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In this paper, angular displacement and angular velocity sensors based on coplanar waveguide (CPW) transmission lines and S-shaped split ring resonators (S-SRRs) are presented. The sensor consists of two parts, namely a CPW and an S-SRR, both lying on parallel planes. By this means, line-to-resonator magnetic coupling arises, the coupling level being dependent on the line-to-resonator relative angular orientation. The line-to-resonator coupling level is the key parameter responsible for modulating the amplitude of the frequency response seen between the CPW ports in the vicinity of the S-SRR fundamental resonance frequency. Specifically, an amplitude notch that can be visualized in the transmission coefficient is changed by the coupling strength, and it is characterized as the sensing variable. Thus, the relative angular orientation between the two parts is measured, when the S-SRR is attached to a rotating object. It follows that the rotation angle and speed can be inferred either by measuring the frequency response of the S-SRR-loaded line, or the response amplitude at a fixed frequency in the vicinity of resonance. It is in addition shown that the angular velocity can be accurately determined from the time-domain response of a carrier time-harmonic signal tuned at the S-SRR resonance frequency. The main advantage of the proposed device is its small size directly related to the small electrical size of the S-SRR, which allows for the design of compact angular displacement and velocity sensors at low frequencies. Despite the small size of the fabricated proof-of-concept prototype (electrically small structures do not usually reject signals efficiently), it exhibits good linearity (on a logarithmic scale), sensitivity and dynamic range.

Interferometric Synthetic Aperture Radar (InSAR) provides constraints on lithospheric kinematics at high spatial resolution. Interpreting InSAR‐derived deformation maps at continental scales is challenged by long‐wavelength correlated noise and the inherent limitation of measuring relative displacements within the data footprint. We address these issues by applying corrections to InSAR time series to estimate ground velocity fields with millimeter‐per‐year precision over hundreds of kilometers. We use these velocity fields to determine the angular velocity of the local tectonic plate, assuming negligible long‐wavelength vertical and intra‐plate deformation. The uncertainty of the angular velocity is primarily influenced by observational errors and the limited imaging geometries available. Using the Arabian plate as an example, this work demonstrates the potential to improve plate motion models and evaluate intra‐plate deformation in regions with sparse ground‐based instrumentation.

This article investigates the prescribed performance attitude tracking control issue of rigid spacecraft subject to angular velocity constraints, input saturation, actuator failures, external disturbances and inertia uncertainty. With the aid of a shifting function, we propose the global asymmetrical prescribed performance functions that guarantee the fixed-time convergence of the tracking error, while simultaneously reducing the overshoot and eliminating the dependence on the initial system conditions. To address the fragility problem inherent in the traditional prescribed performance control, a fragility-preventing coefficient is devised to enable the flexible readjustment of the performance boundaries under the different conditions of input saturation and disturbances. Then, a transformation function is introduced to handle attitude performance constraints and angular velocity limits. Moreover, the neural network is employed to estimate the unknown function. Finally, both stability analysis and numerical simulations are provided to manifest the effectiveness and advantages of the proposed approach.

Batters generate bat-head speed using a kinetic chain that transfers mechanical energy from the lower body to upper limbs and bat (Ae et al., 2017; Horiuchi et al., 2021; Welch et al., 1995). [...]exploring the lower limb movements responsible for the generation of mechanical energy and bat-head speed can provide insight into how to improve batting performance. Biomechanical studies of baseball batting have determined that the lower body movements play an important role in the generation of mechanical energy and bat-head speed, and relationships between kinematic characteristics of the motion of the bat and body and bat-head speed have been identified (Escamilla et al., 2009a, 2009b; Dowling and Fleisig, 2016; McIntyre and Pfautsch, 1982; Messier and Owen, 1984; Race, 1961; Welch et al., 1995). The objective of this study was to optimise lower body movements in a computer simulation model to maximise the peak pelvis angular velocity about the vertical axis during baseball tee-batting. The analysis period was defined as the time from the instant of the stride foot contact with the force platform until one frame before ball impact.2.2 Simulation model A seven-segment simulation model of the lower body (comprising pelvis, and left and right foot, shank, and thigh segments) was developed (Fig. 1) in MATLAB and was evaluated using the coordinate data of the standard motion (Ae et al., In press a,b; Ae et al., 2007).

Space manipulators are typically installed on spacecraft using an emergency separation device (ESD). In the event of a malfunction, the ESD ejects the manipulator from the spacecraft. However, due to the relative rotation of the manipulator’s joints during the ejection, the equivalent ejection mass varies depending on different attitudes. This paper focuses on studying manipulators equipped with separation slide rails and analyzes their ejection characteristics under different attitudes to determine the optimal manipulator attitude for ejection. Initially, the ejection dynamics model of the space manipulator is established using the Lagrangian method, based on the kinetic energy equation, kinematics equation, and the boundary condition between the manipulator and ESD. Afterward, the space dynamics model is transformed into the dynamic model of plane ejection state by recursion formula. From this model, the equivalent ejection mass and ejection velocity are obtained, and the joint angular variation during ejection is acquired by considering joint friction torque. Using the law of conservation of angular momentum, the ejection angular velocity is then calculated. Finally, this study selected a 7-DOF space manipulator as an example and adjusted the damping parameter B of the joint for more precise calculations by choosing the attitude with a relatively larger joint angular variation. The modified model was then tested for its applicability to other attitudes. After determining the value of B, the correctness of the algorithm was validated by MATLAB calculation, ADAMS simulation, and real object ejection test.

In this article, the importance of studying the behavior of small-scale rotating materials and structures is highlighted for its valuable contribution to many scientific and engineering fields. As a result, these types of microbeams have been studied using nonlocal elasticity theory (NET) and modified couple stress (MCST) models, as well as Euler–Bernoulli assumptions for thin beams. The temperature-dependent heat conduction model and the Moore–Gibson–Thompson (MGT) model of heat transfer are also integrated. The effects of nonlocal properties, length scale, thermal conductivity factor fluctuation, the angular velocity of rotation, and thermal parameters on the behavior of the studied variables were investigated. The results were validated and applicable, and the data were systematically compared with previous literature and other investigators. The results show that the materials behave differently at the nanoscale than the results of the usual continuum mechanics approach due to taking into account nonlocal and length-scale effects.

Automatic sensor-to-foot alignment is required in clinical gait analysis using inertial sensors to avoid assumptions about sensors initial positions and orientations. Numerous studies have proposed alignment methods. The current study aimed at describing and accessing the performance of a simple rule to automatically recognize the orientation of the sagittal plane foot angular velocity that can be used with any alignment method and any populations including individuals with severe motor disorders such as patients with cerebral palsy (CP). Fifty-five participants (15 healthy, 15 with CP and 25 with various other motor disorders) wore IMUs on both feet during one or several visits of clinical gait analysis (CGA) with optical motion capture system as reference. The foot coordinate system was determined using acceleration during motionless periods and angular velocity during walking, as previously described in the literature. Based on the foot sagittal plane angular velocity, a novel rule is introduced to determine the latest uncertainty related to mediolateral axis direction which often causes errors. It consisted of massively filtering the signal and applying a simple peak detection, omitting the double peaks with the same sign. The time between the negative and positive peaks can inform on the axis direction. This verification showed excellent results with 99,94% sensibility against the reference. This simple rule could be used to further improve existing sensor-to-segment algorithms with inertial sensors located on the feet, and thus improve pathological gait analysis.

A new formula for the angular velocity of equilibrium figures of a self-gravitating rotating fluid mass is derived. An important feature of this formula is that the angular velocity is expressed in terms of the components of the inner and outer gravitational energy of the figure introduced by us earlier. We proved the adequacy of the new formula by establishing that it gives correct values of angular velocity in important special cases for sequences of homogeneous classical Maclaurin spheroids and Jacobi triaxial ellipsoids. The advantage of the new formula is that it can describe not only uniform ellipsoid equilibrium figures, but also equilibrium figures of any other geometric form, including toroidal and non-ellipsoidal configurations. This formula extends the application of the theory of equilibrium figures and provides additional possibilities for studying the equilibrium and stability of complex dynamical systems.

Gravel cushions are widely laid on the top of structures or rock sheds to absorb the impact energy of rockfalls in mountainous districts. Based on the discrete element method, a numerical model of a rockfall impacting a 2D mixed-size gravel cushion layer at an initial angular velocity was established in this study. The penetration depth of the rockfall, impact force of the cushion surface, and energy dissipation ratio were investigated. Increasing the initial angular velocity and decreasing the particle size of the cushion were found to evidently reduce the maximum penetration depth of the rockfall and increase the impact force of the cushion surface, respectively. The energy dissipation ratio after collision was affected by the particle size of the cushion and the ratio of the angular kinetic energy. Omitting the initial angular velocity led to an underestimation of the energy dissipation ratio, by up to 40.8%. With decreasing particle size of the cushion, the energy dissipation ratio first increased but then decreased. The study results provide a theoretical basis for the design of gravel cushions intended for rockfall protection.

A gyroscope-free strapdown inertial navigation system (GFSINS) solves the carrier attitude through the reasonable spatial combination of accelerometers, with a particular focus on the precision of angular velocity calculation. This paper conducts an analysis of a twelve-accelerometer configuration scheme and proposes an angular velocity fusion algorithm based on the Kalman filter. To address the sign misjudgment issue that may arise when calculating angular velocity using the extraction algorithm, a sliding window correction method is introduced to enhance the accuracy of angular velocity calculation. Additionally, the data from the integral algorithm and the data from the improved extraction algorithm are fused using Kalman filtering to obtain the optimal estimation of angular velocity. Simulation results demonstrate that this algorithm significantly reduces the maximum value and standard deviation of angular velocity error by one order of magnitude compared to existing algorithms. Experimental results indicate that the algorithm’s calculated angle exhibits an average difference of less than 0.5° compared to the angle measured by the laser tracker. This level of accuracy meets the requirements for attitude measurement in the laser scanning projection system.