Centroid Trajectory Research Articles

Measurement and Dynamic Analysis of the Centroid Trajectories of Angular-Contact Ball Bearing Cages

When a high-speed rolling bearing cage comes into contact with rollers, it experiences random movement due to friction and collision, which significantly impacts the overall performance of the bearing. To further investigate the motion law of cages, a test bench for a 7010C angular-contact bearing cage was constructed. This setup utilized laser sensors to obtain changes in attitude and displacement during operation. After analyzing how cage deflection errors influenced trajectory measurements, corrections were applied to the measurement results. Additionally, an investigation was conducted into the effects of varying rotational speeds on the dynamic performance of the cage. Simulations were performed using ADAMS software, which verified both the effectiveness of the measuring method and the testing results. The findings indicated that within the tested range of rotational speeds, the centroid trajectory stability of the cage gradually improved as rotational speed increased and then began to show a tendency to deteriorate. Furthermore, there existed a negative correlation between the deflection error of the cage and the centroid trajectory stability.

Critical Threshold-Based Heat Damage Evolution Monitoring to Tea Plants with Remotely Sensed LST over Mainland China

Tea plants (Camellia sinensis (L.) Kuntze) are a cash crop that thrive under warm and moist conditions. However, tea plants are becoming increasingly vulnerable to heat damage (HD) during summer growing seasons due to global climate warming. Because China ranks first in the world in both harvested tea area and total tea production, monitoring and tracking HD to tea plants in a timely manner has become a significant and urgent task for scientists and tea producers in China. In this study, the spatiotemporal characteristics of HD evolution were analyzed, and a tracking method using HD LST-weighted geographical centroids was constructed based on HD pixels identified by the critical LST threshold and daytime MYD11A1 products over the major tea planting regions of mainland China from two typical HD years (2013 and 2022). Results showed that the average number of HD days in 2022 was five more than in 2013. Daily HD extent increased at a rate of 0.66% per day in 2022, which was faster than that in 2013 with a rate of 0.21% per day. In two typical HD years, the tea regions with the greatest HD extent were concentrated south of the Yangtze River (SYR), with average HD pixel ratios of greater than 50%, then north of the Yangtze River (NYR) and southwest China (SWC), with average HD pixel ratios of around 40%. The regions with the least HD extent were in South China (SC), where the HD ratios were less than 40%. The HD LST-weighted geographical centroid trajectories showed that HD to tea plants in 2013 initially moved from southwest to northeast, and then moved west. In 2022, HD moved from northeast to west and south. Daily HD centroids were mainly concentrated at the conjunction of SYR, SWC, and SC in 2013, and in northern SWC in 2022, where they were near to the centroid of the tea planting gardens. The findings in this study confirmed that monitoring HD evolution of tea plants over a large spatial extent based on reconstructed remotely sensed LST values and critical threshold was an effective method benefiting from available MODIS LST products. Moreover, this method can identify and track the spatial distribution characteristics of HD to tea plants in a timely manner, and it will therefore be helpful for taking effective preventative measures to mitigate economic losses resulting from HD.

Dynamic theory and experimental testing in ipsilateral offset dual-motor excitation system

This paper addresses unbalanced trajectories of dual-motor vibrating screens by proposing a dynamic theory and experimental testing. First, based on the Lagrange equation, the dynamic model of ipsilateral offset dual-motor excitation system is established. Subsequently, the steady response is worked out by solving the differential equation of motion of the vibrating body. Then, the synchronization condition and synchronization stability criterion of the system are determined employing the small parameter method and the Routh–Hurwitz criterion. Numerical analysis methods are given to reveal the relationship between structural parameters and synchronization characteristics of the vibration system. Moreover, an mechanical–electric coupling model is developed to study dynamic characteristics. The results demonstrate that synchronization condition can be described with capture torque and difference of output torque between motors. The synchronization ability is enhanced by improving installation distance of the motors. Additionally, increasing angle β or decreasing angle θ of the motors is in favor of optimization of centroid trajectory; swing oscillation of the box can be controlled by adjusting the main inclination angle of motors; in such a condition, equilibrium of motion trajectory of system is enhanced. Finally, the validity method for designing vibrating screen is verified through theoretical calculations, simulation analysis, and experiments.

Design and stability analysis of the gear-type mobile mechanism with a single actuator.

Gear mechanism transmits the motion and power of parallel axes, intersecting axes and staggered axes, which has been widely employed in production and life. Gear-type mobile mechanism is a type of robot that can achieve motion through gear transmission. Due to its unique motion mode, it can handle various tasks in certain unconventional environments, such as particularly steep surfaces. Cylindrical gear, bevel gear and non-cylindrical gear are taken as the main parts of the mechanism to form a novel research series, respectively. The models of gear-type mobile mechanism are established in this paper, and the degrees of freedom of the mechanism are briefly calculated based on the screw theory. Simultaneously, the influence of centroid trajectory on motion stability is discussed to solve the possible problem that opposite rotation occur during the movement. Furthermore, the trajectory model of zero moment point is calculated considering the motion of the gear-type mobile mechanism. After that, the simulation and experimental analysis of its motion capability show that the gear-type mobile mechanism has excellent characteristics in stability, flexibility and continuity.

Wing tip vortices dynamics with crosswind effect using the large eddy simulation (LES) theory

In the operational control of airports it is imperative to reduce the interval between landing and takeoff operations. To this end, it is necessary to address the risk of aircraft vortex wake encounter during these operations. This paper describes a refined numerical method developed to study the phenomenon of aircraft vortex wake interaction with the airport runway, employing the Lagrangian approach with accelerated processing by parallel computing.The numerical methodology relies on a vortex method incorporating the Large Eddy Simulation (LES) theory for the two-dimensional domain.The Image method is used to guarantee the condition of impenetrability on the airport runway. In this context, open multiprocessing (OpenMP) and an algorithm that subdivides the fluid domain into box structures to expedite the calculation of eddy viscosity locally are used in a Fortran code. Quantitative and qualitative results are presented at various Reynolds numbers, in dimensionless crosswind conditions. In addition, preliminary results are presented for a Boeing 757-200, representative of practical aviation problems. The results are in agreement with experimental results and other numerical simulations. It is possible to satisfactorily capture the centroid trajectories of the vortical structures shed from the wingtips, the temporal deformation of these structures, as well as the dynamics of the primary and secondary structures in interaction with the airport runway.

Trajectory Tracking of Variable Centroid Objects Based on Fusion of Vision and Force Perception.

Compared with traditional rigid objects' dynamic throwing and catching by the robot, the in-flight trajectory of nonrigid objects (incredibly variable centroid objects) throwing is more challenging to predict and track. This article proposes a variable centroid trajectory tracking network (VCTTN) with the fusion of vision and force information by introducing force data of throw processing to the vision neural network. The VCTTN-based model-free robot control system is developed to perform highly precise prediction and tracking with a part of the in-flight vision. The flight trajectories dataset of variable centroid objects generated by the robot arm is collected to train VCTTN. The experimental results show that trajectory prediction and tracking with the vision-force VCTTN is superior to the ones with the traditional vision perception and has an excellent tracking performance.

A Hierarchical Control Strategy for a Rigid-Flexible Coupled Hexapod Bio-Robot.

The motion process of legged robots contains not only rigid-body motion but also flexible motion with elastic deformation of the legs, especially for heavy loads. Hence, the characteristics of the flexible components and their interactions with the rigid components need to be considered. In this paper, a hierarchical control strategy for robots with rigid-flexible coupling characteristics is proposed. This strategy involves (1) leg force prediction based on real-time motion trajectories and feedforward compensation for the error caused by flexible components; (2) building upon the centroid dynamics model of the rigid-body chassis, the centroid trajectories (centroid angular momentum (CAM) and centroid linear momentum (CLM)) and the body trajectory are taken into account to derive the optimal drive torque for maintaining body stability; (3) finally, the precise force control of the hydraulic drive units is achieved through the sliding mode control algorithm, integrating the dynamic model of the flexible legs. The proposed methods are validated on a giant hexapod robot weighing 3.5 tons, demonstrating that the introduced approach can reduce the robot's vibrations.

Modeling the long-term transport and fate of oil spilled from the 2021 A Symphony tanker collision in the Yellow Sea, China: Reliability of the stochastic simulation

Coupled with a 3D hydrodynamic model, a well-established 3D oil spill model is used to simulate the transport and fate of oil spilled from the A Symphony oil tanker collision in the Yellow Sea on April 27, 2021. The model is first validated by airborne mini-SAR and shipborne X-band radar observation in a 30-day simulation. Subsequently, the model prediction capabilities are investigated over a longer period when hydrodynamic data may not be available. In these cases, hydrodynamic data in earlier years are used for stochastic simulation, and the reliability of a multi-year stochastic simulation is tested. To evaluate the impact of hydrodynamics and meteorological conditions, indexes including oil sweeping area for surface oil, as well as oil centroid trajectory and oil fate for both the surface and subsurface oil, are statistically analyzed for a period up to 90 days after the spill. Over time, the deviation in the stochastic simulation relative to the deterministic simulation increased in the modeled oil transport, indicating an error accumulation. However, in the modeled oil fate, the deviation showed an interesting variation of first increasing and then gradually decreasing. This phenomenon can be attributed to three contributing factors: (1) limitations in empirical equations used in the model; (2) limited environmental impact of the spill; (3) differential role of small-scale ocean processes in short- and long-term simulations. The uncertainty in stochastic members may serve as an indicator of forecast accuracy.

Evaluating drought monitoring utility of the top-down and bottom-up satellite precipitation products over mainland China from a three-dimensional perspective

Satellite-based quantitative precipitation estimates (QPEs) have shown great potential in the precipitation-related extremes estimation. However, little is known about the capability of different QPEs to monitor the dynamic evolutions of drought on various spatio-temporal scales. Here, the drought utility of two top-down QPEs (i.e., Climate Hazards Group InfraRed Precipitation with Stations, CHIRPS; Integrated Multi-SatellitE Retrievals for Global precipitation measurement-Final run, IMERG-F) and one bottom-up QPE (i.e., Soil Moisture to Rain-Advanced SCATterometer, SM2RAIN-ASCAT), is evaluated comprehensively in mainland China, based on three commonly used drought indices (Standardized Precipitation Index, Standardized Precipitation Evapotranspiration Index, Composite index of meteorological drought). The results indicate that the top-down QPEs generally show better performance in detecting drought occurrence over the humid and low-altitude regions in eastern China than the arid and high-altitude regions in western China. IMERG-F performs best in detecting drought occurrence in the entire mainland China, followed by CHIRPS, and the least satisfactory by SM2RAIN-ASCAT. The trajectory of drought centroids and the temporal variability of drought characteristics are highly dependent on both the drought indices selected and QPEs used. IMERG-F and CHIRPS can better reproduce the trajectories of large-scale drought events (e.g., the locations of drought origin and termination) than SM2RAIN-ASCAT. The ability in tracking the drought centroid trajectory of all three QPEs is higher at the smaller spatial scales, also it improves from the semi-arid to humid regions. Our results highlight the superiority of the top-down QPEs in drought monitoring compared with the bottom-up QPE in mainland China, particularly over the humid regions. The application of SM2RAIN-ASCAT in drought monitoring to the large-scale arid areas should be cautious.

Identification of football teams styles of play by cluster analysis

The aim of this study was to characterize performance patterns of attack and defence of football teams, and the inter-team's relation throughout the game. First and second leg of the Brazilian Cup Final 2018 Under-20 category were recorded using two video cameras. Three hundred twelve attacks and defences sequences in the two football matches were analyzed. All players and the ball were tracked throughout the matches, then notational and spatiotemporal variables were measured: attack duration, number of actions per attack, occupied area, team centroid, ratio between number of action and attack duration, total centroid trajectory, and ball displacement. Those variables were grouped using Ward's minimum variance method. The results showed that: (i) teams presented variated styles of play in attack and defence intra and intermatches; (ii) spatial variables such as positions and displacements contributed the most to separate the patterns; (iii) the interteams synchrony found throughout the game revealed different outcomes; and (iv) specific attacking patterns led to shoot to goal. We concluded that football teams vary their style of play within match and intermatches; spatial variables such as positions and displacements contributed the most to separate the patterns; and the interteam relation revealed synchrony throughout the game.

Flexible modeling and dynamics simulation of four-bar beating-up system with clearance

To explore the actual working characteristic of the beating-up mechanism on looms, the Step function is adopted to convert the beating-up resistance to an equivalent torque acting on the rocking shaft, and a new method of calculating and simulating the resistance is hereby raised. In accordance with the two-state joint clearance, the paper establishes a double-side model of the four-bar beating-up system in clearance status via ADAMS/View software, and under the consideration of both beating-up resistance and flexible deformation conditions, the contact simulation of beating-up motion with different clearances (0.01∼0.12 mm) is achieved. The main findings are as follows: the actual working condition could be reflected more accurately if the beating-up resistance and component flexibility are included into the simulation computing; from the perspective of the impact on sley moving and beating-up loads, 0.08 mm clearance is obviously less then another three clearances (0.01 mm, 0.04 mm and 0.12 mm); the multi-point contact and collision with peak load greater than 4000 N is existed in connecting rod bearing in the 0∼350 Hz low frequency area, which is likely to exacerbate the wear and fatigue rupture of the bearing; the dynamic shock load of rocking shaft on the loom frame is far greater than that of the crankshaft, indicating that the rocking shaft is the main carrier for delivering the beating-up power; compared to the clearance of 0.08 mm and 0.12 mm, the dynamic impact load generated by the clearance of 0.01 mm and 0.04 mm on the loom frame is obvious greater. In addition, under the clearance condition, transverse vibration could be occurred for the flexible crankshaft due to the deviation of its centroid trajectory, which is detrimental to vibration and noise reduction for the loom system. On the basis of the work, a number of viewpoints with theoretical and practical significance could be provided to the design of beating-up system on the loom with clearance.

Dynamical properties of quasiparticles in a tunable Kekulé graphene superlattice

We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekulé distortions (i.e., Kekulé-O, Kekulé-Y and Kekulé-M). On the one hand, we numerically show the visualized evolution process of Kekulé quasiparticles; while on the other hand, we analytically obtain the centroid trajectory of the quasiparticles, and both of them agree well with each other. The results reveal that the relativistic Zitterbewegung (ZB) phenomenon occurs in the Kekulé systems. Furthermore, through analyzing the frequency of ZB, we unveil the one-to-one relationship between ZB and Kekulé textures, i.e., the ZB frequencies of Kekulé-O, Kekulé-Y and Kekulé-M quasiparticles feature single, double and six frequencies, respectively. Finally, we propose a scheme to distinguish among different Kekulé textures from the dynamical perspective. The predictions in this paper are expected to be experimentally verified in the near future, so as to facilitate further research of Kekulé structures in solid materials or artificial systems.

Investigation of Dynamic Characteristics Experiments and Stability Evaluation Criterion of Space Ball Bearing Cage

The operation stability of the oil-impregnated cage, which serves as the lubrication and operation core of space ball bearings, is linked to the stability of the bearing dynamic friction moment. A cage dynamic characteristics test rig based on a high-speed camera system is created in this study to achieve synchronous monitoring of the cage centroid trajectory and bearing dynamic friction torque without changing the bearing structure. The centroid trajectory of the cage is separated into aggregation and discrete areas based on the distribution density of centroid trajectory points. To establish the mapping relationship between the shape and fluctuation of the cage centroid trajectory and the stationarity of the bearing dynamic friction moment, a new characteristic quantity, centroid trajectory fluctuation ratio (the ratio of the distance between the track points in the discrete area and the boundary of the aggregation area to the average width of the aggregation area), is adopted. In addition, a criterion based on the distribution density of the centroid trajectory points is proposed for evaluating the cage's operation stability. The findings of the study led to two primary conclusions: (1) The sudden jump of bearing dynamic friction torque is caused by the fluctuation of the cage centroid trajectory, which is independent of the trajectory shape. (2) The fluctuation ratio of centroid trajectory might effectively reflect the operation stability of the cage.

Discreteness of cell–surface contacts affects spatio-temporal dynamics, adhesion, and proliferation of mouse embryonic stem cells

The self-renewal and lineage-specific differentiation of stem cells are regulated by interactions with their microenvironments, called stem cell niche. Stem cells receive both biochemical and biophysical cues from their niche, which leads to the activation of signaling pathways, resulting in the modulation of gene expressions to guide their fate. Most of previous studies are focused on the effect of substrate stiffness using hydrogels with different Young’s moduli, and information is lacking on the effect of the discreteness of cell–substrate contacts on stem cells. Using mouse pluripotent, embryonic stem cells (mESCs) as the model system for early development, we quantitatively investigated the migration, dynamic deformation, and adhesion of mESCs on sparse and dense gelatin nanofibers deposited on glass surfaces, with a continuous layer of gelatin coated on glass substrates as the control. After confirming the maintenance of pluripotency on all the surfaces throughout the experiments, the centroid trajectories were monitored using timelapse imaging. The mean square displacement analysis indicated that both the diffusion coefficient and exponent were largest on sparse nanofibers, while the diffusion coefficient of mESCs on dense nanofibers was comparable to that on the control. Moreover, power spectral analysis of the shape deformation in the Fourier mode indicated that mESCs predominantly underwent elliptic deformation (mode 2), with the largest energy dissipation on sparse nanofibers. These data suggest that mESCs can deform and move on sparse nanofibers owing to the discrete cell–surface contact points. Intriguingly, using a self-developed technique based on laser-induced shock waves, a distinctly larger critical pressure was required to detach cells from nanofibers than from continuous gelatin. This finding suggests that the continuous but weak cell-substrate contacts suppress the deformation-driven mESC migration. As one of the key biological functions of stem cells, the proliferation rate of mESCs on these surfaces was determined. Although the observed difference was not statistically significant, the highest proliferation rate was observed on nanofibers, suggesting that the discreteness of cell–surface contacts can be used to regulate not only spatio-temporal dynamics but also the biological function of pluripotent stem cells.

Deep learning-based synthetization of real-time in-treatment 4D images using surface motion and pretreatment images: A proof-of-concept study.

To develop a deep learning model that maps body surface motion to internal anatomy deformation, which is potentially applicable to dose-free real-time 4D virtual image-guided radiotherapy based on skin surface data. Body contours were segmented out of 4DCT images. Deformable image registration algorithm was used to register the end-of-exhalation (EOE) phase to other phases. Deformation vector field was dimension-reduced to the first two principal components (PCs). A deep learning model was trained to predict the two PC scores of each phase from surface displacement. The instant deformation field can then be reconstructed, warping EOE image to obtain real-time CT image. This approach was validated on 4D XCAT phantom, the public DIR-Lab, and 4D-Lung dataset respectively, with and without simulated noise. Validation accuracy of the tumor centroid trajectory was observed as 0.04 ± 0.02mm on XCAT phantom. For the DIR-Lab dataset, 300 landmarks were annotated on the end-of-inhalation (EOI) images of each patient, and the mean displacements between their predicted and reference positions were below 2mm for all studied cases. For the 4D-Lung dataset, the average dice coefficients ± std between predicted and reference tumor contours at EOI phase were 0.835 ± 0.092 for all studied cases. A deep learning-based approach was proposed and validated to predict internal anatomy deformation from the surface motion, which is potentially applicable to on-line target navigation for accurate radiotherapy based on real-time 4D skin surface data and pretreatment images.

Dynamic Performance Analysis of Cage in Four-Point Contact Ball Bearing

Due to the special structure of double-half inner rings, four-point contact ball bearings are prone to uneven forces in the inner raceway during movement, which affects the dynamic performance of the rolling element and cage, and even leads to cage sliding. Dynamic performance of the cage is an important factor affecting the working stability of bearings. In this paper, in order to grasp the operation law of the cage so as to guide the application of four-point contact ball bearings, the dynamic model of four-point contact ball bearings is established by the secondary development of Automatic Dynamic Analysis of Mechanical Systems (ADAMS). The dynamic performance of the cage is analyzed and evaluated with the indexes of vortex radius ratio and vortex velocity deviation ratio of the cage centroid trajectory. The results show the following: the cage stability increases and then decreases to a certain degree with rotating speed-rise; it increases and then decreases with the increase in the pure axial load; under a combination of axial and radial load, the cage moves more smoothly with smaller radial force. Rotating speed has little effect on cage stability, while radial force has a great influence on cage stability, followed by axial load. In order to verify the simulation results, a test bench for rolling bearing cages is developed, and the accuracy of the simulation results is verified by the test results.

Centroidal Trajectory Generation and Stabilization Based on Preview Control for Humanoid Multi-Contact Motion

Multi-contact motion is important for humanoid robots to work in various environments. We propose a centroidal online trajectory generation and stabilization control for humanoid dynamic multi-contact motion. The proposed method features the drastic reduction of the computational cost by using preview control instead of the conventional model predictive control that considers the constraints of all sample times. By combining preview control with centroidal state feedback for robustness to disturbances and wrench distribution for satisfying contact constraints, we show that the robot can stably perform a variety of multi-contact motions through simulation experiments.

Joint stiffness of a musculoskeletal bionic leg based on the foot stiffness ellipse model

For the bionic jumping robot, there is contact force between the foot and the environment inevitably. Bionic jumping robots need to interact with the environment for force/position information in a compliant manner. Therefore, it is necessary to analyze the joint stiffness and foot stiffness of a bionic jumping robot. Based on analyzing the muscle arrangement and flexible jumping movement principle of a dog leg, a kind of musculoskeletal leg driven by pneumatic artificial muscles (PAMs) is presented. The centroid trajectory of the bionic leg is planned for jumping. Each joint stiffness is derived by the joint torque, which is changing with PAM inner pressure and joint angular displacement. On the other hand, joint stiffness can be planned by the foot stiffness. A kind of ellipse stiffness model of foot is proposed by analyzing the foot elastic potential energy caused by the contact force, and each joint stiffness of the bionic leg is calculated by the foot stiffness, which is mapping by the Jacobian matrix. The joint angular stiffness is analyzed by changing the foot stiffness ellipse parameters, and the expected joint stiffness of the bionic leg for jumping is planned based on the foot stiffness model. This study will pay a foundation for controlling the joint stiffness to achieve stable jumping of the bionic leg.

Jumping Motion Based on Momentum Optimization Control and Differential Dynamic Programming for a Multilocomotion Robot

AbstractJumping motion is an indispensable motion mode for a multilocomotion robot, which will improve the crossing ability of the robot. This paper proposes a novel jumping control scheme for an MLR to perform jumping motion. The control strategy divides the whole jumping motion into three phases: the launch phase, the flight phase, and the landing phase. In the launch and landing phases, the controller is designed based on the centroid dynamics. By controlling the centroid momentum, the robot can achieve the desired centroid trajectory to obtain the initial take‐off speed in the launch phase and to maintain stability and reduce impact in the landing phase. In the flight phase, Differential Dynamic Programming algorithm is used to adjust the posture of the robot to further improve the jumping height and prepare for a smooth landing. Finally, the effectiveness of the proposed method is evaluated through simulations.

Experimental research on cage motion with different pocket shapes in angular contact ball bearing

The cage motion with different pocket shapes, such as spherical, square, and cylindrical, in an angular contact ball bearing under different operating conditions are studied experimentally. A test rig with two laser displacement sensors is used to obtain the displacements of the cage in five freedom degrees. The results reveal that these three type cage shapes have different trends of the centroid trajectory versus rotating speed or radial load. The whirling radius is equal to half of the pocket clearance for the spherical pocket, and half of the guiding clearance for both square and cylindrical pocket. The slip rates of all cages decrease with increasing radial load, and increase with rotating speed. Both inclination angel and slip rate of the spherical, cylindrical and square pocket decrease in turn.