Rotation Vector Research Articles

Transfer Learning-Based Health Monitoring of Robotic Rotate Vector Reducer Under Variable Working Conditions

Due to their precision, compact size, and high torque transfer, Rotate vector (RV) reducers are becoming more popular in industrial robots. However, repetitive operations and varying speed conditions mean that these components are prone to mechanical failure. Therefore, it is important to develop effective health monitoring (HM) strategies. Traditional approaches for HM, including those using vibration and acoustic emission sensors, encounter such challenges as noise interference, data inconsistency, and high computational costs. Deep learning-based techniques, which use current electrical data embedded within industrial robots, address these issues, offering a more efficient solution. This research provides transfer learning (TL) models for the HM of RV reducers, which eliminate the need to train models from scratch. Fine-tuning pre-trained architectures on operational data for the three different reducers of health conditions, which are healthy, faulty, and faulty aged, improves fault classification across different motion profiles and variable speed conditions. Four TL models, EfficientNet, MobileNet, GoogleNet, and ResNET50v2, are considered. The classification accuracy and generalization capabilities of the suggested models were assessed across diverse circumstances, including low speed, high speed, and speed fluctuations. Compared to the other models, the proposed EfficientNet model showed the most promising results, achieving a testing accuracy and an F1-score of 98.33% each, which makes it best suited for the HM of robotic reducers.

Asymptotic behavior of the equivalent Timoshenko linear beam model used in the analysis of tower buildings

We study the asymptotic properties of a continuous Timoshenko linear beam model immersed in a three-dimensional space and used in the analysis of tower buildings. Assume that the bending and axial behaviors are coupled on the one hand, while the shear and torsional behaviors are coupled on the other hand. If the displacement vector is totally damped and the rotational vector is undamped, or if the rotational vector is totally damped and the displacement vector is undamped, then the system is proved to be exponentially stable, under some assumptions on the physical parameters involved in the problem. We also consider the case when the bending and axial behaviors and/or the shear and torsional behaviors are uncoupled. In this situation, the stability properties are different if the rotational or the displacement vector is damped or not: the system can be exponentially stable, polynomially stable or even unstable.

Study on shift and rotation of image vector in image stabilization system

Study on shift and rotation of image vector in image stabilization system

Long Coherent Processing Intervals for ISAR Imaging: Combined Complex Signal Kurtosis and Data Resampling

Airborne inverse synthetic aperture radar (ISAR) imaging of maneuvering targets is important for maritime surveillance. Long coherent processing intervals (CPIs) can bring better resolution and signal-to-clutter-plus-noise ratio (SCNR). Due to the change in the effective rotation vector (ERV), the conventional Range-Doppler (RD) algorithm is not appropriate for producing a well-focused image. To resolve the above issue, we propose a long CPI imaging algorithm through ERV estimation and data resampling. This algorithm estimates the Doppler length of the sub-aperture image by complex signal kurtosis (CSK) at first. Then, the change in the ERV can be estimated because the ship Doppler length is always proportional to the ERV. Finally, the echo is resampled according to the estimation of the time-varying ERV to obtain the echo from a constant ERV. Computer simulation experiments and measured data have verified the effectiveness of the proposed method. Experimental results demonstrate that the proposed method can achieve ISAR imaging with longer CPIs at low SNR and inhomogeneous clutter.

Anisotropic magnetocapacitance of antiferromagnetic cycloids in BiFeO3

Distinguishing different antiferromagnetic domains by electrical probes is a challenging task, which in itinerant compounds can be achieved, e.g., via the anisotropic magnetoresistance. Here, we demonstrate that in insulators, the anisotropic magnetocapacitance can be exploited for the same purpose. We studied the magnetic field dependence of the dielectric response in BiFeO3, one of the few room-temperature multiferroics. We observed a sizeable dielectric anisotropy upon the rotation of the modulation vector of the antiferromagnetic cycloid in the plane normal to the rhombohedral axis. Importantly, this anisotropy is characteristic of the cycloidal mono-domain state even in zero magnetic field, thus facilitating the determination of the antiferromagnetic domain population. This approach can be utilized to electrically distinguish between antiferromagnetic domains even in complex magnets, such as modulated spin structures, via the magnetodielectric coupling.

A high-precision trajectory capture and playback solver for KUKA iiwa robot

Abstract This paper introduces a sophisticated trajectory capture and playback mechanism for collaborative robots, aimed at enhancing accuracy and operational efficiency through several innovative techniques. The Ju-Gibbs attitude quaternion is utilized for enhanced kinematic modeling across multi-axis systems, which simplifies variables, reduces dimensions, and enhances symbolic clarity, thus surpassing the limitations of traditional rotation vectors and unit quaternions. A new sliding filter is developed to effectively reduce noise and optimize trajectory details more efficiently. Additionally, an automated mechanism is implemented for adjusting the sampling rate and removing static data points at the trajectory’s start and end, further refining data collection accuracy. These advancements have been successfully replicated on the Kuka robot LBR iiwa 7 R800, demonstrating the practical applicability of the solutions in real-world settings.

Вековое геодезическое вращение небесных тел в системе спутников Юпитера

This article studies the relativistic effect of geodetic precession in the rotation around their axes of Jupiter and its 94 satellites for which ephemerides are known. As a result, the most significant secular terms of the geodetic rotation of these celestial bodies were determined for the first time: 1. for Jupiter relative to the barycenter of the Solar System and the plane of the mean orbit of Jupiter at the epoch J2000.0 in Euler angles, in the perturbing terms of physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; 2. for 8 regular (4 inner (Metis J16, Adrastea J15, Amalthea J5 and Thebe J14)) and 4 Galilean (Io J1, Europa J2, Ganymede J3 and Callisto J4))) satellites of Jupiter relative to: a) the barycenter of the Solar system and the plane of the mean orbit of the satellite under study at epoch J2000.0 in Euler angles, in the perturbing terms of the physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; b) the barycenter of the Solar system and the plane of the mean orbit of the barycenter of the Jovian system at epoch J2000.0 in Euler angles, in the perturbing terms of the physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; c) the barycenter of the Jupiter satellite system and the plane of the mean orbit of the studied satellite of the J2000.0 epoch in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the studied body; 3. for 86 irregular satellites (J6–J13, J17–J72, J5501–J5507, J5509–J5523) of Jupiter relative to: a) the barycenter of the Solar system in the absolute value of the angular rotation vector of the geodetic rotation of the studied body; b) the barycenter of the Jupiter satellite system in the absolute value of the angular rotation vector of the geodetic rotation of the studied body. For the J2000.0 epoch, the mean orbits of the studied celestial bodies and the mean orbit of the barycenter of the Jovian system were calculated. For regular satellites, the values of the angles of inclination of their equator to their own orbits were determined. The obtained analytical values of the geodetic precession of the studied celestial bodies can be used for a numerical study of the rotation of these bodies in the relativistic approximation.

Numerical-analytical optimization of orientation algorithms on a spherical model of angular motion of a rigid body

The problem of numerical-analytical optimization of three algorithms for determining orientation quaternions due to refinement of coefficients in the structure of algorithms is considered. Of them, two algorithms use the orientation vector as an "intermediate parameter". The coefficients are refined on the basis of computer modeling and the minimization of the error of the accumulated computational drift using the analytical reference model of the spherical motion of a rigid body as a model rotational motion in a sequence of Krylov angles that change over time according to a linear law. For this, the test motion model is supplemented by modeling ideal information from the outputs of the angular velocity sensors in the form of quasi-coordinates using analytical formulas for the apparent rotation vector. It is shown that the accumulated error of computational drift on the proposed reference model of rotary motion has a linear law of growth with time for all algorithms under consideration. As a result of the numerical experiment, new values ​​of the coefficients in the structures of the algorithms were obtained, which minimize the error of the accumulated drift and improve the characteristics of the trend of this error. The carried out optimization leads to a decrease by an order of magnitude of the maximum error value and a change in the linearly growing nature of the dependence of the calculation drift error on time to an oscillatory one. The results of the computational experiment are given.

Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl_{3}.

In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl_{3}, the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl_{3}. Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl_{3}. We examine the oscillatory features of thermal conductivities (κ//a, κ//b) with fixed external fields and find distinct behavior for the gapped (B//a) and gapless (B//b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ_{a}) and its oscillatory features with the rotation of in-plane magnetic fields from B//b to B//a. The thermal resistivity λ(B,ϕ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl_{3} are closely linked to the putative Kitaev spin liquid phase and its excitations.

Methodology For Extracting Poplar Planted Fields From Very High-Resolution Imagery Using Object-Based Image Analysis and Feature Selection Strategy

Abstract. Poplars (Populus sp.), a tree that grows rapidly species, are significant as industrial forest products. The delineation and monitoring of poplar cultivated areas are invaluable for decision-making processes. With the remote sensing technology, accurate detection of poplar planted areas could be determined much faster, more economically, and with minimum labor requirements. The objective of this research is to create a map of poplar plantations in the Sakarya region of Turkey utilizing Worldview-3 satellite imagery. Object-based image analysis (OBIA) through the application of the multi-resolution segmentation method (MRS) was employed to generate image segments, and then three prevailing machine learning algorithms, namely Support Vector Machine (SVM), Random Forest (RF) and Rotation Forest (RotFor) were implemented to produce LULC maps of the study area including 11 landscape features. The most effective and contributing object features that assure high separability between landscape features were determined using a filter-based Chi-square algorithm for the prediction models constructed with SVM, RF, and RotFor classifiers. Results revealed that the SVM classifier achieved the highest overall accuracy (91.73%) with 38 features out of 88 features, about 3% improvement compared to the other algorithms. According to the SHAP analysis, the IHS feature was the most effective one in the constructed RF model, followed by the CI (red edge), NDVI-1 and NDVI-2 vegetation indices.

A Novel Recognition Method for Complex Power Quality Disturbances Based on Rotation Vector and Fuzzy Transfer Field

A Novel Recognition Method for Complex Power Quality Disturbances Based on Rotation Vector and Fuzzy Transfer Field

Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

A Low-Computational-Complexity Digital Predistortion Model for Wideband Power Amplifier.

This paper proposes a Composition Piecewise Memory Polynomial (CPMP) digital predistortion model based on a Vector Switched (VS) behavioral model to address the challenges of severe nonlinearity and strong memory effects in wideband power amplifiers (PAs). To tackle this issue, two thresholds are calculated and used to segment the envelope values of the input signal according to the nonlinear distortion characteristics of the PA. In this approach, a Generalized Memory Polynomial (GMP) model is employed for the lower segment, a Memory Polynomial (MP) model is employed for the middle segment, and a higher-order GMP model is employed for the upper segment. By sharing the fundamental MP among the proposed segmented models and leveraging a design methodology that configures different cross terms, memory depths, and polynomial orders for each segment, this model achieves superior linearization performance while simultaneously reducing the computational complexity associated with model extraction. The experimental results demonstrate that the adjacent channel power ratio (ACPR) of the predistorted PA output signal using the proposed model improves from -36 dBc to -54 dBc, matching the performance of the GMP model. Furthermore, this performance is 0.5 dBc better than the Piecewise Dynamic Deviation Reduction (PDDR) and Decomposed Vector Rotation (DVR) models. Notably, the complexity of the proposed parameter extraction process is 28.8% of the DVR model, 21.79% of the GMP model, and 12.83% of the PDDR model.

Shape and stability of rotation sets for incompressible flows on the torus

AbstractIn this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ T d , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ T 2 . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤd. If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C0-open and dense among those having proper rotation cones.

A Generalization of the Finsler–Hadwiger Theorem

Summary We give a new generalization of the Finsler–Hadwiger theorem along with a proof using the rotation of vectors.

Analysis of the degradation in transmission accuracy of RV reducers considering the wear clearance between cycloidal wheels and pinwheels

To accurately determine the transmission accuracy degradation pattern of Rotate Vector (RV) reducers due to wear, a predictive method is proposed that simultaneously considers the initial clearance and wear clearance between the cycloid wheel and the pinwheel. The initial clearance is derived from a comprehensive gear system analysis, considering assembly errors, manufacturing errors and modifications. Building on this, the wear depth of the cycloid wheel tooth profile is numerically simulated using Archard's wear theory, revealing the wear distribution pattern under various operating conditions. A Gaussian regression model is used to predict the maximum wear amount for different operational durations. Based on the predicted wear amount, a multi-body dynamic simulation model incorporating wear clearance was established to analyze the transmission error under varying clearance conditions. Results indicate that the wear depth along the tooth profile initially increases and then decreases. The depth and region of wear along the tooth profile gradually increase with load and output speed, with the impact of load on the wear region being greater than that of output speed. Under the initial clearance condition, the maximum transmission error is 22.91″. As the wear clearance increases, transmission accuracy declines sharply. When the cumulative wear clearance reaches 0.2 mm, the transmission error exceeds the allowable backlash limit. This study provides a theoretical reference for predicting accuracy degradation and guides the manufacturing design of RV reducers.

An accurate and locking-free geometric exact beam formulation on the special orthogonal group SO(3)

An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.

Eulerian rates of elastic incompatibilities applied to size-dependent hardening in finite torsion

Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finite-deformation response of anisotropic elastic–inelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as Rij, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations, Rij are equal to the negative of the components of the rate of Nye-Kröner’s dislocation density tensor. In contrast to these small strain components, each Rij is invariant under superposed rigid body motions such that it can be used independently in the constitutive equations to describe the material behavior. Specifically, in this work, Rij provide a size-dependent enhancement to hardening that can increase or decrease during loading history, modeling the generation and annihilation of densities of geometrically necessary dislocations in metal plasticity. The application to the finite-deformation cyclic torsion of thin wires demonstrates the potential of this approach and the importance of the constitutive equation for the plastic spin rate both on the rotations of the microstructural vectors and on the predicted size-effect.

Shear-driven magnetic buoyancy in the solar tachocline: Dependence of the mean electromotive force on diffusivity and latitude

Abstract The details of the dynamo process that is responsible for driving the solar magnetic activity cycle are still not fully understood. In particular, whilst differential rotation provides a plausible mechanism for the regeneration of the toroidal (azimuthal) component of the large-scale magnetic field, there is ongoing debate regarding the process that is responsible for regenerating the Sun’s large-scale poloidal field. Our aim is to demonstrate that magnetic buoyancy, in the presence of rotation, is capable of producing the necessary regenerative effect. Building upon our previous work, we carry out numerical simulations of a local Cartesian model of the tachocline, consisting of a rotating, fully compressible, electrically conducting fluid with a forced shear flow. An initially weak, vertical magnetic field is sheared into a strong, horizontal magnetic layer that becomes subject to magnetic buoyancy instability. By increasing the Prandtl number we lessen the back reaction of the Lorentz force onto the shear flow, maintaining stronger shear and a more intense magnetic layer. This in turn leads to a more vigorous instability and a much stronger mean electromotive force, which has the potential to significantly influence the evolution of the mean magnetic field. These results are only weakly dependent upon the inclination of the rotation vector, i.e. the latitude of the local Cartesian model. Although further work is needed to confirm this, these results suggest that magnetic buoyancy in the tachocline is a viable poloidal field regeneration mechanism for the solar dynamo.

A Calculation Method of Bearing Balls Rotational Vectors Based on Binocular Vision Three-Dimensional Coordinates Measurement

The rotational speed vectors of the bearing balls affect their service life and running performance. Observing the actual rotational speed of the ball is a prerequisite for revealing its true motion law and conducting sliding behavior simulation analysis. To address the need for accuracy and real-time measurement of spin angular velocity, which is also under high-frequency and high-speed ball motion conditions, a new measurement method of ball rotation vectors based on a binocular vision system is proposed. Firstly, marker points are laid on the balls, and their three-dimensional (3D) coordinates in the camera coordinate system are calculated in real time using the triangulation principle. Secondly, based on the 3D coordinates before and after the movement of the marker point and the trajectory of the ball, the mathematical model of the spin motion of the ball was established. Finally, based on the ball spin motion model, the three-dimensional vision measurement technology was first applied to the measurement of the bearing ball rotation vector through formula derivation, achieving the analysis of bearing ball rolling and sliding characteristics. Experimental results demonstrate that the visual measurement system with the frame rate of 100 FPS (frames per second) yields a measurement error within ±0.2% over a speed range from 5 to 50 RPM (revolutions per minute), and the maximum measurement errors of spin angular velocity and linear velocity are 0.25°/s and 0.028 mm/s, respectively. The experimental results show that this method has good accuracy and stability in measuring the rotation vector of the ball, providing a reference for bearing balls' rotational speed monitoring and the analysis of the sliding behavior of bearing balls.