Angular Velocity Research Articles

Nonlinear Dynamics Analysis of Handgrip Strength Using the Poincaré Plot Method Through Video Processing Techniques

Background/Objectives: The aim of this study was to analyze the nonlinear dynamics of handgrip strength (HGS) in young adults, focusing on hand dominance, by employing the Poincaré plot method to assess short- and long-term variability utilizing dynamometry and video motion capture during sustained isometric contractions. Methods: A cross-sectional exploratory study was conducted on 30 healthy subjects (mean age 21.6 ± 1.3 years, 13 males and 17 females), measuring HGS for both the dominant hand (DH) and nondominant hand (NDH) using a Saehan hydraulic dynamometer during 25-s sustained isometric contractions. A GoPro HERO11 Black camera recorded the dynamometer’s needle movements, and the video data were analyzed using Kinovea software. Angular values were converted to force using a calibration-based formula, and the Poincaré plot computed variability indices (short-term variability—SD1, long-term variability—SD2, ratio SD1/SD2, and area of the fitting ellipse) for each hand in relation to HGS and angular velocity (AV). Data analysis included descriptive and inferential statistics. Results: We demonstrated a strong correlation between mechanical and video measurements (p ≤ 0.001), confirming the reliability of the video method. The findings highlight the importance of nonlinear analysis in understanding neuromuscular function and fatigue, revealing significant correlations among HGS, AV, Poincaré indices, and fatigue levels in both hands (p ≤ 0.001). Increased maximum HGS and AV correlated with higher nonlinear variability in force production. Conclusions: This study confirms the reliability of the proposed video-based HGS assessment and demonstrates the effectiveness of Poincaré plot analysis for capturing nonlinear variability in HGS.

Application of Isokinetic Dynamometry Data in Predicting Gait Deviation Index Using Machine Learning in Stroke Patients: A Cross-Sectional Study

Background: Three-dimensional gait analysis, supported by advanced sensor systems, is a crucial component in the rehabilitation assessment of post-stroke hemiplegic patients. However, the sensor data generated from such analyses are often complex and challenging to interpret in clinical practice, requiring significant time and complicated procedures. The Gait Deviation Index (GDI) serves as a simplified metric for quantifying the severity of pathological gait. Although isokinetic dynamometry, utilizing sophisticated sensors, is widely employed in muscle function assessment and rehabilitation, its application in gait analysis remains underexplored. Objective: This study aims to investigate the use of sensor-acquired isokinetic muscle strength data, combined with machine learning techniques, to predict the GDI in hemiplegic patients. This study utilizes data captured from sensors embedded in the Biodex dynamometry system and the Vicon 3D motion capture system, highlighting the integration of sensor technology in clinical gait analysis. Methods: This study was a cross-sectional, observational study that included a cohort of 150 post-stroke hemiplegic patients. The sensor data included measurements such as peak torque, peak torque/body weight, maximum work of repeated actions, coefficient of variation, average power, total work, acceleration time, deceleration time, range of motion, and average peak torque for both flexor and extensor muscles on the affected side at three angular velocities (60°/s, 90°/s, and 120°/s) using the Biodex System 4 Pro. The GDI was calculated using data from a Vicon 3D motion capture system. This study employed four machine learning models—Lasso Regression, Random Forest (RF), Support Vector regression (SVR), and BP Neural Network—to model and validate the sensor data. Model performance was evaluated using mean squared error (MSE), the coefficient of determination (R2), and mean absolute error (MAE). SHapley Additive exPlanations (SHAP) analysis was used to enhance model interpretability. Results: The RF model outperformed others in predicting GDI, with an MSE of 16.18, an R2 of 0.89, and an MAE of 2.99. In contrast, the Lasso Regression model yielded an MSE of 22.29, an R2 of 0.85, and an MAE of 3.71. The SVR model had an MSE of 31.58, an R2 of 0.82, and an MAE of 7.68, while the BP Neural Network model exhibited the poorest performance with an MSE of 50.38, an R2 of 0.79, and an MAE of 9.59. SHAP analysis identified the maximum work of repeated actions of the extensor muscles at 60°/s and 120°/s as the most critical sensor-derived features for predicting GDI, underscoring the importance of muscle strength metrics at varying speeds in rehabilitation assessments. Conclusions: This study highlights the potential of integrating advanced sensor technology with machine learning techniques in the analysis of complex clinical data. The developed GDI prediction model, based on sensor-acquired isokinetic dynamometry data, offers a novel, streamlined, and effective tool for assessing rehabilitation progress in post-stroke hemiplegic patients, with promising implications for broader clinical application.

Developing an accurate finite element model for brake disc in contact with the pad using experimental modal analysis

The brake system is a critical safety component in cars, and its performance is essential for the safety of both the driver and passengers. The stability of the brake disc and understanding the contact area between the disc and the brake pads are crucial aspects of brake system design and performance. This paper aims to create an accurate model of the brake system, especially the contact area between the disc and the pads. This model can be used to investigate the effects of increasing braking pressure and changing the contact surface. Moreover, this model can calculate the dynamic responses of the system when an angular velocity is applied to the disc. First, a braking system was tested experimentally several times. Then a finite element model of the structure was created in ANSYS commercial software with defining suitable elements for the contact area between the disc and the pads. In the following, by an identification process a distribution of contact parameters at different braking pressures was obtained. The results shows that when the braking pressure increases, the dynamic responses of the structure increase, as well as the contact stiffness. A further increase in braking pressure does not have much effect on the contact stiffness and the contact area becomes like a new support.

A Simplified Two-Fluid Model Based on Equilibrium Closure for a Dilute Dispersion of Small Particles

Two-fluid formalisms that fully account for all complex inter-phase interactions have been developed based on a rigorous ensemble-averaging procedure. Here, we apply equilibrium approximation to particle velocity to simplify two-phase flow equations for the case of a dilute dispersion of particles much smaller than the flow scales. First, we extend an earlier approach to consider the rotational motion of the particles and seek an equilibrium approximation for the angular velocity of the particulate phase. The resulting explicit knowledge of the particulate phase translational and rotational velocities in terms of fluid velocity eliminates the need to consider the momentum equations for the particulate phase. The equilibrium approximations also provide precise scaling for various terms in the governing equations of the two-fluid model, based on which a simplified set of equations is obtained here. Three different regimes based on the relative strength of gravitational settling are identified, and the actual form of the simplified two-phase flow equations depends on the regime. We present two simple examples illustrating the use of the simplified two-fluid formalism.

Velocity coding in the central brain of bumblebees

Moving animals experience wide-field optic flow due to the displacement of the retinal image during motion. These cues provide information about self-motion and are important for flight control and stabilization, and for more complex tasks like path integration. While in honeybees and bumblebees the use of wide-field optic flow in behavioral tasks is well investigated, little is known about the underlying neuronal processing of these cues. Furthermore, there is a discrepancy between the temporal frequency tuning observed in most motion-sensitive neurons described so far from the optic lobe of insects and the velocity tuning that has been shown for many behaviors. Here we investigated response properties of motion-sensitive neurons in the central brain of bumblebees. Extracellular recordings allowed us to present a large number of stimuli to probe the spatiotemporal tuning of these neurons. We presented moving gratings that simulated either front-to-back or back-to-front optic flow and found three response types. Direction-selective responses of one of the groups matched those of TN-neurons, which provide optic flow information to the central complex, while the other groups contained neurons with purely excitatory responses that were either selective or non-selective for stimulus direction. Most recorded units showed velocity-coding properties at lower angular velocities, but showed spatial frequency dependent responses at higher velocities. Based on behavioral data, neuronal modelling work has previously predicted the existence of non direction-selective neurons with such properties. Our data now provides physiological evidence for these neurons and shows that neurons with TN-like properties exhibit a similar velocity-dependent coding.

The rotation rate of single- and double-lined southern O stars. Determining what increases the rotation rate in binaries

We determined the projected rotational velocity ($v i$) of 238 southern O stars selected from the Galactic O-star Survey. The sample contains 130 spectroscopic single stars (C) single-lined binaries (SB1), and SB2 systems (including eight triples). We applied the Fourier method to high-resolution spectra taken at Cerro Murphy, Chile, and supplemented by archival spectra. The overall $v i$ statistics peaks at slow rotators (40-100\,km/s) with a tail towards medium (100-200\,km/s) and fast rotators (200-400\,km/s). Binaries, on average, show increased rotation, which differs for close orb < 10$\,d) and wide binaries (10\,d $< orb <$ 3700\,d), and for primaries and secondaries. The spin-up of close binaries is well explained by the superposition of spin-orbit synchronisation and mass transfer via Roche-lobe overflow. The increased rotation of wide binaries, however, needs another explanation. Therefore, we discuss various spin-up mechanisms. Timescale arguments lead us to favour a scenario where wide O binaries are spun-up by a combination of cloud or disk fragmentation, which lays the basis of triple and multiple stars, and the subsequent merging or swallowing of low-mass by higher-mass stars or proto-stars.

Rotating nonlinear states in trapped binary Bose-Einstein condensates under the action of the spin-orbit coupling

Abstract We report results of systematic analysis of confined steadily rotating patterns in the two-component BEC including the spin-orbit coupling (SOC) of the Rashba type, which acts in the interplay with the attractive or repulsive intra-component and inter-component nonlinear interactions and confining potential. The analysis is based on the system of the Gross-Pitaevskii equations (GPEs) written in the rotating coordinates. The resulting GPE system includes effective Zeeman splitting. In the case of the attractive nonlinearity, the analysis, performed by means of the imaginary-time simulations, produces deformation of the known two-dimensional SOC solitons (semi-vortices and mixed-modes). Essentially novel findings are reported in the case of the repulsive nonlinearity. They demonstrate patterns arranged as chains of unitary vortices which, at smaller values of the rotation velocity $\Omega $, assume the straight (single-string) form. At larger $\Omega $, the straight chains become unstable, being spontaneously replaced by a trilete star-shaped array of
vortices. At still large values of $\Omega $, the trilete pattern rebuilds itself into a star-shaped one formed of five and, then, seven strings. The transitions between the different patterns are accounted for by comparison of their energy. It is shown that the straight chains of vortices, which form the star-shaped structures, are aligned with boundaries between domains populated by plane waves with different wave vectors. A transition from an axisymmetric higher-order (multiple) vortex state to the trilete pattern is investigated too.

Modeling and analysis of nonlinear dynamics of axisymmetric vector nozzle based on deep neural network

Abstract The axisymmetric nozzle mechanism is the core part for thrust vectoring of aero engine, which contains complex rigid-flexible coupled multibody system with joints clearance and significantly reduces the efficiency in modeling and calculation, therefore the kinematics and dynamics analysis of axisymmetric vectoring nozzle mechanism based on deep neural network is proposed. The deep neural network model of the axisymmetric vector nozzle is established according to the limited training data from the physical dynamic model and then used to predict the kinematics and dynamics response of the axisymmetric vector nozzle. This study analyses the effects of joint clearance on the kinematics and dynamics of the axisymmetric vector nozzle mechanism by a data-driven model. It is found that the angular acceleration of the expanding blade and the driving force are mostly affected by joint clearance followed by the angle, angular velocity and position of the expanding blade. Larger joint clearance results in more pronounced fluctuations of the dynamic response of the mechanism, which is due to the greater relative velocity and contact force between the bushing and the pin. Since axisymmetric vector nozzles are highly complex nonlinear systems, traditional numerical methods of dynamics are extremely time-consuming. Our work indicates that the data-driven approach greatly reduces the computational cost while maintaining accuracy, and can be used for rapid evaluation and iterative computation of complex multibody dynamics of engine nozzle mechanism.

The Two-Thirds Power Law Derived from a Higher-Derivative Action

The two-thirds power law is a link between angular speed ω and curvature κ observed in voluntary human movements: ω is proportional to κ2/3. Squared jerk is known to be a Lagrangian leading to the latter law. However, it leads to unbounded movements and is therefore incompatible with quasi-periodic dynamics, such as the movement of the tip of a pen drawing ellipses. To solve this drawback, we give a class of higher-derivative Lagrangians that allow for both quasi-periodic and unbounded movements, and at the same time lead to the two-thirds power law. The current study extends this framework and investigates a wider class of Lagrangians admitting generalised conservation laws.

The ESO SupJup Survey. III. Confirmation of 13CO in YSES 1 b and Atmospheric Detection of YSES 1 c with CRIRES+

Abstract High-resolution spectroscopic characterization of young super-Jovian planets enables precise constraints on elemental and isotopic abundances of their atmospheres. As part of the ESO SupJup Survey, we present high-resolution spectral observations of two wide-orbit super-Jupiters in YSES 1 (or TYC 8998-760-1) using the upgraded VLT/CRIRES+ ( R ∼ 100,000 ) in K-band. We carry out free atmospheric retrieval analyses to constrain chemical and isotopic abundances, temperature structures, rotation velocities ( v sin i ), and radial velocities. We confirm the previous detection of 13CO in YSES 1 b at a higher significance of 12.6σ, but point to a higher 12CO/13CO ratio of 88 ± 13 (1σ confidence interval), consistent with the primary’s isotope ratio 66 ± 5. We retrieve a solar-like composition in YSES 1 b with a C/O = 0.57 ± 0.01, indicating a formation via gravitational instability or core accretion beyond the CO iceline. Additionally, the observations lead to detections of H2O and CO in the outer planet YSES 1 c at 7.3σ and 5.7σ, respectively. We constrain the atmospheric C/O ratio of YSES 1 c to be either solar or subsolar (C/O = 0.36 ± 0.15), indicating the accretion of oxygen-rich solids. The two companions have distinct v sin i , 5.34 ± 0.14 km s−1 for YSES 1 b and 11.3 ± 2.1 km s−1 for YSES 1 c, despite their similar natal environments. This may indicate different spin axis inclinations or effective magnetic braking by the long-lived circumplanetary disk around YSES 1 b. YSES 1 represents an intriguing system for comparative studies of super-Jovian companions and linking present atmospheres to formation histories.

Internal Model‐Based Anti‐Disturbances Low‐Level Control for Drones Considering Actuator Dynamics

ABSTRACTLow‐level control plays a critical role in the overall flight performance of drones. Despite some progress, existing methods do not adequately consider the complex electromechanical characteristics of actuators and aerodynamic disturbances of propellers, which deteriorates low‐level control performance. To tackle these issues, we propose a new nonlinear low‐level controller for higher precision control. First, a high‐precision low‐level model that integrates the actuator dynamics and angular velocity dynamics is presented. Based on this model, a dynamic compensator is designed using the internal model method to handle aerodynamic disturbances. Next, a high‐gain observer is designed to estimate the actuator states without adding new sensors, and an observer‐based low‐level controller is proposed through a recursive design process. Finally, the local asymptotic stability of the closed‐loop system is analyzed. The effectiveness and superiority of the proposed method are validated through simulations and physical experiments.

Fault detection of RV reducer cycloidal gear under robot working conditions based on optimization improved envelope spectrum sideband energy ratio

Abstract Under industrial robot operating conditions, the cycloidal gear in the rotary vector(RV) reducer in the robot joint runs in a compound rotation motion with a low-speed and incomplete cycle, which complicates the fault detection for the cycloidal gear. Until now, no effective detection method for the cycloidal gear tooth fault under industrial robot operating conditions has been reported. Consequently, a method based on optimization improved envelope spectrum sideband energy ratio is proposed in this paper. Firstly, encoder signals are acquired and used to estimate the instantaneous angular speed (IAS) signals, which are then separated into two sets of data based on rotational directions. Then, the data corresponding to the approximately stable speed is truncated and connected to form a constructed signal. Next, the coherence of the constructed signal is calculated using the fast spectral coherence algorithm. Subsequently, the improved envelope spectrum sideband energy ratio is used as the objective value, and a global optimization algorithm is employed to determine the integration frequency band of the improved envelope spectrum (IES). Finally, the IES of this frequency band is calculated to obtain the fault-relatedorder characteristics. An RV reducer test rig was used for the experiment, and the analysis results from the proposed approach, cyclic spectral coherence (CSCoh), and improved envelope spectrum via feature optimization-gram (IESFOgram) were contrasted. Experiment results show that the proposed method is valid for the detection of tooth faults in the cycloidal gear of the RV reducer in robot operating conditions.

Integration of in-wheel motor sensorless systems and hierarchical direct yaw moment control for distributed drive electric vehicles

Ensuring robust and reliable control of distributed vehicles powered by in-wheel motor systems poses a significant challenge due to the harsh operating environments and high costs of such motor systems. Poor motor control, parameter variations, and sensor malfunction under these conditions can compromise the vehicle yaw stability. Integrating permanent magnet synchronous motor (PMSM) sensorless systems with vehicle yaw moment control offers a cost-effective solution for this issue without wheel angular speed sensors while enhancing yaw stability. In this paper, a composite nonlinear feedback sliding mode controller that can enhance the PMSM speed response is proposed. The proposed scheme exhibits a rotor speed overshoot and transient time of only 0.64% and 0.07s, respectively, which are smaller and shorter compared with other methods under motor parameter changes. Subsequently, the key states and tire-road friction coefficients required for vehicle control were estimated using sensorless rotor speeds and unscented Kalman filters, enabling the integration of the PMSM sensorless system with the vehicle yaw moment control. Additionally, a fuzzy adaptive hybrid sliding mode method is presented for yaw moment control enhancement. This method maintained the smallest sideslip angle root mean square error during double lane changes (0.4192 deg) compared with other methods. Analysis results show that different motor controllers and parameter changes significantly affect the vehicle dynamics performance. The proposed integrated scheme is feasible and effectively enhances the yaw moment control via high-performance sensorless PMSM systems.

The effects of target distance on kinematic sequence of the short game in male collegiate golfers

ABSTRACT Golf is an international sport that has become increasingly more popular in recent times. Previous literature has shown that golf approach shots are crucial to the success of elite golfers. However, there is no known publication investigating distances less than 100 yards, known as the short game. The primary purpose of this study was to collect comprehensive data on 3D biomechanical variables of the short game at four target distances in college-aged, male golfers. Participants were instructed to hit five successful shots at each target distance: 30 yards, 50 yards, 70 yards and full swing (maximal distance) yardage. A motion capture system recorded kinematic and temporal parameters of golfer movement, additional to a golf simulator that collected ball carry distance of each shot. Distance did have a significant (p ≤ 0.05) effect on swing phase timing, angular velocities and motion sequencing. Movement sequencing within the short game displayed irregular patterns across all distances and phases, with a partial proximal-to-distal pattern (pelvis → shoulder girdle → arms → club) at best. The findings of this study show that the short game swing did present its own unique motion patterns that will require practice as its own skill.

North Polar Spur: Gaseous plume(s) from star-forming regions ~3-5 kpc from the Galactic Center?

We argue that the North Polar Spur (NPS) and many less prominent structures are formed by gaseous metal-rich plumes associated with star-forming regions (SFRs). The SFRs located at the tangent to the 3-5 kpc rings might be particularly relevant to the NPS. A multi-temperature mixture of gaseous components and cosmic rays rises above the Galactic disk under the action of their initial momentum and buoyancy. Eventually, the plume velocity becomes equal to that of the ambient gas, which rotates with different angular speeds than the stars in the disk. As a result, the plumes acquire characteristic bent shapes. An ad hoc model of plumes' trajectories shows an interesting resemblance to the morphology of structures seen in the radio continuum and X-rays.

Impact of Static Electric Field on Dielectrophoretic Alignment of Silicon Nanowires

AbstractAmong numerous approaches to assembling nanowires onto electrodes, dielectrophoresis (DEP) is a potential candidate to place the nanowires. However, its yield is still far from perfection, urging fundamental understanding of its dynamics. Here, the impact of a static electric field on dielectrophoretic nanowire assembly on gold electrodes is investigated. Specifically, a 4 peak‐to‐peak alternating voltage with 700 Hz is applied and modulate the offset voltage from 0 to 2V. The highest yield in the alignment of the nanowires at 0.5 V offset voltage is found. With the optical investigation of misaligned nanowires, it is found that rotating wires on top of electrodes, and the analysis of their angular velocity suggest the impact of the induced static charges. The numerical analysis quantifies the length scale of competing two forces, dielectrophoretic force and electric double layer force. This work suggests a quantitative understanding of the interplay between dielectrophoresis and electric double layer, which contributes to the advances in scalable nanowire fabrications.

On the Effect of Current Stabilizer on Dynamics of a Small Hybrid Wind Power Generator

The use of small wind power generators remains quite relevant. In particular, they can be efficient for charging batteries in remote locations where there is no centralized power supply (including in the Arctic, Far East, etc.). They can also be used as part of missions to planets with atmospheres. One of the promising design solutions for a small wind power generator with a vertical axis of rotation is a hybrid device. It consists of two wind turbines that have a common axis of rotation: external (Darrieus wind turbine) and internal (Savonius rotor). This scheme represents a compromise between the relatively high power coefficient of the Darrieus turbine and the good startup characteristics the Savonius rotor. It is known that one of the typical battery charging modes is constant current charging. Here we consider a hybrid installation, the generator of which is connected to a current stabilizer. The load is simulated with an active resistance. It is assumed that the generator is a DC generator. A closed mathematical model of the studied system is constructed. The aerodynamic load is described using the quasi-steady approach. It is assumed that the characteristic time of electrical processes is much smaller than the characteristic time of mechanical processes. The influence of load resistance on the behavior of the system is investigated. It is shown that, under certain conditions, several steady modes (up to five) exist in the system. In this case, at least two of them are attracting. Therefore, the hysteresis of the angular speed of the steady mode is possible when the load resistance changes. It should be noted that in a number of situations, an unstable steady mode (which corresponds to a lower angular speed of the turbine than a stable one) may be preferable (for example, to reduce the load on bearings). In this regard, a resistance control strategy has been proposed to ensure stabilization of the unstable stationary regime.

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

Experimental investigation of the electromagnetic acceleration mechanisms in an Applied-field Magnetoplasmadynamic Thruster

Abstract The high specific impulse and efficiency of the applied-field magnetoplasmadynamic thruster make it one of the most promising electric thrusters in deep space exploration. However, the crucial electromagnetic acceleration mechanisms are still not clearly investigated, which limits performance improvement. The electromagnetic acceleration mechanism is closely related to the current path and magnetic field distribution in the plume. Experiments are conducted using a water-cooled Hall probe in the steady-state applied-field magnetoplasmadynamic thruster plume. The radial, azimuthal and axial magnetic fields are measured, then the current density and Lorentz force density are calculated. The results show that the outflow current accounts for 63% to 82% of the thruster discharge current depending on the strength of the applied magnetic field. Moreover, the outflow current can extend the range of electromagnetic force action, which in turn increases the effect of electromagnetic acceleration. The radial Lorentz force is numerically dominant, and the combined effect of the radial Lorentz force and axial Lorentz force is to compress the plasma toward the axis. In electromagnetic acceleration, Self-field contributions are less than 5%, while E × B acceleration constitutes -12.2-21.2%, and Diamagnetic acceleration dominates at approximately 76.7-90.5%. Finally, a method for evaluating the rotational velocity was presented based on the MHD equations. The centrifugal force was then calculated by combining this with the plasma density. At the thruster outlet, the centrifugal force is significant and cannot be ignored in comparison to the radial Lorentz force.

The effect of simulated basketball game load on patellar tendon load during stop-jump movement

Patellar tendinopathy (PT) is frequently observed among basketball players, particularly in sports involving repetitive jumping movements. However, the overall impact of accumulated exercise load on the patellar tendon is still not fully comprehended. Therefore, the goal of this study is to examine how a simulated basketball game affects the biomechanics of stop-jump movements, specifically focusing on the effects on the patellar tendon. The kinematic and kinetic data were collected immediately after the warm-up and each phase of the simulated basketball game (P1, P2, P3, and P4). A musculoskeletal model was built to calculate patellar tendon force (PTF) and the key biomechanical metrics during the horizontal landing and vertical jumping phases were explored separately, followed by correlation analyses. Linear regression analyses were performed on variables strongly correlated with PTF. The accumulation of load led to significant differences (p < 0.05) in the angles, velocities, torques, work contributions, peak patellar tendon force (PTF), and anterior-posterior ground reaction force (APGRF) observed during the landing and vertical jump phases at the hip, knee, and ankle joints. PTF showed strong correlations with knee flexion angle, knee extension angular velocity, ankle plantarflexion angular velocity, and APGRF, with R2 values of 0.50, 0.58, 0.70, and 0.56, respectively. PTF significantly decreased in P3 and P4, possibly due to the subjects’ adaptation and adjustment of their stop-jump posture strategy after load accumulation, including reducing knee and hip flexion angles and decreasing the net knee extension moment.