall schlieren and end-wall CH* emission imaging was utilized to track the propagation of outwardly expanding laminar flames initiated by laser-induced spark ignition behind reflected shock waves. The linear curvature model with an area-averaged formulation was used to extrapolate laminar flame speeds to zero-stretch. The high-temperature laminar flame speed results were compared with 1D simulations performed using two detailed kinetic models, NUIG 1.3 and Aramco 3.0, and two skeletal models, USC Mech II and San Diego 2016. The experimental results agree with the NUIG 1.3 model within 3.5%, while the predictions of the models disagree by up to 16%. Sensitivity analyses conducted using the models revealed six chemical reactions that strongly impact the prediction of laminar flame speed. In order for the present data to be compatible with practical combustion systems using air as the oxidizer, the propane/airgon measurements were scaled to obtain laminar flame speeds of propane/air using ratios calculated from 1D simulations. The scaled experimental measurements showed good agreement with literature propane/air results at 650 K. Empirical correlations of laminar flame speed as a function of unburned-gas temperature are then reported for the studied equivalence ratios.

Fragranced consumer products: Formulation practices, related models, and recommendations to enable wider hydrophilic–lipophilic difference (HLD) application

AbstractFragrances in consumer products are essential for appeal and market success. However, creating optimal stable formulas are especially challenging due to the polar nature of many fragrance ingredients. This perspective discusses how fragrances are currently dealt with within the industry, current surfactant and solvent models, and the barriers that today's industrial practice that prevent advancement to modeling and simulation. Recommendations for chemical suppliers, fragrance houses, and formulators are made regarding the implementation of the Hydrophilic‐Lipophilic Difference with Net Average Curvature (HLD‐NAC) model, which is the most comprehensive model for fragranced aqueous consumer products.

Physics-based generative model of curvature sensing peptides; distinguishing sensors from binders.

Proteins can specifically bind to curved membranes through curvature-induced hydrophobic lipid packing defects. The chemical diversity among such curvature "sensors" challenges our understanding of how they differ from general membrane "binders" that bind without curvature selectivity. Here, we combine an evolutionary algorithm with coarse-grained molecular dynamics simulations (Evo-MD) to resolve the peptide sequences that optimally recognize the curvature of lipid membranes. We subsequently demonstrate how a synergy between Evo-MD and a neural network (NN) can enhance the identification and discovery of curvature sensing peptides and proteins. To this aim, we benchmark a physics-trained NN model against experimental data and show that we can correctly identify known sensors and binders. We illustrate that sensing and binding are phenomena that lie on the same thermodynamic continuum, with only subtle but explainable differences in membrane binding free energy, consistent with the serendipitous discovery of sensors.

Restricted curvature model on a tetrahedral fractal substrate

Restricted curvature model on a tetrahedral fractal substrate

Numerical Simulation of Microstructure Evolution of Directionally Annealed Pure Iron by Cellular Automata

In order to understand the effects of drawing velocity, initial grain size and texture on the microstructure evolution during directional annealing, a cellular automata model based on grain boundary (GB) curvature, GB energy and GB mobility was established with a modified calculation model of the GB curvature. The simulation results show that there is a lower limit and an upper limit to the drawing velocity for the formation of columnar grains, and the columnar grains can only be formed between the upper limit and the lower limit. The simulation results are consistent with the experimental results. When the drawing velocity is lower than the lower limit, the equiaxed grains grow at the front of the hot zone, which hinders the formation of the columnar grains. With the increase of initial grain size, the driving force of GB migration decreases, and the grain boundaries are difficult to move with the hot zone, which is not conducive to the formation of columnar grains. There is an upper limit of initial grain size for the formation of columnar grains. The abnormal growth induced by texture prevents the growth of columnar grains during directional annealing. The weaker the texture strength, the more conducive to the growth of columnar grains.

Clathrin coats partially preassemble and subsequently bend during endocytosis.

Eukaryotic cells use clathrin-mediated endocytosis to take up a large range of extracellular cargo. During endocytosis, a clathrin coat forms on the plasma membrane, but it remains controversial when and how it is remodeled into a spherical vesicle. Here, we use 3D superresolution microscopy to determine the precise geometry of the clathrin coat at large numbers of endocytic sites. Through pseudo-temporal sorting, we determine the average trajectory of clathrin remodeling during endocytosis. We find that clathrin coats assemble first on flat membranes to 50% of the coat area before they become rapidly and continuously bent, and this mechanism is confirmed in three cell lines. We introduce the cooperative curvature model, which is based on positive feedback for curvature generation. It accurately describes the measured shapes and dynamics of the clathrin coat and could represent a general mechanism for clathrin coat remodeling on the plasma membrane.

A Simplified Method for Inverse Kinematics of a Flexible Panel Continuum Robot for Real-Time Shape Morphing

Continuum robots are good candidates for shape morphing. However, due to the coupled problem between kinematics and statics, the inverse kinematics of continuum robots is highly nonlinear, posing a challenging problem for real-time applications. This paper presents a simplified approach to solving the inverse kinematics of a flexible panel continuum robot efficiently. Through an experiment, two approximate relationships are discovered. First, the arc length of the middle backbone can be estimated from the arc lengths of the two panels; second, the length difference between the two panels can be related to the tip angle of the end-effector. Based on these two discovered relationships, a simplified inverse kinematics method is proposed based on a constant curvature model. This method has been validated by the experimental data with high accuracy of less than 2% error, thereby demonstrating the effectiveness of the proposed method for real-time applications.

Curvature and Bending Direction Error Correction Model of FBG Shape Sensor

Curvature and Bending Direction Error Correction Model of FBG Shape Sensor

Image denoising based on a new anisotropic mean curvature model

A number of variational models for image denoising have been proposed in the last few years in order to advance the denoising performance. To improve the denoising quality, it is very significant to describe the local structure of image in the proposed models. To this end, this paper proposes a novel denoising model which combines the gradient operator $ \nabla $ with the adaptive weighted matrix $ W $ in the mean curvature regularized term such that the proposed model can describe the local features in image efficiently. Since the proposed model is a high-order nonlinear and nonconvex optimization problem, we need to use the operator splitting method to tansform it into a multi-variable optimization problem and then the alternating direction method of multipliers (ADMM) can be applied to solve it. Numerical experiments demonstrate that the proposed model yields good performance compared with other well-known gradient-based models.

The Variation of Surface Shape in the Gas Jet Forming

This study investigated the the gas jet forming process for optical aspherical mirror blanks. The trend of the influence of the gas jet parameters on the surface shape of the mirror blanks was inferred by analysing the variation in the morphology of the gas jet stream. Based on the theoretical analysis, the inference was verified by numerical simulation. The experimental results were compared with the simulation predictions, and it was found that the average prediction deviation for the diameter was 1.07 mm, while the average prediction deviation for the principal curvature was 0.03665 mm−1, which is challenging to correct in simulation. Therefore, we developed a dimensionless prediction model of the surface curvature and surface diameter of the mirror blanks by considering the jet parameters using experimental data. The model’s average prediction error for the surface diameter of the formed surface was 0.3192 mm, and the average prediction error of the principal curvature for the formed surface was 0.00269 mm−1.

The characteristic curvature (Cc) definition and its use in assessing Cc for single ionic surfactants

AbstractThe hydrophilic–lipophilic‐difference (HLD) is a set of empirical equations that correlate the formulation conditions at phase inversion (HLD = 0). Based on partition studies for nonionic surfactants, the HLD can be interpreted as a normalized chemical potential difference between the surfactant dissolved in water and oil. The net‐average curvature (NAC) model extrapolates this interpretation into a curvature form that has been used to fit and predict the phase behavior of surfactant‐oil–water (SOW) systems. The curvature interpretation led to renaming the HLD surfactant parameter, sigma (σ), as the characteristic curvature (Cc). This work tests the validity of the curvature interpretation of the HLD, and the Cc concept, for single ionic surfactants and the use of this concept as a method to assess the Cc without the use of reference surfactants or alcohols. To this end, the net curvature of six anionic and two cationic surfactants was evaluated from solubilization data at the characteristic condition of 25°C, no added cosolvent, in the presence of an oil mixture with equivalent alkane carbon number (EACN) of zero, and as a function of salinity. These studies showed that the original HLD equation for ionic surfactant could not be interpreted as chemical potential or curvature because a salinity prefactor (coefficient) “bi” was missing. The revised equation, HLDbi = bi∙ln(S)‐kbi∙EACN+Ccbi ‐aTbi∙(T‐25°C), could now be interpreted as a curvature expression, and it was demonstrated that Cc could be obtained from curvature using the expression Cc = Ccbi/bi. This single surfactant method produces uncertainties that, for most surfactants, ranged from 0.2 to 1 Cc units, similar to the uncertainty obtained with the conventional method of Cc determination using mixtures of test and reference surfactants.

Manipulated deformation of lipid bilayer vesicles in magnetic fields

ABSTRACTWe have extended the Helfrich’s spontaneous curvature model of the equilibrium vesicle by adding the interaction between magnetic field and the constituent molecules to supply an explaination in principle of the emerging manipulated deformation of a magnetic vesicles such as the reversibly deformation of artificial stomatocyte. The small deformation can be measured by birefringence. Here, we present the derivations of formulas in detailed to reveal the perturbation of deformation ψ under two cases. New features, for example, a ‘phase transition’ of shape will occur with increasing of B from B1∗ to B2∗ for Δχ<0, in which the major axis of ellipse was rotated by 90°, have been revealed. It is worthy for experimenter to demonstrate the ‘phase transition’. The significance of imaginary relation (B1∗<B<B2∗) is also waiting to be uncovered.

Challenges in modeling microemulsion phase behavior

AbstractModeling the complex phase behavior of microemulsions has been the subject of research for decades for hydrocarbon oil and organic contaminant recoveries. The empirical Hand model has been the standard scheme for calculating phase behavior in reservoir simulators. On the other hand, the hydrophilic–lipophilic deviation (HLD) model in conjunction with the net curvature and average curvature models (HLD‐NAC) has provided some theoretical basis for modeling microemulsions. While the HLD‐NAC has been successful in describing salinity scans, only recently an HLD‐NAC approach was devised that could represent binodal curves with physical behavior, resulting in a succession of new microemulsion flash algorithms. While these new algorithms claimed to include the effects of cosolvent, there are only few works in the literature, which give an in‐depth description of the cosolvent modeling. Furthermore, to the best of our knowledge, no work has investigated the capability of HLD‐NAC models for predicting data for different cosolvent concentrations nor did any work present a comprehensive study of the application of HLD‐NAC against Hand model for formulations including cosolvents. This paper aims to contribute in filling such gap. We modify different versions of the new HLD‐NAC approach with physical binodal curves by providing more flexibility into controlling the binodal heights with the cosolvent concentration and investigate how well they can calibrate and predict data. Experimental data sets were considered here. The results suggest that some of the HLD‐NAC approaches produced negative solubilization ratios and the Hand model gave better predictions of the ternary diagram for extreme salinity values.

Comparison of Modern Control Methods for Soft Robots

With the rise in new soft robotic applications, the control requirements increase. Therefore, precise control methods for soft robots are required. However, the dynamic control of soft robots, which is required for fast movements, is still an open topic and will be discussed here. In this contribution, one kinematic and two dynamic control methods for soft robots are examined. Thereby, an LQI controller with gain scheduling, which is new to soft robotic applications, and an MPC controller are presented. The controllers are compared in a simulation regarding their accuracy and robustness. Additionally, the required implementation effort and computational effort is examined. For this purpose, the trajectory tracking control of a simple soft robot is studied for different trajectories. The soft robot is beam-shaped and tendon-actuated. It is modeled using the piecewise constant curvature model, which is one of the most popular modeling techniques in soft robotics. In this paper, it is shown that all three controllers are able to follow the examined trajectories. However, the dynamic controllers show much higher accuracy and robustness than the kinematic controller. Nevertheless, it should be noted that the implementation and computational effort for the dynamic controllers is significantly higher. Therefore, kinematic controllers should be used if movements are slow and small oscillations can be accepted, while dynamic controllers should be used for faster movements with higher accuracy or robustness requirements.

Fiber Bragg Grating-based sensor system for sensing the shape of flexible needles

Shape sensing is of importance for the manipulation of flexible needles. In this work, a 0.6 mm diameter stylet with five Fiber Bragg Gratings (FBGs) installed as triplets was designed and implemented and a novel model of local curvature was established. A gradient-based optimization method has been integrated into the complete algorithm for shape sensing and this was used to reduce the difference between the midpoint curvature and the mean curvature. The experimental results obtained show that the mean tip errors are 0.35 mm, 0.30 mm, 0.38 mm in the single-bending, double-bending and space-bending experiments, respectively. In a torsion test experiment which was performed, when the rotation angle of the tip was less than 25°, the error seen was less than 0.5 mm. Furthermore, when the needle designed in this work was used to puncture a 60 mm thickness, ex vivo biological tissue, the mean error of the measurement of the needle tip was 0.39 mm.

A systematic study on three-roll continuous straightening process for LSAW pipes

Aiming at the low efficiency and unstable accuracy of the current mold-pressing straightening for LSAW pipes, a three-roll continuous straightening process is proposed in this study, which uses the roller straightening instead of mold bending. According to the novel technology, the calculation model of the theoretical straightening moment is derived based on the springback equation of plane bending with small curvature, and the calculation model of initial curvature is established for the new deflection detection method. Furthermore, the numerical simulation analysis is carried out for the LSAW pipe case, and a straightening experimental platform is built for experiments. The research shows that the accuracy of the theoretical moment equation required for straightening is directly related to the initial curvature, rather than the fitting accuracy of the deflection curve, and the low-order simple-fitting curvature calculation model has the highest reliability. In order to control the section distortion and the straightening blind area, the straightening roller should follow the equal diameter design principle, and the empirical formula of span estimation is given. Under the optimal conditions, the straightness of the corrected tubes can be controlled within 1.5‰ and the ovality of the section can be within 0.5%, which proves the feasibility and reliability of the new process. What’s more, the straightening system built in this work, including process analysis software, is conducive to the automation and popularization of the new process.

The isoperimetric problem on Riemannian manifolds via Gromov–Hausdorff asymptotic analysis

In this paper, we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov–Hausdorff asymptoticity to the suitable simply connected model of constant sectional curvature. The previous result is a consequence of a general structure theorem for perimeter-minimizing sequences of sets of fixed volume on noncollapsed Riemannian manifolds with a lower bound on the Ricci curvature. We show that, without assuming any further hypotheses on the asymptotic geometry, all the mass and the perimeter lost at infinity, if any, are recovered by at most countably many isoperimetric regions sitting in some (possibly nonsmooth) Gromov–Hausdorff limits at infinity. The Gromov–Hausdorff asymptotic analysis allows us to recover and extend different previous existence theorems. While studying the isoperimetric problem in the smooth setting, the nonsmooth geometry naturally emerges, and thus our treatment combines techniques from both the theories.