Torque Research Articles

Eccentric external and internal rotation peak torque ratios predict shoulder injuries with national judokas; a prospective cohort study

Eccentric external and internal rotation peak torque ratios predict shoulder injuries with national judokas; a prospective cohort study

Understanding turbulence suppression in JET D–T plasma with highly energetic fast ions via global gyrokinetic GENE simulations

Abstract This study focuses on understanding how turbulence is suppressed in particularly heated JET plasma discharges showing enhanced confinement, namely $\#99896$, which uses a nearly 50-50 deuterium-tritium mixture, showing signs of enhanced plasma confinement. The discharge was heated primarily using ion-cyclotron-resonance heating (ICRH), with a small contribution from neutral beam injection (NBI), to minimize external torque and toroidal rotation, resembling conditions expected in future fusion reactors. Global gyrokinetic simulations using the GENE code are performed to analyze the turbulent transport and its stabilization mechanisms associated with the improved confinement observed in the experiment. The results reveal that multiple mechanisms contribute to turbulence suppression acting at different radial domains: wave-particle resonance stabilization reduces the fluxes up by $80\%$, electromagnetic beta-stabilization accounts for a $20-30\%$ reduction, and toroidal Alfv'en eigenmode (TAE) suppression decreases the fluxes up by $80\%$. This suppression is attributed to an enhancement of zonal flow activity driven by TAEs, whose nonlinear saturation is influenced by the effect of zonal currents. In the presence of an unstable TAE, we observe a shift in the dominant turbulence regime, transitioning from drift-wave turbulence to TAE-dominated turbulence. This transition modifies the cross-phase between the electrostatic potential and temperature fluctuations at TAE scales. However, these changes do not impact turbulence fluxes at ITG scales. These findings highlight the complex interplay between energetic particles, electromagnetic effects, and TAE modes in controlling plasma turbulence and improving confinement in future fusion reactors.

Genesis of similar collective states in DNA molecules under various viscosity of the medium and external torque

The nucleotide sequence determines the structural properties of B-DNA; this fact is considered key in recognizing protein binding sites and changing its activity. Our study has established that, using an angular mathematical model, it is possible to determine areas of similar collective states and bends in the nucleotide sequence that arise even under small torque influences. Calculations were performed for two genes that differ slightly in length (B2M and fragment of the Drosophila gene to compare). The dependence of the formation of similar collective states on the viscosity of the medium and the magnitude of the external torque effect was established. The work also found that for different genes, bending zones are observed in different parts of the genes, which confirms the dependence of the rigidity of the area on the nucleotide sequence and correlates with known data.

Comparison of External Rotation Torque of Short External Rotator Muscles in Hip Flexion Position.

Preservation of the short external rotator muscles of the hip is effective in preventing dislocation after total hip arthroplasty. The external rotation torque exerted by the short external rotator muscles can resist internal rotation of the hip joint; however, the absence of quantitative data on external rotation torque makes it difficult to determine which short external rotator muscles should be preserved. We compared the external rotation torque of individual short external rotator muscles in hip flexion. The external rotation torque of the piriformis, obturator internus, conjoined tendon, and obturator externus was evaluated in 15 fresh-frozen cadaveric hips from 0° to 105° of hip flexion, by applying muscle force based on physiological cross-sectional area to the muscle-string model constructed along the anatomical course of each muscle on the pelvis. External rotation torque of the piriformis, obturator internus, and conjoined tendon peaked at 15° hip flexion, and then decreased as the hip flexed. External rotation torque of the obturator externus increased as the hip flexed. At 75° of flexion or more in deep flexion, ranges associated with a high risk of dislocation, the obturator externus had the highest external rotation torque. External rotation torque of the obturator externus was, on average, 2.18 times greater than that of the conjoined tendon at 90° of hip flexion, and 3.80 times greater at 105° flexion. These findings, which include the element of muscle force, suggest that preservation of the obturator externus is the most effective in resisting dislocation among the short external rotator muscles. CLINICAL RELEVANCE: No study has evaluated dislocation resistance based on external rotation torque, including both a force component and muscle course. In this study, we estimated the muscle force of the short external rotator muscles from the PCSA, and quantitatively evaluated how that muscle force changes as external rotation torque during hip flexion. While approaches to hip replacement surgery and the preservation of tissues vary, our results suggest criteria for which muscles should be effectively preserved to resist dislocation in selective dissection of the posterior soft tissues of the hip joint. In future, surgeons will be able to advocate surgical approaches that are less invasive and more resistant to dislocation, which will require clinical evaluation.

A new machine vision-based industrial robot system for garbage management

In response to challenges such as low efficiency, slow processing speed, and potential harm to human operators, this study presents the design and implementation of a machine vision-based garbage sorting system. The system integrates a robotic arm with advanced machine vision technologies to enhance sorting performance. Initially, a garbage sorting system is constructed around a robotic arm framework. Subsequently, the study evaluates various network architecture models and develops a neural network using MobileNetV3 and YOLOv4 (You Only Look Once version 4) by optimizing the backbone network components. The optimal grasp of the mechanical claws is determined using a method and minimum external torque algorithm, enabling the robotic arm to autonomously execute garbage sorting and classification tasks. Experimental results demonstrate that the system achieves a sorting accuracy of 90% for individual garbage items with the target category neural network and an overall classification accuracy of 91.2%. In scenarios involving multiple, non-adhering waste items, the system consistently maintains a 100% sorting rate. Even when dealing with adhesive or stacked waste items, the neural network’s target detection capabilities remain operational, although the accuracy of sorting success may decrease. This research validates the feasibility and reliability of the machine vision-based garbage sorting system through comprehensive experimental evaluations.

A Novel Double-Sided Electromagnetic Dog Clutch with an Integrated Synchronizer Function

Dog clutches are superior to synchromesh units due to much less wear caused by friction but require an external torque source to synchronize the rotation speeds. The current trend in e-mobility to use the driving motor of an electric vehicle as this source just creates another problem, which is known as torque holes. In this work, we propose a novel double-sided dog clutch that synchronizes the speeds electromagnetically by itself avoiding mechanical contact between the parts. A shift sleeve, two coils placed coaxially in their stators, and two complementary rings form an electromagnetic reluctance actuator, which is integrated inside the gearbox between two gearwheels and represents the double-sided clutch. Thus, intermediate parts between the shift sleeve and the actuator are not required. Both actuator sides can produce axial force and electromagnetic torque. However, torques and forces are generated simultaneously on both sides. Therefore, a special control algorithm is developed to keep the resulting axial force approximately equal to zero while the torque is generated in the neutral gear position. After the synchronization, the axial force is applied on the corresponding side to shift the required gear engaging the shift sleeve teeth directly with the slots of the complementary ring mounted on the gearwheel. So, an axial contact of the teeth at an unaligned state, which can lead to unsuccessful shifting, is avoided. A testrig, which includes a clutch prototype and a testing two-speed gearbox, has been designed and built. The developed theoretical ideas have been verified during the experiments under different conditions. The experiments confirm that the actuator can reduce positive and negative speed differences on both sides and subsequently shift the gear without a shift sleeve collision at misaligned angular positions.

Comparing the hamstring muscle activity between injured and non-injured sides during a variety of Nordic hamstring exercises

ObjectivesTo compare the electromyographic activity of the Biceps femoris long head and Semitendinosus muscles during bilateral and unilateral isometric Nordic hamstring exercise performed on an inclined platform at different knee flexion angles between leg side with and without a history of hamstring strain injury.MethodsTen physically active male volunteers with a history of hamstring strain injury in either leg performed isometric Nordic hamstring exercise, maintaining the exercise position for 5 s under the following conditions: (1) bilateral, 150° knee angle on a 50° inclined platform (BL50); (2) bilateral, 140° knee angle on a 40° inclined platform (BL40); (3) unilateral, 150° knee angle on a 50° inclined platform (UL50); and (4) unilateral, 140° knee angle on a 40° inclined platform (UL40). External torque on the knee joint was controlled to ensure equivalence across conditions. Electromyographic activity of the Biceps femoris long head, Semitendinosus, and related muscles was measured in both legs with and without a history of hamstring strain injury.ResultsThe Biceps femoris long head muscle demonstrated significantly higher electromyographic activity during the unilateral Nordic hamstring exercise tasks, irrespective of hamstring strain injury history (p < 0.05). The Biceps femoris long head electromyographic activity was higher than Semitendinosus activity only in unilateral Nordic hamstring exercise conditions.. Additionally, no significant differences in the electromyographic activity were observed across the different slope angles when the external torque at the knee joint was matched (p > 0.05).ConclusionsThese findings suggest that performing isometric unilateral Nordic hamstring exercise at shallow knee flexion angles preferentially enhances the muscle activation of biceps femoris long head muscle regardless of hamstring strain injury history.

Comparing the hamstring muscle activity between injured and non-injured sides during a variety of Nordic hamstring exercises.

To compare the electromyographic activity of the Biceps femoris long head and Semitendinosus muscles during bilateral and unilateral isometric Nordic hamstring exercise performed on an inclined platform at different knee flexion angles between leg side with and without a history of hamstring strain injury. Ten physically active male volunteers with a history of hamstring strain injury in either leg performed isometric Nordic hamstring exercise, maintaining the exercise position for 5 s under the following conditions: (1) bilateral, 150° knee angle on a 50° inclined platform (BL50); (2) bilateral, 140° knee angle on a 40° inclined platform (BL40); (3) unilateral, 150° knee angle on a 50° inclined platform (UL50); and (4) unilateral, 140° knee angle on a 40° inclined platform (UL40). External torque on the knee joint was controlled to ensure equivalence across conditions. Electromyographic activity of the Biceps femoris long head, Semitendinosus, and related muscles was measured in both legs with and without a history of hamstring strain injury. The Biceps femoris long head muscle demonstrated significantly higher electromyographic activity during the unilateral Nordic hamstring exercise tasks, irrespective of hamstring strain injury history (p < 0.05). The Biceps femoris long head electromyographic activity was higher than Semitendinosus activity only in unilateral Nordic hamstring exercise conditions.. Additionally, no significant differences in the electromyographic activity were observed across the different slope angles when the external torque at the knee joint was matched (p > 0.05). These findings suggest that performing isometric unilateral Nordic hamstring exercise at shallow knee flexion angles preferentially enhances the muscle activation of biceps femoris long head muscle regardless of hamstring strain injury history.

Physics of Gyroscopic Inertial Torques Nullification

Recent publications on gyroscopic effects describe the specificity of the action of inertial torques generated by the rotating mass of a spinning object. All inertial torques acting on the spinning object include resistance and precession torques generated by the external load. The external and inertial torques of the spinning object express their independent potential and kinetic energies, respectively, but the physics of their interaction needs to be clarified. The inertial torques and the motions of the gyroscope are based on the mechanical energy conservation law and presented by mathematical models about the axes of a Cartesian coordinate system. These motions arise from the combined action of a set of inertial torques produced by centrifugal and Coriolis forces, along with changes in angular momentum. Blocking of the gyroscope’s precessional motion nullifies all inertial torques except for the torque of the changes in angular momentum. The physics behind the selective nullification or deactivation of the inertial torques remains poorly understood. Identifying the reasons for the interrelated inertial torques’ nullification is a significant challenge for physicists. Addressing this issue within gyroscopic theory can simplify analytical solutions for various problems involving gyroscopic devices. This study describes the physics of inertial torque nullifications, offering valuable insights for researchers working on gyroscopic effects.

Adaptive Control of the Aerodynamic Flaps of the Savonius Rotor Under Variable Wind Loads

This study presents the development of an adaptive control system for aerodynamic flaps of a two-tier vertical-axis Savonius wind rotor to improve performance under variable wind loads. The approach includes detailed kinematic and dynamic modeling of the flap actuation mechanism, accounting for real-world nonlinearities such as backlash, friction, and impact loads. The mechanical transmission system is analyzed to evaluate the influence of design parameters on system dynamics and control accuracy. A mathematical model of an adaptive PID controller is proposed, capable of real-time adjustment of gain parameters based on external wind torque. Numerical simulations under various wind conditions demonstrate that adaptive tuning significantly enhances system stability, reduces overshoot, and ensures faster response compared to fixed-parameter controllers. Sensitivity analysis confirms the importance of mass distribution, mechanical stiffness, and damping in minimizing vibrations and ensuring durability. The developed system provides a reliable solution for efficient wind energy conversion in dynamic environments, including urban and coastal applications.

Rotation-Direction-DependentMechanism of the InhibitorProtein IF1 for Mitochondrial ATP Synthase from AtomisticSimulations

ATPase inhibitory factor 1 (IF1) is an endogenousregulatoryprotein for mitochondrial FoF1-ATP synthase.It blocks the catalysis and rotation of the F1 part bydeeply inserting itself into the rotor–stator interface. Recentsingle-molecule manipulation experiments have elucidated that forciblerotations only in the ATP-synthesis direction eject IF1, rescuing F1 from the IF1-inhibited state.However, the molecular mechanism of the rotation-direction-dependentprocess at an atomic resolution is still elusive. Here, we have performedall-atom molecular dynamics (MD) simulations of the IF1-bound F1 structure with a torque applied to the rotorγ subunit. In the torque-applying simulations, we first foundthat the core part of the γ subunit rotated more in responseto an external torque in the synthesis direction than in the hydrolysisdirection. Further rotations of the γ subunit up to 120°revealed that the conformational change of the IF1-boundαβ was only allowed in the synthesis direction. Also,the 120° rotation in the synthesis direction disrupted its contactswith IF1, destabilizing the short helix of IF1. After additional rotation up to the synthetic 240° state,the closed-to-open conformational change of the IF1-boundβ subunit pulled IF1 outwardly, deforming the longhelix of IF1. These stepwise destabilizations of the IF1 helices should be crucial for IF1 ejection. Oursimulations also provided insight into the nullification mechanismof the hydrolytic rotation, highlighting the steric clash betweenF22 of IF1 and the βTP subunit. Finally,we discuss a sufficient proton motive force to rescue FoF1-ATP synthase from the IF1-inhibited state.

Fuzzy Disturbance Observer-Based Adaptive Nonsingular Terminal Sliding Mode Control for Multi-Joint Robotic Manipulators

This study proposes a novel fuzzy disturbance observer (FDO)-augmented adaptive nonsingular terminal sliding mode control (NTSMC) framework for multi-joint robotic manipulators, addressing critical challenges in trajectory tracking precision and disturbance rejection. Unlike conventional disturbance observers requiring prior knowledge of disturbance bounds, the proposed FDO leverages fuzzy logic principles to dynamically estimate composite disturbances—including unmodeled dynamics, parameter perturbations, and external torque variations—without restrictive assumptions about disturbance derivatives. The control architecture achieves rapid finite-time convergence by integrating the FDO with a singularity-free terminal sliding manifold and an adaptive exponential reaching law while significantly suppressing chattering effects. Rigorous Lyapunov stability analysis confirms the uniform ultimate boundedness of tracking errors and disturbance estimation residuals. Comparative simulations on a 2-DOF robotic arm demonstrate a 97.28% reduction in root mean square tracking errors compared to PD-based alternatives and a 73.73% improvement over a nonlinear disturbance observer-enhanced NTSMC. Experimental validation on a physical three-joint manipulator platform reveals that the proposed method reduces torque oscillations by 58% under step-type disturbances while maintaining sub-millimeter tracking accuracy. The framework eliminates reliance on exact system models, offering a generalized solution for industrial manipulators operating under complex dynamic uncertainties.

An Experimental and Theoretical Study of Gear Vibro-Impacts Caused by Torque Reversals

Abstract Rapid shift toward electrified powertrains has provided gear train dynamics researchers with new challenges, one of them being transient vibro-impact behavior caused by torque reversals during the drive and regenerative braking modes of operation. Contrary to ample studies on the steady-state dynamic behavior to aid with gear whine and rattle related noise and vibration problems, the transient behavior associated with such torque reversals has not been investigated extensively. Accordingly, this paper studies the dynamic response of a single-mesh gear system subjected to external torque reversals. A reduced-order dynamic model is proposed, accompanied by a computationally efficient piecewise-linear solution method. An experimental setup of the same system is developed. Measurements within a wide spectrum of operating conditions and system parameters are compared to the model predictions for its validation. At the end, the model is employed for key parameter sensitivity studies on the influence of drivetrain stiffness, backlash and torque magnitudes on the resultant vibro-impact behavior depicted by an impact severity index.

Extended State Observer Based Robust Nonlinear PID Attitude Tracking Control of Quadrotor with Lumped Disturbance

The paper presents a robust nonlinear PID controller for the attitude tracking problem of quadrotors subject to disturbance. First, to suppress the influence caused by external disturbance torque, considering the fact that the angular velocity can be obtained by the inertial measurement unit (IMU), a reduced-order extended state observer (ESO) is applied as a feedforward compensation to improve the robustness of the tracking system. Then, an ESO-based nonlinear PID controller is constructed to track the desired attitude command, and the rigorous proof of the convergence of the closed-loop system is derived by utilizing the Lyapunov method. Finally, the effectiveness of the proposed method is illustrated by numerical simulations and platform experiments.

Axial torque estimation based on backlash detection for reduction gear using encoder information

Geared motors are widely used in robotics; however, reduced backdrivability due to amplified friction remains a critical issue. To improve backdrivability, accurate estimation and control of external torque is essential. Yet, noise generated by backlash can significantly impair external torque estimation performance. This study addresses this challenge by identifying backlash in reduction gears through shaft torsional angular velocity analysis. The methodology begins with establishing a backlash model based on the torsion angle. By excluding backlash from the torsion angle calculations using the identified model, both torsion torque estimation and control performance are enhanced. While model errors are particularly critical for motors with high torsional stiffness, these errors can be significantly reduced by updating model parameters based on relative angular velocity measurements. The research demonstrates that compensating for backlash dead zone parameters improves torque estimation accuracy, with particularly notable effects when dealing with small external forces. Although parameter values vary depending on external force application methods, this variation can be effectively managed through online parameter estimation.

Biomechanical Comparison of Transverse Capsulotomy Versus Longitudinal Capsulotomy of the Hip: A Cadaveric Study.

Biomechanical effect on hip joint stability between the transverse interportal capsulotomy and the longitudinal capsulotomy in arthroscopy has not been fully investigated. To evaluate whether rotational stability and distraction resistance differ between the 2 capsulotomy directions using fresh-frozen cadavers. Controlled laboratory study. Twelve hips of 6 fresh-frozen cadavers, including intact femur and pelvis, were tested in 3 conditions: intact, capsulotomy, and repaired. Two capsulotomy patterns were made: a 4-cm transverse capsular resection based on a transverse interportal capsulotomy, and longitudinal capsulotomy. Six hips were transverse capsulotomy and 6 hips were longitudinal capsulotomy. The pelvis was fixed to a wooden plate, and the intramedullary nail was inserted into the femur. To evaluate rotational stability, internal and external torques of 5 N·m were applied at 15° of hip extension and 0°, 15°, 30°, 45°, and 60° of hip flexion, respectively. To test for distraction, the specimens were axially loaded from 0- to 150-N distraction forces at different flexion angles (0°, 30°, 45°, 60°). The external rotation laxity increased significantly after the transverse capsulotomy at all flexion angles and longitudinal capsulotomy only at 0°. The separation distance increased significantly after the transverse and longitudinal capsulotomies. The change in external rotation laxity was significantly greater in transverse capsulotomy at 15° of hip extension and 0° than longitudinal capsulotomies in unrepaired conditions compared with intact conditions. With distraction loads, the transverse capsulotomy resulted in a significantly greater separation distance than the longitudinal capsulotomy at all flexion angles with 100 N, and at 0° and 60° with 50 N. Significant differences were observed after capsular repaired compared with intact for external rotation angle at 15° extension and 0°, and separation distance at 60° flexion with 150 N and 100 N between capsulotomy directions. This cadaveric study demonstrated that the hips with the longitudinal capsulotomy resulted in less external rotation laxity, especially at 15° extension and 0°, and less distraction laxity compared with those with the transverse capsulotomy; and these differences remained after repair of capsulotomy. Either capsulotomy direction is effective if the capsular repair is performed properly because the standard capsular repair improves capsular stability. However, surgeons should note that the longitudinal incision tends to be more stable at lower levels of hip flexion.

A Task-Agnostic Knee Exoskeleton for Reducing Osteoarthritis Pain Across Activities of Daily Life: A Pilot Study.

Patellofemoral osteoarthritis is a prevalent musculoskeletal disorder characterized by knee pain during physically demanding activities like stair climbing and sit-to-stand transitions. These movements require high knee extension torques, leading to increased quadriceps activation and patellofemoral joint compression, which aggravates pain. While external torque assistance at the knee joint could theoretically reduce joint loads, traditional exoskeletons have not proven effective in managing osteoarthritis due to their rigid actuation, cumber-some attachments, and inadequate control systems. We address these limitations by modifying a commercial post-operative knee brace with a highly-backdrivable actuator and adapting a task-agnostic torque-assist controller, originally designed for lifting and carrying tasks, to accommodate osteoarthritis patients. In pilot trials with four participants with patellofemoral osteoarthritis, our device facilitated substantial reductions in both pain and perceived difficulty across daily activities including stair/ramp navigation, walking, and sit-to-stand transitions. Across all participants and tasks, pain and difficulty were reduced by 0.82 and 0.57 points, respectively (on a scale of 0 to 4). Electromyography revealed decreased quadriceps activation, varying by participant and task. These preliminary findings motivate future research on backdrivable knee exoskeletons as a novel conservative treatment for patellofemoral osteoarthritis.

Ring or No Ring—Revisiting the Multiphase Nuclear Environment in M31

Abstract Nuclear rings, prevalent in barred galaxies, are essential to understanding gas transport toward galactic nuclei. However, the peculiar nuclear ring in our neighboring galaxy M31 remains poorly understood. Here we present a comprehensive study of this multiphase gas structure, originally revealed by its dust emission, based on newly acquired CO mappings and archival spectroscopic imaging of atomic hydrogen and warm ionized gas, along with custom numerical simulations. These multiwavelength data offer an unprecedented view of the surface mass density and kinematics of the nuclear ring, challenging the notion of it being a single coherent structure. In particular, the ring shows significant asymmetry in its azimuthal mass distribution, with neutral gas concentrated in the northeast and ionized gas prominent in the southwest. The observed off-centered and lopsided morphology disfavors an interpretation as gas streamers or resonance rings driven solely by a barred potential known to exist in M31. Furthermore, the ring’s line-of-sight velocity distribution suggests circular motion in a plane inclined by ∼30° relative to M31’s outer disk, implying external torque likely from M32’s recent close-in passage. Our hydrodynamical simulations tracking the evolution of nuclear gas in M31 influenced by both a barred potential and an oblique collision with M32 reveal the natural formation of asymmetric spiral arms several hundred Myr after the collision, which could appear ringlike at appropriate viewing angles. Therefore, we suggest that M31’s nuclear gas structure, instead of being a persistent rotating ring, comprises recently formed, asymmetric spirals with a substantial tilt.

464 Loading of the medial knee ligaments and anterior cruciate ligament during clinical tests of anteromedial rotatory instability

Objectives/Goals: Injury to the medial knee ligaments (sMCL, dMCL, POL) and anterior cruciate ligament (ACL) can cause anteromedial rotatory instability (AMRI). AMRI can cause knee instability and ACL graft failure, but it is unclear how the sMCL, dMCL, POL, and ACL resist AMRI. We aimed to characterize the in-situ forces of the sMCL, dMCL, POL, and ACL under loading conditions involved with AMRI. Methods/Study Population: We characterized the in situ forces of the sMCL, dMCL, POL, and ACL under 1) isolated external tibial rotation torque (ER), 2) isolated anterior tibial force (Ant), and 3) combined ER+Ant loading. Twenty-eight human cadaveric knees (18 male; mean age, 48±13; 21–65 years) were tested on a robotic manipulator with force sensing. Tibiofemoral kinematics were recorded under isolated ER (4Nm, 0–90°), isolated Ant (134N at 0–90°), and combined ER+Ant (4Nm+100N at 15, 30, 90°). The sMCL, dMCL, POL, and ACL were dissected in random order. The in situ force (N) in the sMCL, dMCL, POL, and ACL at the peak applied load for each loading condition was calculated using superposition and compared with Kruskal–Wallis tests with post hoc pairwise testing using a Bonferroni–Holm correction for multiple comparisons (α = 0.05). Results/Anticipated Results: Under isolated ER, the force in the sMCL (32–52N) from 0°-90° exceeded that of the ACL, dMCL, and POL at each flexion angle (p0.05). Force in the ACL was the second highest (26–6N from 0°-90°). Force in the dMCL and POL was low (≤12N). Under isolated Ant, the ACL carried the highest force at all flexion angles (≥113N) (p0.05), but at 90° the sMCL carried the highest force of all ligaments (p0.05). At 90°, force in the dMCL diminished (Discussion/Significance of Impact: We show that the sMCL is the major stabilizer to external rotation torques and combined anterior and external loading conditions related to anteromedial rotatory instability across the arc of knee flexion, while the dMCL, POL, and ACL play a less prominent role, with the exception of the ACL and dMCL near full extension.

The Persistent Shift in Spin-down Rate Following the Largest Crab Pulsar Glitch Rules Out External Torque Variations due to Starquakes

Abstract It was previously believed that the long-term persistent increase in the spin-down rate of the Crab pulsar following a glitch is direct evidence of a starquake-induced glitch or at least related to a starquake. Using radio data covering 1710 days following the 2017 glitch, we obtain an extreme persistent increase of the spin-down rate, which allows us to test the two prevailing models related to a starquake through an interrelation analysis between the glitch size (the amplitude of the frequency step at a glitch) and the persistent increase in the spin-down rate of the star. Our results do not support the hypothesis that glitches induce the external torque variation of the Crab pulsar, which may indicate no occurrence of a starquake during the Crab pulsar glitch. This can explain why no changes in the radio and X-ray flux, pulse profile, and spectrum of the Crab pulsar have been observed. We also suggest an internal mechanism due to superfluidity as an explanation for the long-term persistent shift in the spin-down rate of the Crab pulsar following the relatively large glitches.