Rotational Degrees Of Freedom Research Articles

Estimating ski orientation using IMUs in alpine skiing

Ski-snow interaction is the essential component of alpine skiing. To understand how a skier manipulates his ski to turn, we need to develop methods to measure the orientation of the ski throughout a complete run. Recent studies tried to use IMUs to estimate edge angle (EA) during skiing. We introduce and validate a method on how to calibrate and employ IMUs to precisely and accurately measure roll angles (RA) as a matter of changing orientation of the ski around its longitudinal axis in 3D space during skiing. Static orientation measurements on an inclined plane perfectly correlate (r2 = 1) with 3D motion capturing: RMSE = 0.18° and 0.24° respectively. Bland Altman showed a mean bias of 0.23° (95% CI: -0.16°, 0.63°) and 0.21° (95% CI: -0.3°, 0.73°). Accuracy and drift tests against constant standardised rotational velocities showed no drift behaviour over time, but RA estimation accuracy is reduced with increasing angular velocities (SD @ ±300°/s: 0.57°, max. difference from average at ±300°/s: 2.7°). During skiing on a ski ergometer the comparison of maximum RA against Vicon showed a mean bias of 0.13° (95% CI: -0.86° to 1.1°). Even though ski ergometer skiing has a similar frequency and angular velocity profile like outdoor skiing, there are more rotational degrees of freedom in outdoor skiing. The foundation is provided in this paper. To understand how a skier manipulates the ski on snow and to understand RA and EA progression during a turn in detail, further research should validate the method in the field and additionally look into RA progression within individual turns.

Self-starting and performance improvement of a Darrieus type wind turbine using the plasma actuator

Although the popularity of Darrieus-type vertical axis wind turbines is growing for small-scale electricity generation, these turbines have severe challenges in self-starting. This paper proposes a flow control method, namely, the plasma actuator, to solve the self-starting problem besides enhancing the turbine performance. The Darrieus turbine is numerically investigated using a pressure-based finite volume method to solve the unsteady Reynolds-averaged Navier–Stokes and the γ–Reθt transitional model equations. Simulation of the blade rotation is performed using the sliding mesh technique accompanied by the turbine equation of motion to enable the blade rotational degree of freedom. Furthermore, the body forces associated with the plasma actuator are determined by calibrating the Shyy plasma model parameters. The plasma actuator is assessed at both the constant and free rotational speeds. The constant rotational speed results in plasma off condition show negative torque generation for tip speed ratios lower than 1.5, known as the origin of turbine self-starting challenges. The plasma actuator improves the negative torque by 128% in the tip speed ratio of 0.5 and turns it positive. Also, at larger tip speed ratios, it reduces the negative torque generation and enhances the turbine power production by up to 260%. Furthermore, the plasma actuator in free rotational speed improves the tip speed ratio increment by up to 8%, reducing the total time of turbine self-starting.

Exact Transport Coefficients from the Inelastic Rough Maxwell Model of a Granular Gas

Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier–Stokes–Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.

Emergent gauge symmetry in active Brownian matter.

We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).

Operator Formulation of Feynman Path Centroid Dynamics for Rotations.

An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.

On the lattice ground state of densely packed hard ellipses.

Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favorable states. The free energies of these two states are computed for several system sizes employing the Einstein crystal method. An accurate calculation of the free energy difference between the two states reveals the parallel lattice as the state with the lowest free energy. The origin of the entropic difference between the two states is further elucidated by assessing the roles of the translational and rotational degrees of freedom.

Hexahedral Solid Element with Rotational Degrees of Freedom Based on a Novel Trail-Correction Displacement Interpolation Scheme

Hexahedral Solid Element with Rotational Degrees of Freedom Based on a Novel Trail-Correction Displacement Interpolation Scheme

Depletion forces in dense mixtures of spheres and rods.

We evaluate depletion forces in molecular dynamics simulation of a binary mixture of spheres (depleted particles) and rods (depletant particles) for a wide range of densities for both species. This evaluation was carried out using a recently proposed least squares fitting algorithm. We found that the restriction of the rods' rotational degrees of freedom, when the distance between two spheres is less than the rods length, creates a shallow, and apparently linear, attractive force ramp. For intersphere distances smaller than the rods' diameter, a much stronger attractive force is found, and a large repulsive barrier appears between these aforementioned regimes, roughly at the distance of the rods' thickness. The evaluated forces are validated via a comparison of the pairwise correlation functions obtained from molecular dynamics simulation of a mono-disperse sphere fluid, using the evaluated effective forces, against the original (full system) pairwise correlation functions. Agreement is excellent. We also record the angular pairwise correlation function, using the P2(x) Legendre polynomial, and find that for high densities of both species, a local nematic ordering starts to appear. This nematic order may be a factor in the small differences found between original and effective pairwise correlation functions at high densities of rods.

Disorder-induced heating in molecular atmospheric pressure plasmas

Recent work has shown that ions are strongly coupled in atmospheric pressure plasmas when the ionization fraction is sufficiently large, leading to a temperature increase from disorder-induced heating (DIH) that is not accounted for in standard modelling techniques. Here, we extend this study to molecular plasmas. A main finding is that the energy gained by ions in DIH gets spread over both translational and rotational degrees of freedom on a nanosecond timescale, causing the final ion and neutral gas temperatures to be lower in the molecular case than in the atomic case. A model is developed for the equilibrium temperature that agrees well with molecular dynamics simulations. The model and simulations are also applied to pressures up to ten atmospheres. We conclude that DIH is a significant and predictable phenomena in molecular atmospheric pressure plasmas.

Frictional vibration analysis of train braking system considering wheel-rail attachment and multi-body friction

Train vibration and noise have always been problems that affect the service life of relevant components and passenger comfort. This paper focuses on the vibration of the train braking system and establishes a torsional vibration model of the train braking system considering wheel-rail attachment and multi-body friction, which includes three rotational degrees of freedom of the brake disc, brake block, and wheelset. The periodic vibration and chaotic bifurcation of the braking system under low-speed working conditions are studied by numerical calculation. An optimization strategy is proposed for the chaotic bifurcation behavior, which eliminates the chaotic interval at low speeds through the reasonable matching of particle parameters, so as to ameliorate the brake groan problem of the train.

Platonic solids bouncing on a vibrating plate.

The energy transfer between bouncing particles and rigid boundaries during impacts is crucially influenced not only by restitution coefficients of the material but also by particle shapes. This is particularly important when such particles are mechanically agitated with vibrating plates. Inertial measurement units are able to measure all acceleration and rotational velocity components of an object and store these data for subsequent analysis. We employ them to measure the dynamics of cubes and icosahedra on vibrating plates to study the efficiency of energy transfer into the individual degrees of freedom (DOFs) of the excited object. The rotational DOFs turn out to be much less excited than the vertical translational motion. Most remarkably, there is only little difference between the two Platonic solids in both the absolute energies and the energy partition ratios.

Anti-galloping analysis of iced quad bundle conductor based on compound damping cables

Based on the strain displacement relationship of spatial curved beam theory, a nonlinear dynamic equation for a hybrid model of iced bundle conductor galloping analysis with three translational degrees of freedom and one rotational degree of freedom was established. The element independence is numerically studied, and the impact of modal truncation on the galloping response is analyzed to verify the accuracy of the model. In addition, the compound damping cable is applied to transmission lines for the first time to prevent galloping, and a corresponding nonlinear vibration control finite element equation for the iced quad bundle conductor with a compound damping cable structure under wind load is developed. The study also examines the influence of various parameters on galloping amplitude. The results show that the hybrid model accurately predicts the galloping response of transmission lines. The compound damping cable can effectively suppress the galloping of the quad bundle conductor, and the vibration reduction effect reaches more than 85%. Increasing the installation height of the compound damping cable improves its damping effect. At the same installation height, when the horizontal installation position is close to the mid-span of the conductor, the damping effect first increases and then decreases, suggesting an optimal installation position exists. Moreover, properly increasing the stiffness of the primary cable and reducing the stiffness of the return spring can improve the vibration reduction effect of the compound damping cable. Additionally, if the damping coefficient and the mass of the primary cable are properly increased, the vibration reduction effect of the compound damping cable will be better.

Algebraic cluster model calculations for shape phase transitions of boson-fermion systems

The Algebraic Cluster Model (ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine [Formula: see text] Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions [Formula: see text], [Formula: see text] and [Formula: see text], respectively. We offer that this method can be used to study [Formula: see text] nucleon structures with [Formula: see text] and [Formula: see text] in specific [Formula: see text] such as structures [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text]. Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even–even boson core is discussed along the shape transition and, in particular, at the critical point.

Synchronization of optically self-assembled nanorotors.

Self-assembly of nanoparticles by means of interparticle optical forces provides a compelling approach toward contact-free organization and manipulation of nanoscale entities. However, exploration of the rotational degrees of freedom in this process has remained limited, primarily because of the predominant focus on spherical nanoparticles, for which individual particle orientation cannot be determined. Here, we show that gold nanorods, which self-assemble in water under the influence of circularly polarized light, exhibit synchronized rotational motion at kilohertz frequencies. The synchronization is caused by strong optical interactions and occurs despite the presence of thermal diffusion. Our findings elucidate the intricate dynamics arising from the transfer of photon spin angular momentum to optically bound matter and hold promise for advancing the emerging field of light-driven nanomachinery.

An Experimental Study of the Effects of Asymmetric Pitching Motion on the Hydrodynamic Propulsion of a Flapping Fin

An Experimental Study of the Effects of Asymmetric Pitching Motion on the Hydrodynamic Propulsion of a Flapping Fin

Three DOF Rotation Compensation in Floating HFSWR for Ocean Current Inversion

High-frequency surface wave radar (HFSWR) has been widely used for ocean surface current inversion. Floating this radar can realize the ocean surface inversion among large areas far away from the coastline. However, six degree-of-freedom (DOF) movements will set the barrier for the ocean current inversion on its radial velocity estimation and direction of arrival estimation. Among these movements, three DOF rotations can cause both Doppler modulation and azimuth modulation while three DOF translations only cause Doppler modulation which is dependent on the arrival direction of echoes. Hence, the analysis and compensation for three DOF rotations are first to be solved. In this paper, we analyse the Doppler modulation and azimuth modulation of three DOF rotations and further develop the global adaptive beamforming method to compensate for these rotations. Adaptive beamforming is used to compensate for rotations to make the real-time beams fixed to the ground when the platform is rotating. Simulations indicate that the global adaptive beamforming can perfectly compensate for the reasonable rotations, among which the yaw rotation is the dominant factor for both Doppler spectrum modulation and azimuth modulation. The rotation compensation using global adaptive beamforming can greatly improve the precision of ocean surface inversion.

A solid-shell model of hard-magnetic soft materials

Hard-magnetic soft materials (HMSMs) consisting of an elastomer matrix filled with high remnant magnetic particles can exhibit flexible programmability and rapid shape changing under non-contact activation, showing promising potential applications in soft robotics, biomedical devices and flexible electronics. Precise predictions of large deformations of hard-magnetic soft materials would be a key for relevant applications. Here, we develop a magneto-mechanical theoretical framework to model large deformations of magneto-active elastomers by applying solid-shell formulations based on the variational principle. Within the 3D geometric description, the complete Green–Lagrange strain tensors are considered and thus 3D nonlinear material laws can be employed straightforwardly, without presupposing Kirchhoff–Love hypothesis and plane stress constraints. In addition, the solid-shell model avoids introducing rotational degrees of freedom in computation and thus does not require complex finite-rotation update, which also works well for thick shells at large strains. We adopt the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods to overcome locking effects. Several representative examples with various deformed configurations are explored, showing precise predictions of morphological transformations of HMSMs based on our model, in good agreement with experiments. Our model provides a versatile tool to harness large deformations of magneto-elastic structures, and could be used for rational designs of active flexible devices and robots.

Assessing the significance of nonlinear rotational behavior in high damping rubber bearings for seismic performance of base‐isolated RC frame building

AbstractUtilizing high‐damping rubber bearings (HDRBs) for seismic isolation significantly enhances building seismic performance. However, previous studies have often neglected the nonlinear rotational behavior of these bearings when assessing base‐isolated systems using HDRBs. This study introduces two numerical models of the HDRBs, each comprising six springs. The first model, referred to as the BIL model, assumes linear behavior for the rotational degrees of freedom of the bearings. The second model, referred to as the BINL model, accounts for the nonlinear rotational behavior. The parameters of the bearing shear springs and the rotational springs of the two models are calibrated using experimental data. In order to investigate the influence of nonlinear rotational behavior of HDRBs on the seismic performance of base‐isolated buildings, nonlinear time history analysis is conducted on a six‐story base‐isolated RC frame building. Comparative analysis between the BIL model and the BINL model covers bearing behavior, superstructure response, and energy dissipation distribution. Results indicate a significant influence of considering nonlinear rotational behavior on column bending moments. These findings provide crucial insights for enhancing seismic design strategies for base‐isolated buildings.

An improved methodology to restrict the range of motion of mechanical joints

Joints with rotational degrees of freedom, for instance, revolute, spherical, or universal joints, are commonly utilized in real-world scenarios. In the multibody systems methodology, mechanical joints usually are formulated as classical kinematic constraints such that there is no restriction of the range of motion (RoM) of the joint. Thus, the formulation must include additional restrictions to prevent the joints from performing unacceptable movements and to avoid unrealistic configurations of the connected bodies. Therefore, the aim of this work is to propose a methodology to restrict the RoM of mechanical joints. Joint resistance moments are applied to the bodies connected by the joint to mimic the dissipative behavior of the materials constituent of joints and to prevent unacceptable configurations of those bodies. The proposed methodology aims to extend and improve a previously published study, specifically in the definition of the RoM limits, calculation of the penalty moments, and establishment of their direction of application. Enhanced methods to deal with the detection of unacceptable joint configurations, namely the elliptical and polynomial approaches, are proposed. A parametrization procedure is described to correctly calculate the direction of the penalty moments to apply to the connected bodies. The methodology is investigated in the dynamic modeling and simulation of one demonstrative example of application, namely a simple pendulum. A parametric analysis is performed to assess the influence of the methodology parameters in the response of the model. The methodology allows the correct restriction of the RoM of joints, while preserving the mechanical energy of the system.

Simulating whole-body vibration for neonatal patients on a tire-coupled road simulator.

Exposure to excessive whole-body vibration is linked to health issues and may result in increased rates of mortality and morbidity in infants. Newborn infants requiring specialized treatment at neonatal intensive care units often require transportation by road ambulance to specialized care centers, exposing the infants to potentially harmful vibration and noise. A standardized Neonatal Patient Transport System (NPTS) has been deployed in Ontario, Canada, that provides life saving equipment to patients and safe operation for the clinical care staff. However, there is evidence that suggests patients may experience a higher amplitude of vibration at certain frequencies when compared with the vehicle vibration. In a multi-year collaborative project, we seek to create a standardized test procedure to evaluate the levels of vibration and the effectiveness of mitigation strategies. Previous studies have looked at laboratory vibration testing of a transport system or transport incubator and were limited to single degree of freedom excitation, neglecting the combined effects of rotational motion. This study considers laboratory testing of a full vehicle and patient transport system on an MTS Model 320 Tire-Coupled Road Simulator. The simulation of road profiles and discrete events on a tire-coupled road simulator allows for the evaluation of the vibration levels of the transport system and the exploration of mitigation strategies in a controlled setting. The tire-coupled simulator can excite six degrees-of-freedom motion of the transport system for vibration evaluation in three orthogonal directions including the contributions of the three rotational degrees of freedom. The vibration data measured on the transport system during the tire-coupled testing are compared to corresponding road test data to assess the accuracy of the vibration environment replication. Three runs of the same drive file were conducted during the laboratory testing, allowing the identification of anomalies and evaluation of the repeatability. The tire-coupled full vehicle testing revealed a high level of accuracy in re-creating the road sections and synthesized random profiles. The simulation of high amplitude discrete events, such as speed hump traverses, were highly repeatable, yet yielded less accurate results with respect to the peak amplitudes at the patient. The resulting accelerations collected at the input to the manikin (sensor located under the mattress) matched well between the real-world and road simulator. The sensors used during testing included series 3741B uni-axial and series 356A01 tri-axial accelerometers by PCB Piezotronics. These results indicate a tire-coupled road simulator can be used to accurately evaluate vibration levels and assess the benefits of future mitigation strategies in a controlled setting with a high level of repeatability.