Magnitude Of Force Research Articles

A low-cost prosthetic arm with real-time haptic feedback and gesture control for enhanced user autonomy

In daily life, manipulating and feeling objects is essential for autonomy and engagement in various activities. However, individuals relying on prosthetic limbs often encounter barriers such as high costs, ineffective feedback, and limited design adaptability. Unlike conventional prosthetic limbs, which frequently struggle to integrate seamlessly and provide intuitive control, the robotic arm outlined in this study represents a leap in functionality and user experience. At the core of its design lies a specialized glove outfitted with a calibrated array of flex-sensing resistors capable of precisely detecting and interpreting the wearer's movements. These sensors input to the robotic arm, translating the user's gestures into motions that follow human hands. The fingertips are equipped with force-sensing resistors to discern the magnitude of force applied during gripping actions. This real-time sensory feedback is conveyed to the user through a haptic system integrated into the glove. By modulating the intensity and pattern of vibrations, users can gauge their grip strength and manipulate their grasp of the object accordingly. Comprehensive experiments were conducted across various scenarios to assess its performance, agility, strength, and sensory accuracy. Through refinement, the author aims to optimize functionality and reliability, enhancing practicality for users. This project has broader implications for the prosthetics community. By utilizing the scalability and cost-effectiveness of this model, the author envisions tailored solutions that empower individuals with limb differences to live more independently.

Task demands modulate distal limb handedness: A comparative analysis of prehensile synergies of the dominant and non-dominant hand

The dynamic dominance hypothesis of handedness suggests a distinct control strategy for the dominant and the non-dominant limb. The hypothesis demonstrated that the dominant proximal limb is tuned for optimal trajectory control while the non-dominant limb is tuned for a stable grasp. Whether the hypothesis can be extended to distal segments like fingers, especially during a five-fingered grasp, has been studied little. To examine this, an attempt was made to compare the prehensile synergies and force magnitudes of the dominant (DOM) and non-dominant hands (NDOM) during a 5-fingered prehension task. Participants traced a trapezoidal and inverse trapezoidal path with their thumbs on a sliding platform while holding a handle in static equilibrium. The DOM hand performed better only in the inverse trapezoid condition, exhibiting a reduced grip force and increased synergy index aligning with the dynamic dominance hypothesis. No differences were observed for the trapezoid condition, likely due to reduced task demands. The study also explored changes in anticipatory synergy adjustments between the DOM and NDOM hands, but the differences were non-significant. Overall, the DOM hand demonstrated better force coordination than the NDOM hand in challenging conditions. Applications of the study in the objective assessment of handedness were proposed.

Mechanism of Centrifugal Force Amplitude–Frequency Decoupling Exciters for Fruit Tree Vibration Harvest

Centrifugal force is often used as an exciting force for fruit vibration harvest. However, the magnitude of centrifugal force varies quadratically with angular velocity. When the frequency of excitation force remains constant, the amplitude of vibration force cannot be freely adjusted. This study achieves decoupling of the amplitude and frequency of centrifugal force by varying the eccentricity of the eccentric block. Different combinations of eccentric blocks with varying quantities and parameters enable the creation of different types of centrifugal force amplitude–frequency decoupling exciters. Both the amplitude and frequency of excitation force produced by these exciters can be freely adjusted. Furthermore, a physical prototype of a symmetrical dual eccentric block exciter with centrifugal force amplitude–frequency decoupling is developed and tested. It is found that when the exciter frequency or excitation force amplitude remains constant, the vibration acceleration amplitude generated by the exciter changes by adjusting the eccentricity of the eccentric blocks. As the eccentricity of the eccentric blocks decreases, their moment of inertia and kinetic energy decrease. Utilizing mechanisms to adjust the eccentricity of the eccentric block’s center of mass to the rotation axis achieves the dynamic adjustment of the size and frequency of centrifugal force.

A Study on the Influence of Hydraulic Compactor Reinforcement on the Force Law of an Independent Foundation Under a Column and Its Safety Standard

Due to the complexity of the actual geotechnical environment, the backfill compaction design theory and calculation method are not reflected in the current specification. Therefore, in order to investigate the effect of the hydraulic compactor on the foundation structure during the treatment of the backfill of an independent foundation under a column, the Menard formula was modified. At the same time, relying on an independent foundation project under a column in Jinan, the dynamic model of compactor tamping backfilling soil was established. The applicability of the calculation formula is verified by simulating the single-point multiple tamping on the backfill directly above the foundation tie beam, and the influence law of two factors, the thickness of the backfill and the tamping energy, on the force of the foundation tie beam is elucidated. The results show that after reaching the optimum number of tamping, the cumulative soil settlement and the effective reinforcement depth of tamping show a stable trend, and their simulation results are in good agreement with the analytical solution, which provides a supplement to the relevant safety standards. At this critical point, the force on the tie beams peaked and showed up and down fluctuations under the subsequent ramming action. The tamping action of the compactor has a significant effect on the structural forces within the effective reinforcement range, and there is a negative correlation between the magnitude of the structural forces and the thickness of the backfill. According to the numerical calculation results to choose the best construction programme, the on-site monitoring shows that under 42 KJ tamping energy and 1.5 m single backfilling thickness, the tie beam reinforcement stress reaches 18.5~55.5% of the specification warning value, which meets the safety standard. The research results of this paper can provide important guidance for the hydraulic tamping treatment of an independent foundation backfill project.

On the rate-limiting dynamics of force development in muscle.

Skeletal muscles produce forces relatively slowly compared with the action potentials that excite them. The dynamics of force production are governed by multiple processes, such as calcium activation, cycling of cross-bridges between myofilaments, and contraction against elastic tissues and the body. These processes have been included piecemeal in some muscle models, but not integrated to reveal which are the most rate limiting. We therefore examined their integrative contributions to force development in two conventional types of muscle models: Hill-type and cross-bridge. We found that no combination of these processes can self-consistently reproduce classic data such as twitch and tetanus. Rather, additional dynamics are needed following calcium activation and facilitating cross-bridge cycling, such as for cooperative myofilament interaction and reconfiguration. We provisionally lump such processes into a simple first-order model of 'force facilitation dynamics' that integrate into a cross-bridge-type muscle model. The proposed model self-consistently reproduces force development for a range of excitations including twitch and tetanus and electromyography-to-force curves. The model's step response reveals relatively small timing contributions of calcium activation (3%), cross-bridge cycling (3%) and contraction (27%) to overall force development of human quadriceps, with the remainder (67%) explained by force facilitation. The same set of model parameters predicts the change in force magnitude (gain) and timing (phase delay) as a function of excitatory firing rate, or as a function of cyclic contraction frequency. Although experiments are necessary to reveal the dynamics of muscle, integrative models are useful for identifying the main rate-limiting processes.

Engineering of a Bio-Inspired Tiltable Oscillating Fin Submersible Thruster

Oscillating fins are devices designed to produce thrust through periodic undulating movements. However, these structures lack flexibility and often provide thrust in only one fixed direction. Observation and biological references suggest that the dorsal fin rays of seahorses can tilt longitudinally in the spine direction, changing the thrust direction. This study aims to analyze the dynamic effects of seahorse dorsal fin inclining and design a flexible bionic thruster based on this principle. Computational fluid dynamics analysis hypothesizes that fin inclination controls the net force direction in the vertical plane. A force sensor and pulley system test platform were constructed to examine the influences of wave features and the inclination angle on thrust in both vertical and horizontal directions, with discrete fin surfaces used to eliminate force interference. Force testing and snapshots indicate that wave velocity positively impacts net force magnitude, while fin inclination allows for control over force orientation. This tiltable oscillating fin thruster possesses more degrees of freedom, leading to better flexibility and providing controllable thrust orientation.

Determination of Load Forces on the Upper Part of Orthopedic and Postoperative Shoes

Determined patterns of force load on the sole and upper of orthopedic and postoperative shoes when bending the foot while walking. To determine the force of the load on the top of the postoperative orthopedic shoes, the frictional forces between the lateral surfaces of the shoes and the outer lateral sides of the foot can be neglected. Thus, the task will be reduced to the compilation of equilibrium equations of a plane system of forces. As can be seen from the load diagram of the top of the shoe, we have a flat arbitrarily located system of forces. To determine the unknown forces, it is necessary to compile a system of two equilibrium equations, which will represent the algebraic sums of the projections of all forces on the horizontal and vertical axes. To automate the design process of orthopedic and postoperative shoes, a computer program was developed that allows you to perform calculations of the corresponding forces and tension depending on the design and types of material of individual elements, as well as obtain regression equations for determining the effect of tension on the magnitude of the detachment force.

Dimensions of Posterior Implant Restorations Related to Intra-Coronal Cantilever and Occlusal Forces: An In Vitro Study.

The aim of the present study was to investigate the relation of the implant position to the implant crown and analyze the location and magnitude of bite force. The dimensions of 49 posterior implant-supported restorations were recorded in terms of: 1. implant diameter, 2. crown length, 3. crown width, 4. crown height, 5. occlusal surface of the restoration. The crown/implant height was measured and the distance between the implant center and the restoration center revealed the size of intra-coronal cantilevers. The occlusal force analysis determined the point and magnitude of loading. Correlation coefficient r was used for the statistical process and statistical control was carried out with the aid of t-test with minimum level of significance p < 0.05. - The mean crown-to-implant ratio was 0.9 and in short implants (< 10mm) the ratio was 1.28. - Intra-coronal cantilever extensions ranged from 2.1 mm to 6.35 mm depending on crown size. - Occlusal loading was identified in cantilever areas of the crown. - Implant center deviates from crown center in 71%-82% of the cases depending on site location. - Implants with non-ideal position may support a functionally occluding crown. Intra-coronal cantilevers are a critical factor to avoid clinical complications and should be taken under consideration both in the planning and fabrication phase of implant restorations.

Comparative Analysis of Machine Learning Techniques for Identifying Multiple Force Systems from Accelerometer Measurements.

The knowledge of the forces acting on a structure enables, among many other factors, assessments of whether the component's useful life is compromised by the current machine condition. In many cases, a direct measurement of those forces becomes unfeasible, and an inverse problem must be solved. Among the solutions developed, machine learning techniques have stood out as powerful predictive tools increasingly applied to engineering problem-solving. This study evaluates the ability of different machine learning models to identify parameters of multi-force systems from accelerometer measurements. The models were assessed according to their prediction potential based on correlation coefficient (R2), mean relative error (MRE), and processing time. A computational numerical model using the finite element method was generated and validated by vibration measurements performed using accelerometers in the laboratory. A robust database created by the response surface methodology in conjunction with Design of Experiment (DOE) was used for the evaluation of the ability of machine learning models to predict the position, frequency, magnitude, and number of forces acting on a structure. Among the six machine learning models evaluated, k-NN was able to predict with a 0.013% error, and Random Forests showed a maximum error of 0.2%. The innovation of this study lies in the application of the proposed method for identifying parameters of multi-force systems.

Cortical drive may facilitate enhanced use of the paretic leg induced by random constraint force to the non-paretic leg during walking in chronic stroke.

The goal of this study was to determine the effects of applying random vs. constant constraint force to the non-paretic leg during walking on enhanced use of the paretic leg in individuals post-stroke, and examine the underlying brain mechanisms. Twelve individuals with chronic stroke were tested under two conditions while walking on a treadmill: random vs. constant magnitude of constraint force applied to the non-paretic leg during swing phase of gait using a custom designed robotic system. Leg kinematics, muscle activity of the paretic leg, and electroencephalography (EEG) were recorded during treadmill walking. Paretic step length and muscle activity of the paretic ankle plantarflexors significantly increased after walking with random and constant constraint forces. Cortico-cortical connectivity between motor cortices and cortico-muscular connectivity from the lesioned motor cortex to the paretic ankle plantarflexors significantly increased for the random force condition but not for the constant force condition. In addition, individuals post-stroke with greater baseline gait variability showed greater improvements in the paretic step length after walking with random force condition but not with the constant force condition. In conclusion, application of random constraint force to the non-paretic leg may enhance the use of the paretic leg during walking by facilitating cortical drive from the lesioned motor cortex to the paretic ankle plantarflexors. Results from this study may be used for the development of constraint induced locomotor intervention approaches aimed at improving locomotor function in individuals after stroke.

A Computational Study of Temperature Driven Low Engine Order Forced Response In High Pressure Turbines

Abstract This paper reports the results of computational studies of the effect of combustor exit temperature distortions on Low Engine Order (LEO) forced response of a High Pressure Turbine (HPT). Forced response of this kind occurs at frequencies below the Stator Vane Passing Frequency (SVPF) and can be a major cause of High Cycle Fatigue (HCF) in turbines due to its tendency to excite fundamental modes of vibration. This paper investigates the extent through which temperature distortions act as a forcing stimulus in HPT rotor rows, through measuring unsteady pressure and modal force magnitude recorded from full annulus unsteady simulations of the MT1 stage: a low temperature, unshrouded, HPT rig. Rotor relative incidence angle variations are shown to be the key mechanism through which temperature acts as a forcer in HPT rotor rows, whilst temperature driven forced response is shown to be dependent on the magnitude of the modal content of the upstream temperature waves. These findings are used to build a reduced domain tool for blocked burner forced response prediction, which is shown to be accurate to an RMS error of 2.66%, far beyond the current accepted standard for forcing prediction of this kind.

Dynamic modeling and simulation of a new conceptual design of a magnetic capsule robot by application of endoscopic capsule

This paper investigates design, modeling, simulation, and dynamic issues related to self-propelled endoscopic capsule navigated inside the human body through external magnetic fields. A novel magnetic propulsion system is proposed and fabricated, which has great potential of being used in the field of noninvasive gastrointestinal endoscopy. The endoscopic capsule dynamic is studied on a medical silicone plate as the closest available material for the stomach tissue. First, the mechanical characteristics of the medical silicone plate is measured. Next, the forces acted on the endoscopic capsule which are friction, hydrodynamic and magnetic forces are determined by means of test and numerical techniques such as finite element method. Having known the magnitude of forces and torques on the endoscopic capsule, the dynamics of capsule are calculated under different initial conditions and external magnetic fields.

Substrate stiffness-dependent activation of Hippo pathway in cancer associated fibroblasts

The tumor microenvironment (TME) comprises a heterogenous cell population within a complex three-dimensional (3D) extracellular matrix (ECM). Stromal cells within this TME are altered by signaling cues from cancer cells to support uncontrolled tumor growth and invasion events. Moreover, the ECM also plays a fundamental role in tumor development through pathological remodeling, stiffening and interaction with TME cells. In healthy tissues, Hippo signaling pathway actively contributes to tissue growth, cell proliferation and apoptosis. However, in cancer, the Hippo signaling pathway is highly dysregulated, leading to nuclear translocation of the YAP/TAZ complex, which directly contributes to uncontrolled cell proliferation and tissue growth, and ECM remodeling and stiffening processes. Here, we compare the effect of increasing cell culture substrate stiffness, derived from tumor progression, upon the dysregulation of the Hippo signaling pathway in colorectal cancer-associated fibroblasts (CAFs) and normal colorectal fibroblasts (NFs). We correlate the dysregulation of Hippo pathway with the magnitude of the traction forces exerted by healthy and malignant stromal cells. We found that ECM stiffening is crucial in Hippo pathway dysregulation in CAFs, but not in normal fibroblasts.

Oblique propagation of dust acoustic solitary waves in a magnetized plasma in the presence of cairns-tsallis distributed ions

We investigate the effects of non-extensivity (q), non-thermality (α), obliqueness (l z ), the strength of the magnetic field (ω c ), and dust grain temperature (σ d ) on the basic features (viz., amplitude, width, velocity, and soliton energy) of obliquely propagating dust-acoustic solitary waves (DASWs) in a magnetized dusty plasma, which consists of highly negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal non-extensive Cairns-Tsallis(C-T)-distributed ions. First, we derived the expression of the C-T polarization force and analyzed the combined effects of the ions’ non-extensivity (q) and non-thermality (α) parameters on the magnitude (R) of this polarization force. Our results show that R strongly depends on both the q-parameter and the α-parameter. Specifically, for q < 1, the ions’ non-extensivity and non-thermality weaken the polarization force, whereas for q > 1, R shifts toward higher values. Thus, the obliquely propagating DASWs are more likely to form in a magnetized non-extensive plasma rather than in a magnetized extensive plasma q = 1. Subsequent key findings are as follows: The wave phase velocity increases linearly as the obliquity (l z ) decreases. This implies that a reduced obliqueness results in faster soliton motion and spikier solitary structures. Moreover, the amplitude (width) of DASWs decreases (increases) with increasing l z . An increase in the magnetic field magnitude (ω c ) affects only the width of the DASWs. The amplitude (width) of DASWs decreases (increases) with higher dust grain temperature (σ d ). This indicates that dust temperature significantly affects wave excitation. Specifically, at higher dust temperatures, dispersion dominates over nonlinear effects, resulting in smoother solitary structures. The soliton’s energy increases with α and becomes more pronounced as q decreases (from 1 to 0.75). It increases also with higher ω c and dust temperature (σ d ), especially in the presence of nonthermal energetic particles. This investigation provides valuable insights into the propagation mechanisms of nonlinear DASWs in both space and laboratory plasmas containing non-extensive, nonthermal C-T-distributed ions and dust grains.

Reprogramming multi-stable snapping and energy dissipation in origami metamaterials through panel confinement.

With a focus on a class of origami-inspired metamaterials, this work explores the role of panel confinement in their mechanical response under cyclic loading. The goal is twofold: (i) quantify the magnitude change in snapping force and energy dissipation attained by varying the severity of confinement of selected panels; and (ii) leverage insights to modulate in situ their mechanical response as dictated by a given application, hence propose panel confinement modulation as a practical design route for response reprogrammability. Through computational modelling, proof-of-concept fabrication and cyclic testing, we first identify and characterize the governing factors enabling either the alteration or the preservation of the snapping force magnitude during repeated cycles of forward and backward loading. Then, we demonstrate how the in situ modulation of the constrained distance between selected panels enables reprogramming their snapping sequence and energy dissipation. The results contribute to expanding the versatility and application of this class of origami metamaterial across sectors, from aerospace to protective equipment, requiring precise control of mechanical damping and energy dissipation.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Simulation method for dynamic characteristics of rotor-support system subjected to environmental loads

An improved finite element method was proposed to investigate the dynamic characteristics of rotor system with environmental loads (temperature and aerodynamic forces) in aeroengines. According to the axial temperature distribution within shaft elements, the polynomials were established for physical properties of material. The derivation for coefficient matrices under thermal loads, and the tensile stiffness matrix considering axial aerodynamic forces were completed, based on the Timoshenko beam theory. A high-pressure rotor was simulated with operating temperature 200∼600∘C, and the magnitude of aerodynamic force is 105N. Furthermore, a squeezed film damper (SFD) was adopted to this rotor-support system, its steady responses were solved by the equivalent coefficient method, and the Newmark-HHT method was utilized to solve the transient responses. The results indicate that the first two critical speeds are reduced by 1.85 % and 2.07 %, which is mainly caused by thermal loads. The rising temperature leads to lower elastic modulus, higher Poisson's ratio and expansion ratio. With the amount of a mass unbalance being 500 g·mm located at the 1st-stage compressor disk (CD1): the 1st resonance peaks at CD1 and turbine disk (TD) increase by 4.56 % and 4.98 %, respectively, and the 2nd resonance peaks at CD1 and TD rise 5.88 % and 5.00 %, separately. Owing to SFD damping, the first two resonance peaks at CD1 and TD decrease by 69 % and 51 %, respectively. Compared to 40 °C, the first two resonance peaks at CD1 increase by 88 % and 55 % at the oil temperature 100 °C. The oil-film damping deteriorates significantly due to the lower oil viscosity in higher temperature. When operating near the first-order critical speed, the transient responses of rotor perform as simple harmonics, circular precession trajectory, dominant rotational frequency, and periodic motions. Overall, the dynamic characteristics of rotor-SFD-support systems exposed to environmental loads can be predicted by the proposed simulation method.

Characterization of plugging and unplugging process for electric vehicle charging connectors based on Force/Torque measurements

Understanding the magnitude and profile of forces and torques (F/T) to properly execute the plugging and unplugging for electric vehicles (EVs) charging is crucial for designing reliable robots in automated charging stations (ACS). Previous research focuses on F/T measurement for controlling force during robotic tasks. In contrast, this study aims to refine automation workflows for smoother operation. By utilizing the comprehensive F/T measurements, it becomes possible to extract precise information during the plugging and unplugging process. This data provides insight into interaction dynamics, improving the robot’s ability to perform tasks more accurately and efficiently. Through experiments involving 40 participants, anthropometric and F/T data were analysed using statistics, uncovering key relationships between height, weight, and forces. The F/T profiles were predicted using polynomial, Fourier series, and Gaussian models, with the Gaussian proving the most accurate. Peak force and impulse are significantly higher during plugging (74.15 Ns) than unplugging(57.92Ns).

Automatic shock excitation system for dynamic calibration of six-axis force/torque sensor

The coupling behavior between the six-axis force/torque (F/T) sensor and the mechanical environment introduces variations in the dynamic parameters obtained through different calibration methods and devices, which poses challenges in proposing dynamic performance criteria. This paper presents a comprehensive automatic calibration system for determining the dynamic characteristics of the six-axis F/T sensor. Impulse force generators (IFGs), positioned at various orientations, apply three mutually orthogonal directional force and torque components to the sensor using a cruciform artifact. The system ensures repeatable impulse excitation by maintaining consistent spring compression in the IFG, measured by the displacement control system's grating ruler. The pulse width and frequency response function (FRF) are determined based on the response signal without measuring the input signal. The calibration frequency and the impact force magnitude can be controlled by selecting appropriate system parameters. Compared to manual impulse hammers, IFGs exhibit superior features such as high bandwidth, repeatability, and controllable force amplitude. They provide high-quality impulse excitation with calibration frequencies and forces up to 30 kHz and 2500 N or even higher, respectively. Furthermore, a linear relationship between peak value of impulse excitation and spring compression is studied to ensure effective excitation application. The consistency of dynamic calibration results of the six-axis F/T sensor verifies the effectiveness of this automatic calibration system.

Conformal Iontronic Sensing Clear Aligner

AbstractThe clear aligner, commonly utilized in orthodontic treatment for malocclusion, necessitates the quantification of orthodontic forces, which is highly demanded by doctors for enhancing risk management and treatment efficiency. However, the current technology still faces obstacles in achieving conformal integration of pressure sensors onto clear aligners with large curvature for the quantification and real‐time monitoring of orthodontic forces. In this paper, a conformal iontronic sensing clear aligner (CSA) is proposed based on flexible iontronic sensing mechanism, which conformally integrates the sensor with the aligner to quantify orthodontic forces throughout the treatment process while preserving the aligner's original function. Specifically, the ionic coating is seamlessly integrated onto the diaphragm by applying a layer of ionic paint before molding the clear aligner, while the sensing electrode array, designed using a kirigami‐based structure, is seamlessly adhered to the ionic coating. By integrating the CSA into a dental model, its exceptional sensitivity and precise pressure mapping capabilities have been demonstrated. This enables the identification of various tooth movement patterns, discernment of orthodontic force magnitude, and continuous monitoring of forces throughout the orthodontic treatment. Consequently, this research is expected to significantly advance risk management, outcome prediction, and treatment efficiency in orthodontic treatments.

Influences of mechanical decompression using different forces on knee joint space, range of motion, and hamstring flexibility in asymptomatic subjects

INTRODUCTION: Knee joint decompression is one of the promising methods for the treatment of osteoarthritis. Yet, the most appropriate decompression force is not conclusive. OBJECTIVES: To compare the effect of different distraction force magnitudes on knee joint space, active range of motion (ROM), hamstring flexibility, and self-reported discomfort in asymptomatic subjects. METHODS AND MATERIALS: Twenty-five asymptomatic participants were recruited in this study. The dominant knee was distracted for 30 minutes in a 30° flexion position using three force magnitudes (10%, 20%, and 30% body weight (BW)). The traction forces were randomized with one week in between knee distractions. Joint space, range of motion (ROM), and hamstring flexibility were assessed before, immediately after, and 30 minutes after the distraction. The self-reported discomfort was assessed immediately after the distraction only. RESULTS: Medial joint space, ROM, and discomfort showed a significant difference between different force magnitudes post-distraction. The 20% and 30% BW force magnitudes significantly, but equally, increased joint space and ROM post distraction. The discomfort level was directly related to distraction force magnitude and the least comforting was the 30% BW force. Follow-up data was not significantly different than that for post-distraction. Hamstring muscle flexibility showed a significant. Yet, small increase after the 30% BW distraction force. CONCLUSION: Continued mechanical distraction of the knee joint using force magnitudes of 20% and 30% of body weight was effective in increasing medial joint space, active knee ROM, and hamstring flexibility in asymptomatic individuals. 20% force magnitude was more comfortable than the 30% percent.