Rotational Degrees Of Freedom Research Articles

Development of Rail Camera for Bridge inspection with Attitude Control using Thrust of Rotors

A lot of concrete structures are deteriorating to dangerous levels throughout Japan. These concrete structures need to be inspected regularly to ensure they are safe enough to be used. According to national standards, a visual inspection of the bridge is required once every five years. In the visual inspection, the worker checks the bridge with their own eyes directly. So, it is necessary to set up scaffolding to access the bridge's underside for visual inspection. Alternatively, it is an essential aerial work platform. However, setting up of scaffolding and aerial work platforms is not economical in time and money. So, we developed an inspection device for the check of bridges called a Rail camera. This inspection device connects a rod and a rail and the connection has a rotational degree of freedom. Rotors are attached to the tip of the rod and it can be attitude controlled by thrust of rotors. So, half of the device's weight is lifted by the thrust of the rotors. And it can be taken with a camera mounted on an electric slider on the rail. The worker on the bridge can check the underside of the bridge safely by holding the rod with one hand and operating the rail camera with another hand. The rail camera developed had a rail length of 2 m and a weight of 2.5 kg. Magnesium was used for the rail and rod to reduce weight. Coaxial rotors were used to cancel the counter-torque caused by the rotation of the propeller. To verify the performance, a visual inspection was performed on the bridge. As a result, it was confirmed that the horizontal attitude was maintained by the rotor thrust.

The Interior Contact-Aided Rolling Element

Abstract This work introduces an interior contact-aided rolling element (I-CORE) compliant mechanism that draws upon the concepts used for the contact-aided rolling element, cross-axis flexural pivot, and pre-curved flexible beam. The I-CORE incorporates a bilinear compressive stiffness response with an initial tailorable stiffness governed by the flexural geometry, followed by a stiffness curve governed by the material stiffness at the contact point. The I-CORE mechanism can achieve one or two degrees of rotational freedom as well as a single degree of translational freedom. The purpose of the present work was to introduce the I-CORE mechanism, as well as a pseudo-rigid-body replacement model (PRBM) of the I-CORE mechanism which was subsequently validated using both finite element analysis and benchtop mechanical testing. A pseudo-rigid body model was created for the I-CORE to simplify the rapid adaptation of this mechanism to different design applications. This model was validated using both finite element analysis and benchtop mechanical testing under both compression and rotation loading conditions. Additionally, multiple configurations of the device were created and evaluated in order to test its sensitivity to certain design features including the flexure width, flexure thickness, and the radius of the rounded contact surfaces. It was found that the model is sensitive to the thickness of the flexures and that despite some limitations, the pseudo-rigid body model is sufficiently accurate for initial design work. Some possible applications of the mechanism are proposed.

Enhanced Attractive Force via Torsion Spring as Rotatable Tip Structure in Beam-Structure Electrostatic Chucks

This research aims to replace ball joints of beam-structure electrostatic chucks (BSESC), which are limited by issues such as structural friction and inconsistent operation, thus enhancing the applicability in industrial settings. Torsion springs are used as rotational degree-of-freedom (RDOF) mechanisms at the tip of BSESCs to reduce friction and improve repeatability, while also highlighting the positive relationship between tip rotatability and the attractive force generated. Following the law of conservation of energy, an analytical calculation was performed using a beam-spring-capacitor model to establish the correlation between tip rotatability and the maximum attractive force generated through energy system analysis. An analytical solution was derived, explicitly defining the relationship between tip rotatability and the achievable attractive force. The results were plotted using MATLAB. Experimental validations were carried out by fabricating devices that differed only in tip rotatability, and measurements of the attractive force were taken. Both analytical and experimental results clearly demonstrate a positive relationship between tip rotatability and attractive force generation in BSESCs. The use of torsion springs effectively reduces the energy concentration at the tip, delaying detachment while simultaneously increasing the attractive force, significantly improving the overall performance of BSESCs. These findings provide a foundation for future industrial applications, particularly for automated large-area manipulation of irregularly shaped targets in industries such as screen production and semiconductors.

Comment on: “Analytical solutions to the Schrödinger equation for a generalized Cornell potential and its applications to diatomic molecules and heavy mesons”

We analyze a recent calculation of the energy levels of some quantum-mechanical models derived from the so-called generalized Cornell potential. We argue that the authors obtained essentially the same spectrum for potentials with considerably different spectra. We show that the authors obtained negative eigenvalues in the case of a positive-definite potential. The reason is due to the approximation used in the solution of the Schrödinger equation. We point out that the omission of the sum over the rotational degrees of freedom in the canonical partition function leads to incomplete expressions for the thermodynamic functions.

A preliminary biomechanical assessment and user perceptions of a motorized lifter for patient transfer

ABSTRACT A “no-lift” policy in healthcare discourages manual patient lifting to reduce worker injuries. This study explores modifications to a floor lift (NEAR-1) to align with this policy. NEAR-1 features a shorter lower lifting arm and a redesigned sling, enabling patients to (a) transfer in a sitting position, unlike a floor lift’s semi-reclining position, and (b) feel more in control by removing the sling’s rotational degree of freedom and letting the patient’s feet rest on the lifter base. The device also reduced patient weight-bearing, compared to sit-to-stand lifts. Biomechanical analysis was done to map the risk to the nurses and capture the patient’s experience with the modified lift (NEAR-1). Thirteen subjects carried out patient transfer tasks using both the NEAR-1 and the manual transfer approach, and this comparison will provide the baseline data for future systematic reviews. From the results, NEAR-1 significantly reduced the L5-S1 compression, the mediolateral shear forces, and the anteroposterior shear forces, with the exception of the muscle activities in the lower back, the shoulder, and the biceps. Moreover, patients felt safer and more comfortable with the device. Overall, the NEAR-1 lifter presents a biomechanically beneficial and user-friendly option for patients with limited weight-bearing capability.

Pyrazolo-Pyrimidinones with Improved Solubility and Selective Inhibition of Adenylyl Cyclase Type 1 Activity for Treatment of Inflammatory Pain.

Adenylyl cyclase isoform 1 (AC1) is considered a promising target for treating inflammatory pain. Our group identified the pyrazolyl-pyrimidinone scaffold as potent and selective inhibitors of Ca2+/CaM-mediated AC1 activity; however, the molecules suffered from poor aqueous solubility. The current study presents a strategy to improve aqueous solubility of the scaffold by reduction of crystal packing energy and increasing rotational degrees of freedom within the molecule. Structure-activity and property relationship studies identified the second generation lead 7-47A (AC10142A) that demonstrated and AC1 IC50 value of 0.26 μM and aqueous solubility of 74 ± 7 μM. After in vitro ADME characterization, the scaffold advanced to in vivo pharmacokinetic evaluation, demonstrating adequate levels of exposure. Finally, 7-47A exhibited antiallodynic efficacy in a rat complete Freund's adjuvant model for inflammatory pain showing improvement over previous iterations of this scaffold. These results further validate AC1 inhibition as a viable therapeutic strategy for treating chronic and inflammatory pain.

Study of chemiluminescence of methane–air flame stabilized on a flat porous burner

In this work, the spatial distribution and spectral characteristics of the chemiluminescence of chemically excited species, OH∗ and CH∗, are experimentally and numerically studied by using a stationary premixed methane–air flame stabilized on the surface of a flat porous burner for various equivalence ratio and normal pressure. Numerical simulations are carried out using detailed reaction mechanisms, and the experimental study includes high-resolution spatial and spectral optical measurements. Despite the data reported in the literature, it is found that (i) the rotational degrees of freedom of OH∗ and CH∗ are not in thermal equilibrium with the surrounding gas and therefore cannot be used to measure flame temperature; (ii) there is no direct correlation between the heat release rate and the distribution of OH∗ and CH∗; (iii) the detailed reaction mechanisms not only quantitatively, and also qualitatively differ in description of the OH∗ and CH∗ concentrations. Since the chemically excited species are well localized in a direction normal to the flame surface, they are demonstrated to be a very accurate markers of flame location. The shape of the combustion front can be reconstructed and resolved up to the accuracy of tens of microns, which is very important for estimation of blow-off critical parameters and measurement of the laminar burning velocity.Novelty and significance statementCurrently, there is a growing interest in the development of sensors for combustion control systems, including active control and suppression of instabilities, in combustion chambers of various devices and engines based on chemiluminescence of excited reaction species. The possibility of non-invasive determination of parameters such as flame temperature, stoichiometry, heat release rate location, etc. using this technique is discussed. We have found that most of these parameters cannot be estimated either due to fundamental limitations or insufficient knowledge of the reaction kinetics involved in the production of these species. Nevertheless, since OH* and CH* are well localized in the direction normal to the flame surface, they can be used as very accurate markers of flame shape and position, allowing us to reconstruct the flame surface to within tens of microns resolution, which is very important for estimating blow-off critical parameters and measuring laminar burning velocity.

Machine-learned coarse-grained potentials for particles with anisotropic shapes and interactions

Computational investigations of biological and soft-matter systems governed by strongly anisotropic interactions typically require resource-demanding methods such as atomistic simulations. However, these techniques frequently prove to be prohibitively expensive for accessing the long-time and large-length scales inherent to such systems. Conversely, coarse-grained models offer a computationally efficient alternative. Nonetheless, models of this type have seldom been developed to accurately represent anisotropic or directional interactions. In this work, we introduce a straightforward bottom-up, data-driven approach for constructing single-site coarse-grained potentials suitable for particles with arbitrary shapes and highly directional interactions. Our method for constructing these coarse-grained potentials relies on particle-centered descriptors of local structure that effectively encode dependencies on rotational degrees of freedom in the interactions. By using these descriptors as regressors in a linear model and employing a simple feature selection scheme, we construct single-site coarse-grained potentials for particles with anisotropic interactions, including surface-patterned particles and colloidal superballs in the presence of non-adsorbing polymers. We validate the efficacy of our models by accurately capturing the intricacies of the potential-energy surfaces from the underlying fine-grained models. Additionally, we demonstrate that this simple approach can accurately represent the contact function (shape) of non-spherical particles, which may be leveraged to construct continuous potentials suitable for large-scale simulations.

Rotational properties of two interacting cold polar molecules: Linear, symmetric, and asymmetric tops

We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024

An efficient isogeometric buckling optimization framework for multi-patch laminated shells: Leveraging 3D solid elements, lamination parameters and penalty method

Buckling is a common failure mode of laminated shell structures during service, and isogeometric analysis methods are highly suitable for the buckling analysis due to their accurate geometric modeling capability and high-order continuity. However, the isogeometric buckling analysis for a multi-patch structure and its optimal design still face challenges in computational efficiency. To address this issue, this paper proposes an integrated framework for the buckling optimization of multi-patch laminated shells, which leverages 3D solid elements, lamination parameters, and the penalty coupling method. Solid-shell elements have advantages in shell analysis due to their simplicity, absence of rotational degrees of freedom, and adaptive layering in the thickness direction. Lamination parameters simplify the optimization of fiber orientations in laminated shells by condensing the design variable space and improving the convexity of the optimization problem. The penalty method can handle the coupling in multiple patches at a relatively low cost. Nevertheless, lamination parameters are rarely applied to the case of solid-shell elements. In addition, despite using lamination parameters, the number of design variables for multi-patch structures remains significantly large. To tackle these issues, this study derives the solid-shell formulation in lamination parameters and the sensitivity analysis formulae in the reverse mode. Experiment validation is conducted to assess the accuracy of the proposed method based on lamination parameters with solid elements, the feasibility of the multi-patch optimization model, and the computational efficiency of optimization sensitivity based on the reverse mode compared to the forward counterpart common in the literature.

Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model

For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property (ensuring bounded linearized strains even under high stresses). Such strain-limiting Cosserat model can find potential applications in solids and biological fibers. However, Cosserat media with naturally rotational degrees of freedom, nonlinear constitutive relations, high contrast, and heterogeneities may produce challenging multiscale characteristics in the solution, and upscaling by multiscale methods is necessary. Therefore, we utilize the offline and residual-based online (adaptive or uniform) GMsFEM in this context while handling the nonlinearity by Picard iteration. Through various two-dimensional experiments (for perforated, composite, and stochastically heterogeneous media with small and big strain-limiting parameters), our numerical results show the approaches' convergence, efficiency, and robustness. In addition, these results demonstrate that such approaches provide good accuracy, the online GMsFEM gives more accurate solutions than the offline one, and the online adaptive strategy has similar accuracy to the uniform one but with fewer degrees of freedom.

Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions.

From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics. The solution accounts for discrete degeneracy of topologically distinct free energy minima which can be obtained by defect braiding. The derived formalism can be readily applied to equilibrium and slowly evolving nematic textures for active or passive fluids with multiple defects present within the orientational order.

Fracture and size effect in mechanical metamaterials

We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized explicitly in terms of the solution of the zeroth-order continuum problem by the method of Γ-expansion. We present explicit expressions of the second-order correction for octet frames. As an application, we evaluate the compliance of double-cantilever octet specimens to second order and use the result to elucidate the dependence of the apparent toughness of the specimen on cell size. The analysis predicts the discreteness of the metamaterial lattice to effectively shield the crack-tip, a mechanism that we term lattice shielding. The theory specifically predicts anti-shielding, i. e., coarser is weaker, in agreement with recent experimental observations.

Inverse kinematics in cervical spine models: Effects of scaling and model degrees of freedom for extension and flexion movements

Intervertebral kinematics can affect model-predicted loads and strains in the spine; therefore knowledge of expected vertebral kinematics error is important for understanding the limitations of model predictions. This study addressed how different kinematic models of the neck affect the prediction of intervertebral kinematics from markers on the head and trunk. Eight subjects executed head and neck extension-flexion motion with simultaneous motion capture and biplanar dynamic stereo-radiography (DSX) of vertebrae C1-C7. A generic head and neck model in OpenSim was scaled by marker data, and three versions of the model were used with an inverse kinematics solver. The models differed according to the number of independent degrees of freedom (DOF) between the head and trunk: 3 rotational DOF with constraints defining intervertebral kinematics as a function of overall head-trunk motion; 24DOF with 3 independent rotational DOF at each level, skull-T1; 48DOF with 3 rotational and 3 translational DOF at each level. Marker tracking error was lower for scaled models compared to generic models and decreased as model DOF increased. The largest mean absolute error (MAE) was found in extension-flexion angle and anterior-posterior translation at C1-C2, and superior-inferior translation at C2-C3. Model scaling and complexity did not have a statistically significant effect on most error metrics when corrected for multiple comparisons, but ranges of motion were significantly different from DSX in some cases. This study evaluated model kinematics in comparison to gold standard radiographic data and provides important information about intervertebral kinematics error that are foundational to model validity.

Development of a large stroke 3-DOF piezoelectric steering mirror for optical system

The steering mirrors and the focusing mechanisms are the key components of the optical system. Traditional steering mirrors driven by voice coil actuator or piezoelectric stack actuator have the disadvantages of short stroke, self-locking difficulty and poor structural reliability. These defects limit the performance of the steering mirrors and make it difficult to be compatible with the focusing mechanism. As a result, additional focusing devices are required in the optical system, which significantly increases the complexity of the system. To simplify the optical system, a large stroke three-degree-of-freedom (3-DOF) piezoelectric steering mirror (PSM) which can realize both light path adjustment and focus adjustment is proposed in this study. Two rotational degrees of freedom of the PSM are used to adjust the light path, and a translational degree of freedom is used to adjust the focus. The screwed-typed piezoelectric actuators (STPAs) are designed to drive the PSM by exciting the travelling wave. The feasibility of the operating principle and reliability of the proposed PSM have been verified by finite element simulation. A prototype of the PSM is fabricated and tested. The experimental results show that the PSM achieves rotational degrees of freedom around the x-axis, y-axis and translational degree of freedom along the z-axis with maximum ranges of ±0.17 rad, ±0.17 rad, and ±10 mm, respectively, meeting the application requirements of the optical systems. The resolutions of the two rotary motions of the PSM are 28 μrad, and 21 μrad, respectively, and that of the translational motion is 0.5 μm. Finally, the position adjustment and focusing operations of the image are demonstrated to validate the potential application of PSM in optical systems.

Revisiting Aspirin Polymorphic Stability Using a Machine Learning Potential.

In this study, we present a systematic computational investigation to analyze the long-debated free energy stability of two well-known aspirin polymorphs, denoted as Form I and Form II. Specifically, we developed a strategy to collect training configurations covering diverse interatomic interactions between representative functional groups in aspirin crystals. Utilizing a state-of-the-art neural network interatomic potential (NNIP) model, we trained an accurate machine learning potential to simulate aspirin crystal dynamics under finite temperature conditions with ∼0.46 kJ/mol/molecule accuracy. Employing the trained NNIP model, we performed thermodynamic integration to assess the free energy difference between aspirins I and II, accounting for the anharmonic effects in a large supercell consisting of 512 molecules. For the first time, our results convincingly demonstrated that Form I is more stable than Form II at 300 K, ranging from 0.74 to 1.83 kJ/mol/molecule, aligning with experimental observations. Unlike the majority of previous simulations based on (quasi)harmonic approximations in a small super cell, which often found degenerate energies between aspirins I and II, our findings underscore the importance of anharmonic effects in determining polymorphic stability ranking. Furthermore, we proposed the use of the rotational degrees of freedom of methyl and ester/phenyl groups in aspirin crystals as characteristic motions to highlight rotational entropic contribution that favors the stability of Form I. From the structural perspective, we also found that the subtle free energy difference can be used to explain the distinct thermal expansion responses as observed in both experimental and simulation data. Beyond the aspirin polymorphism, we anticipate that such entropy-driven stabilization can be broadly applicable to many other organic systems, suggesting that our approach holds great promise for stability studies in small-molecule drug design.

Analytical Linearization of Aerodynamic Loads in Unsteady Vortex-Lattice Method for Nonlinear Aeroelastic Applications

This paper presents the analytical linearization of aerodynamic loads (computed with the unsteady vortex-lattice method), which is formulated as tangent matrices with respect to the kinematic states of the aerodynamic grid. The loads and their linearization are then mapped to a nonlinear structural model by means of radial-basis functions, allowing for a two-way strong interaction scheme. The structural model comprises geometrically exact beams formulated in a director-based total Lagrangian description, circumventing the need for rotational degrees of freedom. The structural model is spatially discretized into finite elements and temporally discretized with the help of an implicit scheme that identically preserves momenta and energy. The resulting nonlinear discrete equations are solved by applying Newton’s method, requiring calculating the Jacobians of the whole aeroelastic system. The correctness of the linearized loads is then shown by direct comparison with their numerical counterparts. In addition, we employ our strongly coupled aeroelastic model to investigate the nonlinear static and dynamic behavior of a suspension bridge. With this approach, we successfully investigate the numerical features of the aeroelastic system under divergence and flutter conditions.

Rotational and translational motions in a homogeneously cooling granular gas

A granular gas composed of monodisperse spherical particles was studied in microgravity experiments in a drop tower. Translations and rotations of the particles were extracted from optical video data. Equipartition is violated, the rotational degrees of freedom were excited only to roughly 2/3 of the translational ones. After stopping the mechanical excitation, we observed granular cooling of the ensemble for a period of three times the Haff time, where the kinetic energy dropped to about 5% of its initial value. The cooling rates of all observable degrees of freedom were comparable, and the ratio of rotational and translational kinetic energies fluctuated around a constant value. The distributions of translational and rotational velocity components showed slight but systematic deviations from Gaussians at the start of cooling.

Molecular structure refinement based on residual dipolar couplings using magnetic-field rotational sampling.

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using magnetic-field rotational sampling of the rotational degrees of freedom of a molecule in conjunction with molecule-internal configurational sampling. By applying rotational sampling, as is occurring in the experiment, leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and, therefore, the assumptions that the overall rotation of the molecule is decoupled from its internal motions and that the molecule is rigid. Two simple molecules, a relatively rigid and a very flexible cyclo-octane molecule with eight aliphatic side chains containing 24 united atoms, serve as so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility, force-field dominance, and the number of RDC restraints available on the outcome of structure refinement based on RDCs. Magnetic-field rotational sampling is basically equivalent but more efficient than explicitly sampling the rotational degrees of freedom of the molecule. In addition, the performance of the method is less dependent on the number NRDC of measured RDC-values available. The restraining forces bias the overall orientation distribution of the molecule correctly. This study suggests that the information content of RDCs with respect to molecular structure is limited.

Size-dependent vibration analysis of porous 3D-FG microshells in complex thermal environments using a neural network enhanced finite element model

This work aims to investigate the vibration behavior of porous three-directional functionally graded (3D-FG) microshells in thermal environments, where both mechanical and thermal material properties vary along three spatial directions following a power-law distribution, based on the modified couple stress theory (MCST). An isoparametric thermal element is employed for uncoupled heat conduction analysis, followed by dynamic analysis using a penalty solid element with three translation degrees of freedom (DOFs) and three rotation DOFs per node. However, due to the strong nonlinearity of the temperature field in 3D-FG microshells, obtaining exact temperature values at integration points in dynamic analysis requires a pretty dense mesh of the solid element. To overcome this issue, a back propagation (BP) neural network is utilized to predict the temperature field for various gradient indexes, enhancing the efficiency and precision of temperature distribution calculation. Numerical results demonstrate the effectiveness of the neural network enhanced finite element model. Furthermore, the effects of the material length scale parameter (MLSP), temperature difference, and gradient indexes on the natural frequencies are investigated. It is shown that higher structural stiffness weakens the impact of temperature difference on the frequency.