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1.
Understanding the kinetic strategies of turning as expressed in ground reaction forces (GRFs) and impulses (GRIs) is necessary to design therapies and technologies to enable patients with ambulatory difficulties perform daily activities. Previous studies have reported data only for one step of the turn and expressed the data in terms of a global reference frame making it difficult to understand how the forces act on the body to cause a change in heading and orientation during a turn. This study is the first to report GRF and GRI data for three steps of a turn and express that data in terms of a body reference frame. Motion and GRF data were collected from 10 subjects walking at self-selected speeds along a straight path and performing 90 degrees left and right turns. During the left turn, turn initiation and apex steps were collected. During the right turn, turn termination steps were collected. GRF data were rotated to a reference frame whose origin was the body center of mass (COM) and aligned to the COM trajectory and then integrated to find the GRIs. In the medial-lateral direction, straight steps were characterized by a brief medial impulse at heel strike followed by a prolonged lateral impulse. Turn initiation and termination steps were both characterized by medial impulses spanning the entire stance phase while apex steps were characterized by a large lateral impulse. In the anterior-posterior direction, initiation steps had larger braking and smaller propulsive impulses than straight steps. Apex steps had larger propulsive impulses than straight steps, and termination steps had smaller braking and larger propulsive impulses than straight steps.  相似文献   

2.
It was recently shown that short-term changes in the whole body mass and associated changes in the vertical position of the center of mass (COM) modify anticipatory postural adjustments (APAs) [Li X, Aruin AS. The effect of short-term changes in the body mass on anticipatory postural adjustments. Exp Brain Res 2007;181:333–46]. In this study, we investigated whether changes in the body mass distribution and related changes in the anterior–posterior COM position affect APA generation. Fourteen subjects were instructed to catch a 2.2 kg load with their arms extended while standing with no additional weight or while carrying a 9.08 kg weight. Adding weight to a backpack, front pack or belly pocket was associated with an increase of the whole body mass, but it also involved changes in the anterior–posterior (A/P) and vertical positions of the COM. Electromyographic activity of leg and trunk muscles, body kinematics, and ground reaction forces were recorded and quantified within the typical time intervals of APAs. APAs were modified in conditions with changed body mass distribution: increased magnitude of anticipatory EMG activity in leg and trunk muscles, as well as co-activation of leg muscles and decreased anticipatory displacement of the COM in the vertical direction, were seen in conditions with increased body mass. Changes in the COM position induced in both A/P and vertical directions were associated with increased anticipatory EMG activity. In addition, they were linked to a co-activation of muscles at the ankle joints and significant changes in the center of pressure (COP) position. Modifications of the COM position induced in the A/P direction were related to increased anticipatory EMG activity in the leg and trunk muscles. At the same time, no significant differences in anticipatory EMG activity or displacement of COP were observed when changes of COM position were induced in the vertical direction. The study outcome suggests that the CNS uses different strategies while generating APAs in conditions with changes in the COM position induced in the anterior–posterior and vertical directions.  相似文献   

3.
Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.  相似文献   

4.
Yang F  Pai YC 《Journal of biomechanics》2007,40(12):2723-2730
The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 (body weight) during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint-moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip.  相似文献   

5.

Background

The Timed Up and Go (TUG) test is often used to estimate risk of falls. Foot clearance and displacement of the center of mass (COM), which are related to risk of tripping and dynamic stability have never been evaluated during the TUG. Accurate assessment of these parameters using instrumented measurements would provide a comprehensive assessment of risk of falls in hemiparetic patients. The aims of this study were to analyze correlations between TUG performance time and displacement of the COM and foot clearance in patients with stroke-related hemiparesis and healthy subjects during the walking and turning sub-tasks of the TUG and to compare these parameters between fallers and non-fallers.

Methods

29 hemiparetic patients and 25 healthy subjects underwent three-dimensional gait analysis during the TUG test. COM and foot clearance were analyzed during the walking and turning sub-tasks of the TUG.

Results

Lateral displacement of the COM was greater and faster during the walking sub-tasks and vertical displacement of the COM was greater during the turn in the patients compared to the healthy subjects (respectively p<0.01 and p<0.05). Paretic foot clearance was greater during walking and displacement of the COM was slower during the turn in the patients (p<0.01). COM displacement and velocity during the turn were correlated with TUG performance in the patients, however, vertical COM displacement was not. These correlations were significant in the healthy subjects. There were no differences between COM parameters or foot clearance in fallers and non-fallers.

Discussion and Conclusion

Hemiparetic patients are less stable than healthy subjects, but compensate with a cautious gait to avoid tripping. Instrumented analysis of the TUG test appears relevant for the assessment of dynamic stability in hemiparetic patients, providing more information than straight-line gait.  相似文献   

6.
通过对长爪沙鼠和金黄地鼠肺皮蒸发失水量的研究表明,同种内个体间肺皮蒸发失水量与动物体重呈负指数相关。在10-30℃范围内,肺皮蒸发失水量随温度上升呈指数式增加。随着相对湿度的增加,肺皮蒸发失水量呈指数式减少。在10℃和20℃环境温度下,金黄地鼠肺皮蒸发失水量略高于长爪沙鼠,在30℃环境温度下,长爪沙鼠肺皮蒸发失水量略高于金黄地鼠。  相似文献   

7.
Ground reaction (GR) components measured by a dynamometric platform represent the dynamic interaction of the moving human body with the ground and depend on the subject-platform relative position and orientation. The observed variability among the GR measurements of the walking trials of an individual is either due to variability in the motor performance (intrinsic variability) or due to changes in the direction of walking and in the position and orientation of the striking foot relative to the platform (extrinsic variability). A method, based on the median operator, is presented here which lets us quantify the two components of variability. The application of the method to a large data set of normal subjects evidenced changes in progression direction/foot orientation (95th percentile value is 6.9 degrees ), which can dramatically change the patterns of GR components. This result warns about improper analysis of ground reaction measurement.An algorithm for restoring GR measurements affected by artefact was derived from the above method. This tool can be of valuable aid in clinical practice where patients' conditions suggest to not insist on repetition of trials even if the required number of correct foot placements has not been achieved. The artefact correction algorithm has been applied to a large data set artificially corrupted to evaluate its robustness.  相似文献   

8.
We examined the functional role of braking forces observed when humans execute turning maneuvers. Deceleration caused by braking forces contributes to changing the movement direction of the center of mass (COM) and maintaining constant velocity. We argue that braking forces also prevent over-rotation of the body about the vertical axis during maneuvers. We analyzed data from sidestep and crossover cuts at average initial running velocities of 3 m s(-1). Absent braking, lateral forces would result in body rotations 1.4-3 times the change in COM movement direction, causing the orientation of the body to be substantially mis-aligned with the direction of movement at the end of the step. A simple model based on the hypothesis that body rotation should match COM deflection can explain 70% of the variance in braking forces employed during running turns.  相似文献   

9.
In motion capture applications using electromagnetic tracking systems the process of anatomical calibration associates the technical frames of sensors attached to the skin with the human anatomy. Joint centers and axes are determined relative to these frames. A change of orientation of the sensor relative to the skin renders this calibration faulty. This sensitivity regarding sensor displacement can turn out to be a serious problem with movement recordings of several minutes duration. We propose the “dislocation distance” as a novel method to quantify sensor displacement and to detect gradual and sudden changes of sensor orientation. Furthermore a method to define a so called fixed technical frame is proposed as a robust reference frame which can adapt to a new sensor orientation on the skin. The proposed methods are applied to quantify the effects of sensor displacement of 120 upper and lower limb movement recordings of newborns revealing the need for a method to compensate for sensor displacement. The reliability of the fixed technical frame is quantified and it is shown that trend and dispersion of the dislocation distance can be significantly reduced. A working example illustrates the consequences of sensor displacement on derived angle time series and how they are avoided using the fixed technical frame.  相似文献   

10.
The assumption that two subsystems control the balance during quiet standing in humans is considered. Their function is to control the slow movement of the reference point and rapid stabilization of the center of mass (COM) relative to this point. A method allowing the COM trajectory to be divided into the corresponding two components, which was developed earlier, has been used to analyze and compare the time patterns of these processes. The results of this analysis have shown that the movement of the reference point is dominant in terms of the oscillation amplitude. Therefore, the oscillations of the COM trajectory reflect the slow movement of the reference point and are practically unrelated to the stabilization of the COM relative to this point. The possibility of applying the decomposition of the COM trajectory into components to fundamental and clinical research is discussed.  相似文献   

11.
The pirouette turn is often initiated in neutral and externally rotated hip positions by dancers. This provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole-body level when using different leg kinematics. The purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation. Skilled dancers (n=5) performed pirouette turns with and without hip external rotation. Joint kinetics during turn initiation were determined for both legs using ground reaction forces (GRFs) and segment kinematics. Hip muscle activations were monitored using electromyography. Using probability-based statistical methods, variables were compared across turn conditions as a group and within-dancer. Despite differences in GRFs and impulse generation between turn conditions, at least 90% of each GRF was aligned with the respective leg plane. A majority of the net joint moments at the ankle, knee, and hip acted about an axis perpendicular to the leg plane. However, differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh. During the initiation of both turns, most participants used ankle plantar flexor moments, knee extensor moments, flexor and abductor moments at the push leg׳s hip, and extensor and abductor moments at the turn leg׳s hip. Representation of joint kinetics using multiple reference systems assisted in understanding control priorities.  相似文献   

12.
Restoring functional gait speed is an important goal for rehabilitation post-stroke. During walking, transferring of one’s body weight between the limbs and maintaining balance stability are necessary for independent functional gait. Although it is documented that individuals post-stroke commonly have difficulties with performing weight transfer onto their paretic limbs, it remains to be determined if these deficits contributed to slower walking speeds. The primary purpose of this study was to compare the weight transfer characteristics between slow and fast post-stroke ambulators. Participants (N = 36) with chronic post-stroke hemiparesis walked at their comfortable and maximal walking speeds on a treadmill. Participants were stratified into 2 groups based on their comfortable walking speeds (≥0.8 m/s or <0.8 m/s). Minimum body center of mass (COM) to center of pressure (COP) distance, weight transfer timing, step width, lateral foot placement relative to the COM, hip moment, peak vertical and anterior ground reaction forces, and changes in walking speed were analyzed. Results showed that slow walkers walked with a delayed and deficient weight transfer to the paretic limb, lower hip abductor moment, and more lateral paretic limb foot placement relative to the COM compared to fast walkers. In addition, propulsive force and walking speed capacity was related to lateral weight transfer ability. These findings demonstrated that deficits in lateral weight transfer and stability could potentially be one of the limiting factors underlying comfortable walking speeds and a determinant of chronic stroke survivors’ ability to increase walking speed.  相似文献   

13.
《Zoology (Jena, Germany)》2014,117(4):269-281
Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.  相似文献   

14.
This study sought to determine the effect of inaccuracies in body segment parameters and modeling assumptions on the estimate of antero-posterior center of mass (COM) trajectory. Four different methods, one based on segmental kinematics, and three methods based on kinetic recordings were compared via simulation. Kinematic patterns (quiet stance, ankle-related sway, hip-ankle-related sway, sit-up and sit-up-sit-down) were tested with a 2D four-link model of the body and the ground reaction force vector was obtained by inverse dynamics. Errors in the estimation of body segment parameters were simulated by applying a +/-10% variation to one or more parameters at a time. These errors propagated differently to the COM estimated location between methods, between parameters within the same method, and between tasks. The kinematics-based method was the most sensitive to body segment parameters, with special regards to segment lengths and head-arms-trunk parameters. Root mean square error between estimated and simulated COM location reached 19mm in balance-related tasks and 38.3mm in sit-up-sit-down. The kinetics-based methods were largely less sensitive to inaccuracies in body segment parameters. In particular, the technique proposed by Zatsiorsky and King (J. Biomech. 31 (1998) 161), was completely insensitive to segment parameters. On the other hand the kinetics-based methods showed an intrinsic estimation error, due to the underlying model assumptions. The methods based on the double integration of horizontal force had better outcomes with tasks challenging such assumptions, with a maximal error in COM location of 15mm in the sit-up-sit-down. The method proposed by Shimba (J. Biomech. 17 (1984) 53) showed the best trade-off between sensitivity to body segment parameters and estimation performances given the ideal test conditions.  相似文献   

15.
Altered gait kinematics and kinetics are observed in patients with medial compartment knee osteoarthritis. Although various kinematic adaptations are proposed to be compensatory mechanisms that unload the knee, the nature of these mechanisms is presently unclear. We hypothesized that an increased toe-out angle during early stance phase of gait shifts load away from the knee medial compartment, quantified as the external adduction moment about the knee. Specifically, we hypothesized that by externally rotating the lower limb anatomy, primarily about the hip joint, toe-out gait alters the lengths of ground reaction force lever arms acting about the knee joint in the frontal and sagittal planes and transforms a portion of knee adduction moment into flexion moment. To test this hypothesis, gait data from 180 subjects diagnosed with medial compartment knee osteoarthritis were examined using two frames of reference. The first frame was attached to the tibia (reporting actual toe-out) and the second frame was attached to the laboratory (simulating no-toe-out). Four measures were compared within subjects in both frames of reference: the lengths of ground reaction force lever arms acting about the knee joint in the frontal and sagittal planes, and the adduction and flexion components of the external knee moment. The mean toe-out angle was 11.4 degrees (S.D. 7.8 degrees , range -2.2 degrees to 28.4 degrees ). Toe-out resulted in significant reductions in the frontal plane lever arm (-6.7%) and the adduction moment (-11.7%) in early stance phase when compared to the simulated no-toe-out values. These reductions were coincident with significant increases in the sagittal plane lever arm (+33.7%) and flexion moment (+25.0%). Peak adduction lever arm and moment were also reduced significantly in late stance phase (by -22.9% and -34.4%, respectively) without a corresponding increase in sagittal plane lever arm or flexion moment. These results indicate that toe-out gait in patients with medial compartment knee osteoarthritis transforms a portion of the adduction moment into flexion moment in early stance phase, suggesting that load is partially shifted away from the medial compartment to other structures.  相似文献   

16.
Studies have shown that internal representations of manipulations of objects with asymmetric mass distributions that are generated within a specific orientation are not generalizable to novel orientations, i.e., subjects fail to prevent object roll on their first grasp-lift attempt of the object following 180° object rotation. This suggests that representations of these manipulations are specific to the reference frame in which they are formed. However, it is unknown whether that reference frame is specific to the hand, the body, or both, because rotating the object 180° modifies the relation between object and body as well as object and hand. An alternative, untested explanation for the above failure to generalize learned manipulations is that any rotation will disrupt grasp performance, regardless if the reference frame in which the manipulation was learned is maintained or modified. We examined the effect of rotations that (1) maintain and (2) modify relations between object and body, and object and hand, on the generalizability of learned two-digit manipulation of an object with an asymmetric mass distribution. Following rotations that maintained the relation between object and body and object and hand (e.g., rotating the object and subject 180°), subjects continued to use appropriate digit placement and load force distributions, thus generating sufficient compensatory moments to minimize object roll. In contrast, following rotations that modified the relation between (1) object and hand (e.g. rotating the hand around to the opposite object side), (2) object and body (e.g. rotating subject and hand 180°), or (3) both (e.g. rotating the subject 180°), subjects used the same, yet inappropriate digit placement and load force distribution, as those used prior to the rotation. Consequently, the compensatory moments were insufficient to prevent large object rolls. These findings suggest that representations of learned manipulation of objects with asymmetric mass distributions are specific to the body- and hand-reference frames in which they were learned.  相似文献   

17.
Leg stiffness was compared between age-matched males and females during hopping at preferred and controlled frequencies. Stiffness was defined as the linear regression slope between the vertical center of mass (COM) displacement and ground-reaction forces recorded from a force plate during the stance phase of the hopping task. Results demonstrate that subjects modulated the vertical displacement of the COM during ground contact in relation to the square of hopping frequency. This supports the accuracy of the spring-mass oscillator as a representative model of hopping. It also maintained peak vertical ground-reaction load at approximately three times body weight. Leg stiffness values in males (33.9+/-8.7 kN/m) were significantly (p<0.01) greater than in females (26.3+/-6.5 kN/m) at each of three hopping frequencies, 3.0, 2.5 Hz, and a preferred hopping rate. In the spring-mass oscillator model leg stiffness and body mass are related to the frequency of motion. Thus male subjects necessarily recruited greater leg stiffness to drive their heavier body mass at the same frequency as the lighter female subjects during the controlled frequency trials. However, in the preferred hopping condition the stiffness was not constrained by the task because frequency was self-selected. Nonetheless, both male and female subjects hopped at statistically similar preferred frequencies (2.34+/-0.22 Hz), therefore, the females continued to demonstrate less leg stiffness. Recognizing the active muscle stiffness contributes to biomechanical stability as well as leg stiffness, these results may provide insight into the gender bias in risk of musculoskeletal knee injury.  相似文献   

18.
A prey's body orientation relative to a predator's approach path may affect risk of fleeing straight ahead. Consequently, prey often turn before fleeing. Relationships among orientation, turn, and escape angles and between these angles and predation risk have not been studied in terrestrial vertebrates and have rarely been studied in the field. Escape angles are expected to lead away from predators and be highly variable to avoid being predictable by predators. Using approach speed as a risk factor, we studied these issues in the zebra‐tailed lizard, Callisaurus draconoides. Lizards fled away from human simulated predators, but most did not flee straight away. Escape angles were variable, as expected under the unpredictability hypothesis, and had modes at nearly straight away (i.e., 0°) and nearly perpendicular to the predator's approach path (90°). The straight away mode suggests maximal distancing from the predator; the other mode suggests maintaining ability to monitor the predator or possibly an influence of habitat features such as obstacles and refuges that differ among directions. Turn angles were larger when orientation was more toward the predator, and escape angles were closer to straight away when turn angles were larger. Turning serves to reach a favorable fleeing direction. When orientation angle was more toward the predator, escape angle was unaffected, suggesting that turn angle compensates completely for increased risk of orientation toward the predator. When approached more rapidly, lizards fled more nearly straight away, as expected under greater predation risk. Turn angles were unrelated to approach speed.  相似文献   

19.

Background

for many technology-driven visuomotor tasks such as tele-surgery, human operators face situations in which the frames of reference for vision and action are misaligned and need to be compensated in order to perform the tasks with the necessary precision. The cognitive mechanisms for the selection of appropriate frames of reference are still not fully understood. This study investigated the effect of changing visual and kinesthetic frames of reference during wrist pointing, simulating activities typical for tele-operations.

Methods

using a robotic manipulandum, subjects had to perform center-out pointing movements to visual targets presented on a computer screen, by coordinating wrist flexion/extension with abduction/adduction. We compared movements in which the frames of reference were aligned (unperturbed condition) with movements performed under different combinations of visual/kinesthetic dynamic perturbations. The visual frame of reference was centered to the computer screen, while the kinesthetic frame was centered around the wrist joint. Both frames changed their orientation dynamically (angular velocity = 36°/s) with respect to the head-centered frame of reference (the eyes). Perturbations were either unimodal (visual or kinesthetic), or bimodal (visual+kinesthetic). As expected, pointing performance was best in the unperturbed condition. The spatial pointing error dramatically worsened during both unimodal and most bimodal conditions. However, in the bimodal condition, in which both disturbances were in phase, adaptation was very fast and kinematic performance indicators approached the values of the unperturbed condition.

Conclusions

this result suggests that subjects learned to exploit an “affordance” made available by the invariant phase relation between the visual and kinesthetic frames. It seems that after detecting such invariance, subjects used the kinesthetic input as an informative signal rather than a disturbance, in order to compensate the visual rotation without going through the lengthy process of building an internal adaptation model. Practical implications are discussed as regards the design of advanced, high-performance man-machine interfaces.  相似文献   

20.
When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.  相似文献   

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