Magnitude Of Reaction Forces Research Articles

The Etiology of Neuromuscular Hip Dysplasia and Implications for Management: A Narrative Review.

This study summarizes the current knowledge of the etiology of hip dysplasia in children with neuromuscular disease and the implications for management. This article is based on a review of development of the hip joint from embryology through childhood growth. This knowledge is then applied to selective case reviews to show how the understanding of these developmental principles can be used to plan specific treatments. The development of the hip joint is controlled by genetic shape determination, but the final adult shape is heavily dependent on the mechanical environment experienced by the hip joint during growth and development. Children with neuromuscular conditions show a high incidence of coxa valga, hip dysplasia, and subluxation. The etiology of hip pathology is influenced by factors including functional status, muscular tone, motor control, child's age, and muscle strength. These factors in combination influence the development of high neck-shaft angle and acetabular dysplasia in many children. The hip joint reaction force (HJRF) direction and magnitude determine the location of the femoral head in the acetabulum, the acetabular development, and the shape of the femoral neck. The full range of motion is required to develop a round femoral head. Persistent abnormal direction and/or magnitude of HJRF related to the muscular tone can lead to a deformed femoral head and a dysplastic acetabulum. Predominating thigh position is the primary cause defining the direction of the HJRF, leading to subluxation in nonambulatory children. The magnitude and direction of the HJRF determine the acetabular shape. The age of the child when these pathomechanics occur acts as a factor increasing the risk of hip subluxation. Understanding the risk factors leading to hip pathology can help to define principles for the management of neurologic hip impairment. The type of neurologic impairment as defined by functional severity assessed by Gross Motor Function Classification System and muscle tone can help to predict the risk of hip joint deformity. A good understanding of the biomechanical mechanisms can be valuable for treatment planning.

Measurement of bearing reaction force by distributed strain variation

Bearing is a crucial transmission component of aero-engines under high-speed and heavy-load conditions. To design a roller bearing with high loading capacity and reliability, it is essential to focus on the relationship between the external load state (reaction force) and the internal load distribution (load distribution). Therefore, a measurement method for bearing reaction force using load distribution and radial basis function neural network is presented in this study. Unlike conventional static reaction force measurement methods, both the direction and magnitude of the reaction force are considered in the proposed method without modifications to bearing. First, an experimental system is designed to investigate the load distribution in a roller bearing under different reaction forces using strain variation measurements. Then, a finite element analysis is conducted, and simulation results of the strain variations at three interested points match well with the experimental measurements. Finally, a radial basis function neural network with strong nonlinear fitting ability is applied to construct the mapping relationship between strain variation and reaction force. The results demonstrate that the proposed method can predict the reaction force with high accuracy based on the strain variation at three measuring points.

A numerical study of the contact geometry and pressure distribution along the glenoid track

The glenoid track geometry and the contact forces acting on the glenohumeral joint at static positions of 30°, 60°, 90° and 120° of abduction with 90° of external rotation were evaluated using a finite element model of the shoulder that, differently from most usual approximations, accounts the humeral head translations and the deformable-to-deformable non-spherical joint contact. The model was based on data acquired from clinical exams of a single subject, including the proximal humerus, scapula, their respective cartilages concerning the glenohumeral joint, and the rotator cuff and deltoid muscles. The forces acting on the glenohumeral joint were estimated using a simulation framework consisting of an optimization procedure allied with finite element analysis that seeks the minimum muscle forces that stabilize the joint. The joint reaction force magnitude increases up to 680.25N at 90° of abduction and decreases at further positions. From 60° onward the articular contact remains at the anterior region of the glenoid cartilage and follows an inferior to superior path at the posterior region of the humeral head cartilage. The maximum contact pressure of 3.104MPa occurs at 90° abduction. Although translating inferiorly throughout the movement, the projection of the humeral head center at the glenoid plane remains at the central region of the glenoid surface. The model results qualitatively matched the trends observed in the literature and supports the consideration of the translational degrees of freedom to evaluate the joint contact mechanics.

Analysis of equipment for biaxial material testing

This paper aims to analyze the operation of the equipment for biaxial testing. The equipment’s stiffness is one of the main factors influencing the magnitude of reaction forces in the device’s guidance, consequently affecting the measurement accuracy. Based on intensive research on the topic of biaxial testing devices, the present paper deals with the analysis and optimization of the equipment’s current design.

The biomechanics of the rotator cuff in health and disease – A narrative review

The rotator cuff has an important role in the stability and function of the glenohumeral joint. It is a complex anatomic structure commonly affected by injury such as tendinopathy and cuff tears. The rotator cuff helps to provide a stabilising effect to the shoulder joint by compressing the humeral head against the glenoid cavity via the concavity compression mechanism. To appreciate the function of the cuff it is imperative to understand the normal biomechanics of the cuff as well as the mechanisms involved in the pathogenesis of cuff disease.The shoulder joint offers a wide range of motion due to the variety of rotational moments the cuff muscles are able to provide. In order for the joint to remain stable, the cuff creates a force couple around the glenohumeral joint with coordinated activation of adjacent muscles, which work together to contain the otherwise intrinsically unstable glenohumeral joint and prevent proximal migration of the humerus. Once this muscular balance is lost, increased translations or subluxation of the humeral head may result, leading to changes in the magnitude and direction of the joint reaction forces at the glenohumeral joint. These mechanical changes may then result in a number of clinical presentations of shoulder dysfunction, disease and pain.This narrative review aims to highlight the importance of functional rotator cuff biomechanics whilst assessing the kinetics and kinematics of the shoulder joint, as well as exploring the various factors involved in cuff disease.

A comparison of centre of pressure behaviour and ground reaction force magnitudes when individuals walk overground and on an instrumented treadmill

BackgroundInstrumented treadmills facilitate analysis of consecutive strides in ways that typical overground gait data collections cannot. Researchers have quantified differences between joint kinetic measures whilst walking on an instrumented treadmill compared to those walking overground. The reason for such differences has not yet been established. Research QuestionCan we identify the source or sources of these errors by comparing centre of pressure and ground reaction force measurements recorded on a treadmill to those collected overground? MethodsKinematic and kinetic data were recorded while nineteen individuals walked continuously at their self-selected walking speed overground and on a treadmill. Comparisons of the centre of pressure and ground reaction forces were made between the two conditions using 2-tailed paired t-tests and Cohen’s d effect size. ResultsThe results indicated that participants had significantly faster backwards, lateral and medial centre of pressure velocities when walking on a treadmill compared to when they were walking overground. Additionally, participants also had significantly reduced peak propulsive ground reaction forces when walking on a treadmill than walking overground. SignificanceThese results suggest that shear forces caused by the belts sliding over the treadmill force platforms affect the centre of pressure during early stance, and the minimal acceleration of a participant’s centre of mass during treadmill walking results in reduced propulsive force during late stance. Therefore, care should be taken during studies when comparing kinetic gait variables between overground and treadmill walking.

Comparison of methods of derivation of the yank-time signal from the vertical ground reaction force–time signal for identification of movement-related events

Temporal changes in ground reaction force magnitudes reflect movement strategy, and thus underlying muscle activation patterns, during movement tasks. Speculatively, these changes may be observed more readily when the force–time signal is differentiated, yielding the yank-time signal. However, the differentiation process, including the signal filtering used before or after differentiation, can significantly affect the signal-to-noise ratio (SNR) and likelihood of meaningful inference. The aim of the present study was to compare three methods of deriving the yank-time signal: Method 1 derived the yank-time signal using 2nd-order central differentiation subsequent to application of a 4th-order Butterworth filter; Method 2 included the same process as Method 1 but additionally filtered the yank-time data with a Savitzky-Golay smoothing filter; and Method 3 directly and simultaneously derived and smoothed the yank-time signal using a Savitzky-Golay digital differentiation filter. The current analyses revealed Method 2 had the best SNR, followed by Methods 3 and 1, but caused a small loss of signal amplitude. With regards to timing of inflection points in the yank-time data, no significant difference was observed. Therefore, Method 3 led to the best derivation of the yank-time signal due to its efficiency and preservation of signal characteristics and good SNR. Also, a strong association between the first maximum point of the yank-time signal and the start of the downward movement of the body’s centre of mass during a countermovement jump, as identified by 3-D motion analysis, was observed. Thus, subtle events (e.g. start of downward movement) can be easily observed in the yank-time signal.

Upper body postures effect on neuromuscular activities of the lower limb during a squat: musculoskeletal modeling

Spinal manipulative techniques are commonly used in manual therapies but quantified descriptive and reliability data are lacking considering supine thoracic thrust manipulation.The purpose of this study is to explore and compare kinetic parameters during supine thoracic thrust manipulation performed at two different thoracic regions. Intra-rater task repeatability and influence of practitioners were estimated.Exploratory and agreement study.Kinetic parameters were assessed by examining reaction force magnitude and orientation (on the basis of the zenithal angle) using force platforms. Manipulative procedure (consisting in the application of 3 preloads followed by one thrust adjustment) at both intervertebral and costovertebral region was performed by different practitioners at three sessions. Application of thrust was allowed for experienced practitioners only. Preload force, peak force magnitude and vector force orientation were compared between anatomical sites, sessions and practitioners, and bias with limit of agreement were estimated.Repeatability analysis showed that practitioners achieved similar preload and peak force independent of the session, with comparable force orientation. Differences between practitioners were observed for preload and peak force but not regarding the zenithal angle during the thrust phase.The present study is the first that explores kinetic parameters for supine thoracic thrust manipulation applied on two different regions of the thorax. Results confirm consistency of performance among practitioners for supine manipulative techniques at intervertebral and costovertebral region. While task repeatability was confirmed, several differences were observed between practitioners. Further investigations would examine velocity, acceleration and potential neurophysiological effect of such manipulative technique.

Investigation of reaction force magnitude and orientation during supine thoracic thrust manipulation applied to intervertebral and costovertebral regions.

BackgroundSpinal manipulative techniques are commonly used in manual therapies but quantified descriptive and reliability data are lacking considering supine thoracic thrust manipulation. ObjectivesThe purpose of this study is to explore and compare kinetic parameters during supine thoracic thrust manipulation performed at two different thoracic regions. Intra-rater task repeatability and influence of practitioners were estimated. DesignExploratory and agreement study. MethodsKinetic parameters were assessed by examining reaction force magnitude and orientation (on the basis of the zenithal angle) using force platforms. Manipulative procedure (consisting in the application of 3 preloads followed by one thrust adjustment) at both intervertebral and costovertebral region was performed by different practitioners at three sessions. Application of thrust was allowed for experienced practitioners only. Preload force, peak force magnitude and vector force orientation were compared between anatomical sites, sessions and practitioners, and bias with limit of agreement were estimated. ResultsRepeatability analysis showed that practitioners achieved similar preload and peak force independent of the session, with comparable force orientation. Differences between practitioners were observed for preload and peak force but not regarding the zenithal angle during the thrust phase. ConclusionsThe present study is the first that explores kinetic parameters for supine thoracic thrust manipulation applied on two different regions of the thorax. Results confirm consistency of performance among practitioners for supine manipulative techniques at intervertebral and costovertebral region. While task repeatability was confirmed, several differences were observed between practitioners. Further investigations would examine velocity, acceleration and potential neurophysiological effect of such manipulative technique.

Reaction Force Magnitude and Orientation During Supine Thoracic Spine Thrust Manipulation: An Exploratory Analysis and Reliability of Preload and Impulse Phase

ObjectiveThe main purpose of this study was to explore specific kinetic parameters during supine thoracic thrust manipulation and to analyze task reliability and differences between various practitioners MethodsKinetic parameters were assessed by examining ground reaction force magnitude and orientation (on the basis of the zenithal angle) using force platforms. The manipulative procedure (consisting of the application of 3 preloads followed by 1 single thrust adjustment) was performed by different practitioners at 3 sessions. Application of thrust was allowed for trained practitioners only. Preload force, peak force, and vector force orientation were compared between sessions and practitioners. ResultsReliability analysis showed that practitioners achieved similar preload and peak force independent of the session, with comparable force orientation data. Differences between practitioners were observed for preload and peak force but not regarding the zenithal angle during the thrust phase. ConclusionThis study is the first that explores kinetic parameters for supine thoracic thrust manipulation. Task repeatability was confirmed and several differences were observed between practitioners. Certainly, there is a need for further investigation examining both dynamic parameters (ie, velocity and accelerations) and the potential neurologic effect of such manipulative technique.

Soft tissue artifact causes underestimation of hip joint kinematics and kinetics in a rigid-body musculoskeletal model

Rigid body musculoskeletal models have been applied to study kinematics, moments, muscle forces, and joint reaction forces in the hip. Most often, models are driven with segment motions calculated through optical tracking of markers adhered to the skin. One limitation of optical tracking is soft tissue artifact (STA), which occurs due to motion of the skin surface relative to the underlying skeleton. The purpose of this study was to quantify differences in musculoskeletal model outputs when tracking body segment positions with skin markers as compared to bony landmarks measured by direct imaging of bone motion with dual fluoroscopy (DF). Eleven asymptomatic participants with normally developed hip anatomy were imaged with DF during level treadmill walking at a self-selected speed. Hip joint kinematics and kinetics were generated using inverse kinematics, inverse dynamics, static optimization and joint reaction force analysis. The effect of STA was assessed by comparing the difference in estimates from simulations based on skin marker positions (SM) versus virtual markers on bony landmarks from DF. While patterns were similar, STA caused underestimation of kinematics, range of motion (ROM), moments, and reaction forces at the hip, including flexion-extension ROM, maximum internal rotation joint moment and peak joint reaction force magnitude. Still, kinetic differences were relatively small, and thus they may not be relevant nor clinically meaningful.

A neural network method to predict task- and step-specific ground reaction force magnitudes from trunk accelerations during running activities

Prediction of ground reaction force (GRF) magnitudes during running-based sports has several important applications, including optimal load prescription and injury prevention in athletes. Existing methods typically require information from multiple body-worn sensors, limiting their ecological validity, or aim to estimate discrete force parameters, limiting their ability to assess overall biomechanical load. This paper presents a neural network method to predict GRF time series from a single, commonly used, trunk-mounted accelerometer. The presented method uses a principal component analysis and multilayer perceptron (MLP) to obtain predictions. Time-series r2 coefficients with test data averaged around 0.9 for each impact, comparing favourably with alternative approaches which require additional sensors. For the impact peak, r2 was 0.74 across activities, comparing favourably with correlation analysis approaches. Several modifications, such as subject-specific training of the MLP, may help to improve results further, but the presented method can accurately predict GRF from trunk accelerometry data without requiring additional information. Results demonstrate the scope of machine learning to exploit common wearable technologies to estimate GRF in sport-specific environments.

Somatosensory Function Influences Aberrant Gait Biomechanics Following Anterior Cruciate Ligament Reconstruction.

Osteoarthritis is common following anterior cruciate ligament reconstruction (ALCR), and aberrant gait biomechanics are considered a primary contributor. Somatosensory dysfunction potentially alters gait biomechanics, but this association is unclear. Therefore, the purposes of this investigation were to compare somatosensory function between limbs and evaluate associations between somatosensory function and gait biomechanics linked to osteoarthritis development in individuals with ALCR. Seventy-three volunteers with ALCR participated. Gait biomechanics (peak vertical ground reaction force magnitude and loading rate, peak internal knee extension and valgus moments, peak knee flexion and varus angles, and quadriceps/hamstrings co-activation) were assessed as subjects walked at their preferred speed. The somatosensory function was assessed via joint position sense error (knee flexion) and vibratory perception threshold (femoral epicondyles, malleoli, and first metatarsal). Though somatosensory function did not differ between the ACLR and contralateral limbs, poorer joint position sense in the ACLR limb was associated with lower loading rates and internal knee extension moments, and greater co-activation. Poorer vibratory perception at the medial and lateral malleoli and first metatarsal head in the ACLR limb was associated with lower loading rates, greater internal knee valgus moments and varus angles, and greater co-activation. Poorer vibratory perception at the medial malleolus and first metatarsal head in the contralateral limb was associated with greater peak knee varus angles and internal knee valgus moments. These results suggest that future research evaluating rehabilitation approaches for improving somatosensory function is warranted as a potential approach for restoring normal gait biomechanics and reducing osteoarthritis risk. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:620-628, 2020.

Behaviour and analysis of ultra high performance fibre reinforced concrete (UHPFRC) skew slabs

This study presents an experimental and theoretical investigation of the performance of ultra-high performance fibre reinforced concrete (UHPFRC) skew bridge decks. Five simply-supported UHPFRC slabs with different skew angles were tested under monotonically increasing concentrated load. It was observed that an increase in the skewness of a slab led to a more unsymmetrical vertical deflection profile, and also resulted in a decrease in the magnitude of reaction forces at the acute corners and a corresponding increase in the reaction forces at the obtuse corners. The test results also show that, although some reduction in ductility was seen with increasing skewness of a slab, the specimen with over 25° skew angle still maintained a desirable load carrying capacity and ductility compared to those of a conventional RC straight slab. In addition to the experimental investigations, a fundamental mechanics based closed-form model was developed based on strain energy theorem to predict the performance of a UHPFRC skew slab under linear elastic material condition. At its ultimate limit state, a novel yield-line analysis using a numerically-generated mechanics based moment-rotation relationship was adopted to predict the ultimate load carrying capacity of a skew UHPFRC slab. Both the generic analytical procedures were compared and against test results obtained from this study, as well as those reported in literature, and the results show that the models developed can be applied to UHPFRC skew slabs.

Determination of Reaction Forces of a Deck Crane in Wave Motion Using Screw Theory

In this paper, we present a method for calculating reaction forces for a crane mounted on a ship moving in waves. The method is used to calculate the reaction forces between the crane base and the vessel deck. This includes the case where the crane is mounted on the platform that keeps the base of the crane horizontal when the vessel is moving in roll and pitch. The wave motion of the ship is modeled with force response amplitude operators (RAOs) based on the JONSWAP wave spectrum. The combined equations of motion for a vessel and a crane are derived using Kane’s equations of motion, where velocities and angular velocities are formulated in terms of twists, and the associated partial velocities and partial angular velocities are given as lines in Plücker coordinates. The unknown reaction forces are represented as wrenches and are determined using screw transformations. The method is used to study the effect of the roll and pitch compensation platform in numerical simulations. The efficiency of the platform is evaluated in terms of the magnitude of reaction forces and crane payload sway angles.

Co-activation during gait following anterior cruciate ligament reconstruction

BackgroundHeightened co-activation of the quadriceps and hamstrings has been reported following anterior cruciate ligament reconstruction during various tasks, and may contribute to post-traumatic osteoarthritis risk. However, it is unclear if this phenomenon occurs during walking or how co-activation influences gait biomechanics linked to changes in joint health. MethodsCo-activation and gait biomechanics were assessed in 50 individuals with ACLR and 25 healthy controls. Biomechanical outcomes included knee flexion displacement, peak vertical ground reaction force magnitude and rate, peak internal knee extension and valgus moments and rates, sagittal knee stiffness, and the heelstrike transient. Co-activation was calculated for the flexors and extensors collectively (i.e. composite), the medial musculature, and the lateral musculature. FindingsComposite co-activation was greater in the ACLR limb compared to the contralateral limb and the control cohort during the preparatory and heelstrike phases of gait, and co-activation of the medial musculature was greater in the ACLR limb compared to the control cohort during the heelstrike phase. Greater co-activation in multiple gait phases was associated with less knee flexion displacement (r = −0.293 to −0.377), smaller peak vertical ground reaction force magnitude (r = −0.291), smaller peak internal knee extension moment (r = −0.291 to −0.328), and greater peak internal knee valgus moment (r = 0.317). InterpretationIndividuals with ACLR displayed heightened co-activation during walking which was associated with biomechanical outcomes that have been linked to negative changes in joint health following ACLR. These data suggest that excessive co-activation may contribute to the mechanical pathogenesis of post-traumatic osteoarthritis.ClinicalTrials.gov Identifier: NCT02605876.

Effect of Shoe and Surface Stiffness on Lower Limb Tendon Strain in Jumping.

Tendinopathies are painful overuse injuries observed in athletes participating in jumping sports. These injuries are heavily dependent on the resulting strain from the applied mechanical load. Therefore, mechanisms to reduce tendon strain may represent a primary prevention strategy to reduce the incidence of tendinopathy. The purpose of this study was to examine the effect of shoe and surface stiffness on Achilles and patellar tendon strains during jumping. We hypothesized that less stiff shoes and surfaces would reduce Achilles and patellar tendon strains during jumping. Thirty healthy male basketball players performed countermovement jumps in three shoes and on three surfaces with different stiffness properties while motion capture, force platform, and jump height data were collected. Magnetic resonance imaging was used to obtain participant-specific tendon morphology, and a combined dynamometry/ultrasound/electromyography session was used to obtain tendon material properties. Finally, a musculoskeletal model was used to estimate tendon strains in each surface and shoe combination. Achilles tendon strains during landing were reduced by 5.3% in the least stiff shoe compared with the stiffest shoe (P = 0.021) likely due to in bending stiffness altering the center of pressure location. Furthermore, Achilles tendon strains during landing were 5.7% and 8.1% lower on the stiffest surface compared with the least stiff and middle stiffness surfaces, respectively (P ≤ 0.047), because of changes in ground reaction force magnitude and center of pressure location. No effects of shoe stiffness or surface construction were observed for jump height (P > 0.243) or peak patellar tendon strains (P > 0.259). Changes to shoe stiffness and surface construction can alter Achilles tendon strains without affecting jump performance in athletes.

An Ankle-Foot Prosthesis Emulator Capable of Modulating Center of Pressure.

Several powered ankle-foot prostheses have demonstrated moderate reductions in energy expenditure by restoring pushoff work in late stance or by assisting with balance. However, it is possible that center of pressure trajectory modulation could provide even further improvements in user performance. Here, we describe the design of a prosthesis emulator with two torque-controlled forefoot digits and a torque-controlled heel digit. Independent actuation of these three digits can modulate the origin and magnitude of the total ground reaction force vector. The emulator was designed to be compact and lightweight while exceeding the range of motion and torque requirements of the biological ankle during walking. We ran a series of tests to determine torque-measurement accuracy, closed-loop torque control bandwidth, torque-tracking error, and center of pressure control accuracy. Each of the three digits demonstrated less than 2 Nm of RMS torque measurement error, a 90% rise time of 19 ms, and a bandwidth of 33 Hz. The untethered end-effector has a mass of 1.2 kg. During walking trials, the emulator demonstrated less than 2 Nm of RMS torque-tracking error and was able to maintain full digit ground contact for 56% of stance. In fixed, standing, and walking conditions, the emulator was able to control center of pressure along a prescribed pattern with RMS errors of about 10% the length of the pattern. The proposed emulator system meets all design criteria and can effectively modulate center of pressure and ground reaction force magnitude. This emulator system will enable rapid development of controllers designed to enhance user balance and reduce user energy expenditure. Experiments conducted using this emulator could identify beneficial control behaviors that can be implemented on autonomous devices, thus improving mobility and quality of life of individuals with amputation.

A biomechanical shoulder strain index based on stabilizing demand of shoulder joint

Work-related shoulder joint disorders contribute considerably to absenteeism in the workplace. To identify the tasks that are stressful to the shoulder joint, a strain index was formulated based on the concept of concavity compression—a shoulder stabilizing mechanism. The magnitude and direction of the shoulder joint reaction forces were used in formulating the strain index. A two phase experiment was conducted. In Phase 1, participants performed 30 different manual handling tasks. The tasks were categorized into low, medium and high strain tasks based on their strain index values. In Phase 2, out of the 30 tasks, repetitive exertions of three tasks (low, medium and high strain index values) were simulated using three external loads (0.91, 1.81 and 2.72 kg). The muscle activity data recorded from eight shoulder muscles showed that tasks with higher strain index values induced significantly greater activation and muscle fatigue than tasks with lower strain index values.Practitioner Summary: The strain index developed in this study is a conclusive estimation of the concavity compression required for shoulder joint stabilization. It can be used to identify the activities that may contribute to the risks of shoulder disorders.AbbreviationBLSBureau of the Labor Statistics

Numerical and Experimental Analyses of Static and Dynamic Characteristics for Partially Helically Grooved Liquid Annular Seals

Numerical and experimental analyses of the static and dynamic characteristics of the liquid annular seals with axially partial helical grooves were conducted to investigate the effects of the axial length gal of a helically grooved section in a seal stator. The numerical solution and experimental procedures were applied in the same manner as in previous studies on through-helically grooved seals, wherein the grooves extend across the seal length. The numerical results qualitatively agreed with the experimental results, demonstrating the validity of the numerical analysis. The leakage flow rate Q was lower in the partially helically grooved seals than that of conventional through-helically grooved seals across a small range of rotor spinning velocities. In contrast, the reduction in Q due to the pumping effect caused by the spin of the rotor diminished with the decrease in gal. For a small concentric whirling motion of the rotor, the radial dynamic reaction force Fr and magnitude of variation in the tangential dynamic reaction force Ft with the whirling angular velocity increased with the decrease in gal, and their values approached the corresponding values for the smooth-surface seal. Under the same rotor whirling velocity, the Ft for the partially helically grooved seals became lower than that for the smooth-surface seal (similar to the case for the through-helically grooved seal), although decreasing gal tended to increase Ft. These results suggest that partially helically grooved seals can improve the efficiency and stability margin of the pumps because of the reduction in leakage flow rate and suppression of the rotor forward whirling motion (with large radial and tangential dynamic reaction forces) as compared to conventional through-helically grooved seals.