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1.
To our knowledge jumping kinematics have never been studied in elderly persons. This study was aimed at examining the influence of aging on vertical jump performance and on interjoint coordination. Two groups of adults, 11 young men ages 18-25 years and 11 older men ages 79-100 years, were filmed while performing a maximal squat jump. Compared to young adults, jump height was significantly decreased by 28 cm in the elderly. Older adults spontaneously jumped from a more extended position of the hip. Results showed a decrease in hip, knee, and ankle linear velocity and angular amplitude with aging. The decrease in jump height was attributed to a decrease in explosive force and in the range of shortening of extensor muscles. In agreement with the literature, a proximo-distal coordination pattern was observed in young adults. Older adults used a simultaneous pattern. This may indicate that adults adjust their pattern of joint coordination as they age.  相似文献   

2.
Optimal muscular coordination strategies for jumping   总被引:5,自引:0,他引:5  
This paper presents a detailed analysis of an optimal control solution to a maximum height squat jump, based upon how muscles accelerate and contribute power to the body segments during the ground contact phase of jumping. Quantitative comparisons of model and experimental results expose a proximal-to-distal sequence of muscle activation (i.e. from hip to knee to ankle). We found that the contribution of muscles dominates both the angular acceleration and the instantaneous power of the segments. However, the contributions of gravity and segmental motion are insignificant, except the latter become important during the final 10% of the jump. Vasti and gluteus maximus muscles are the major energy producers of the lower extremity. These muscles are the prime movers of the lower extremity because they dominate the angular acceleration of the hip toward extension and the instantaneous power of the trunk. In contrast, the ankle plantarflexors (soleus, gastrocnemius, and the other plantarflexors) dominate the total energy of the thigh, though these muscles also contribute appreciably to trunk power during the final 20% of the jump. Therefore, the contribution of these muscles to overall jumping performance cannot be neglected. We found that the biarticular gastrocnemius increases jump height (i.e. the net vertical displacement of the center of mass of the body from standing) by as much as 25%. However, this increase is not due to any unique biarticular action (e.g. proximal-to-distal power transfer from the knee to the ankle), since jumping performance is similar when gastrocnemius is replaced with a uniarticular ankle plantarflexor.  相似文献   

3.
The vertical jump is a widely used activity to develop explosive strength, particularly in plyometric and maximal power training programs. It is a multijoint action that requires substantial muscular effort from primarily the ankle, knee, and hip joints. It is not known if submaximal performances of a vertical jump have a proportional or differential training effect on the major lower-limb muscles compared to maximal jump performance. Therefore, the purpose of this study was to investigate the contribution that each of the major lower-limb joints makes to vertical jump performance as jump height increases and to comment on the previously mentioned uncertainty. Adult males (N = 20) were asked to perform a series of submaximal (LOW and HIGH) and maximal (MAX) vertical jumps while using an arm swing. Force, motion, and electromyographical data were recorded during each performance and used to compute a range of kinematic and kinetic data, including ankle, knee, and hip joint torques, powers, and work done. It was found that the contribution to jump height made by the ankle and knee joints remains largely unchanged as jump height increases (work done at the ankle: LOW =1.80, HIGH = 1.97, MAX = 2.06 J.kg(-1), F = 3.596, p = 0.034; knee: LOW = 1.62, HIGH = 1.77, MAX = 1.94 J.kg(-1), F = 1.492, p = 0.234) and that superior performance in the vertical jump is achieved by a greater effort of the hip extensor muscles (work done at the hip: LOW = 1.03, HIGH = 1.84, MAX = 3.24 J.kg(-1), F = 110.143, p < 0.001). It was concluded that the role of submaximal and maximal jumps can be differentiated in terms of their effect on ankle, knee, and hip joint muscles and may be of some importance to training regimens in which these muscles need to be differentially trained.  相似文献   

4.
The purpose of this study was to investigate the influence of wearing figure skating skates on vertical jump performance and interjoint co-ordinations described in terms of sequencing and timing of joint rotations. Ten national to international figure skaters were filmed while performing a squat jump (SJ) on a force platform. Three experimental conditions were successively realized: barefoot (BF), lifting a 1.5 kg weight (LW) corresponding to the skates' mass, attached on the distal extremity of each leg and wearing skates (SK). Jump height, angular kinematics as well as joints kinetics were calculated. Relative to the SJ height reached in the BF condition, SJ performance was significantly decreased by 2.1 and 5.5 cm in the LW and SK conditions, respectively. The restriction of ankle amplitude imposed by wearing skates was found to significantly limit the knee joint amplitude while the hip angular motion was not affected. Neither the skates' mass nor the limited ankle angular motion modified the proximo-distal organization of joint co-ordination observed when jumping barefoot. However, with plantar flexion restriction, the delay between hip and knee extensions increased while it was reduced between knee and ankle extensions. Work output at the knee and ankle joints were significantly lowered when wearing skates. The decrease of work at the knee was shown to result from an early flexing moment causing a premature deceleration of the knee and from a reduction of knee amplitude. Taken together, these results show a minimization of the participation of the knee when plantar flexion is limited. It was proposed that constraining the distal joint causes a reorganization of interjoint co-ordinations and a redistribution of the energy produced by knee extensors to the hip and ankle joints.  相似文献   

5.
It is commonly accepted that vertical jump performance is a good indicator of maximal joint power. Some studies, however, have indicated that knee joint power output in the vertical jump is limited due to forward trunk inclination early in the push-off. The aim of this experimental study was to investigate the effect of forward trunk inclination on joint power output in vertical jumping. A group of 20 male subjects performed maximal vertical countermovement jumps from stance while minimizing the contribution of arm swing by holding their hands on their hips (arms akimbo). They also performed maximal jumps while holding the trunk as upright as possible throughout the jump, still holding the arms akimbo. Jump height, joint kinematics (angles), and joint kinetics (torque, power) were calculated. Jump height of vertical jumps while holding the trunk upright was 10% less than in normal jumps. Hip joint power was decreased by 37% while knee joint power was increased by 13%. Ankle joint power did not change. These results demonstrated that maximal jump performance does not necessarily represent maximal power of each individual joint. The implication is that jump performance may well be a good representation of overall joint power; it is, however, not an accurate measure to evaluate maximal individual joint power as part of contemporary training and rehabilitation methods.  相似文献   

6.
To characterize the electromyographic (EMG) activity, ground reaction forces, and kinematics were used in the running jump with different takeoff angles. Two male long jumpers volunteered to perform running jumps at different approach speeds by varying the number of steps (from 3 to 9) in the run-up. Subject TM achieved a greater vertical velocity of the center of gravity (CG) at takeoff for all approach distances. This jumping strategy was associated with greater backward trunk lean at touchdown and takeoff, a lesser range of motion for the thigh during the support phase, more extended knee and ankle angles at touchdown, and a more flexed knee angle at takeoff. Accompanying these differences in kinematics, TM experienced greater braking impulses and lesser propulsion impulses for the forward-backward component of the ground reaction force. Furthermore, TM activated mainly the rectus femoris, vastus medialis, lateral gastrocnemius, and tibialis anterior, while if rarely activated the biceps femoris from just before contact to roughly the first two-thirds of the support phase. These results indicate that TM used a greater takeoff angle in the running jump because he enabled and sustained a greater blocking effect via the coordination patterns of the muscles relative to the hip, knee, and ankle joints. These findings also suggest that the muscle activities recorded in the present experiment are reflected in kinematics and kinetics. Further, the possible influence of these muscle activities on joint movements in the takeoff leg, and their effect on the vertical and/or horizontal velocity of the jump are discussed.  相似文献   

7.
The effect of joint strengthening on standing vertical jump height is investigated by computer simulation. The human model consists of five rigid segments representing the feet, shanks, thighs, HT (head and trunk), and arms. Segments are connected by frictionless revolute joints and model movement is driven by joint torque actuators. Each joint torque is the product of maximum isometric torque and three variable functions of instantaneous joint angle, angular velocity, and activation level, respectively. Jumping movements starting from a balanced initial posture and ending at takeoff are simulated. A matching simulation reproducing the actual jumping movement is generated by optimizing joint activation level. Simulations with the goal of maximizing jump height are repeated for varying maximum isometric torque of one joint by up to +/-20% while keeping other joint strength values unchanged. Similar to previous studies, reoptimization of activation after joint strengthening is necessary for increasing jump height. The knee and ankle are the most effective joints in changing jump height (by as much as 2.4%, or 3 cm). For the same amount of percentage increase/decrease in strength, the shoulder is the least effective joint (which changes height by as much as 0.6%), but its influence should not be overlooked.  相似文献   

8.
A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.  相似文献   

9.
In this study we aimed to determine the reliability of the surface electromyography (EMG) of leg muscles during vertical jumping between two test sessions, held 2 weeks apart. Fifteen females performed three maximal vertical jumps with countermovement. The displacement of the body centre of mass (BCM), duration of propulsion phase (time), range of motion (ROM) and angular velocity of the knee and surface EMG of four leg muscles (rectus femoris, vastus medialis. biceps femoris and gastrocnemius) were recorded during the jumps. All variables were analysed throughout the propulsion and mid-propulsion phases. Intraclass correlation coefficients (ICC) for the rectus femoris, vastus medialis, biceps femoris and gastrocnemius were calculated to be 0.88, 0.70, 0.24 and 0.01, respectively. BCM, ROM and time values all indicated ICC values greater than 0.90, and the mean knee angular velocity was slightly lower, at 0.75. ICCs between displacement of the BCM and integrated EMG (IEMG) of the muscles studied were less than 0.50. The angular velocity of the knee did not correlate well with muscle activity. Factors that may have affected reliability were variations in the position of electrode replacement, skin resistance, cross-talk between muscles and jump mechanics. The results of this study suggest that while kinematic variables are reproducible over successive vertical jumps, the degree of repeatability of an IEMG signal is dependent upon the muscle studied.  相似文献   

10.
Understanding how an arm swing enhances performance in the vertical jump   总被引:1,自引:0,他引:1  
This investigation was conducted to examine the various theories that have been proposed to explain the enhancement of jumping performance when using an arm swing compared to when no arm swing is used. Twenty adult males were asked to perform a series of maximal vertical jumps while using an arm swing and again while holding their arms by their sides. Force, motion and electromyographical data were recorded during each performance. Participants jumped higher (0.086 m) in the arm swing compared to the no-arm swing condition and was due to increased height (28%) and velocity (72%) of the center of mass at take-off. The increased height at take-off was due to the elevation of the arm segments. The increased velocity of take-off stemmed from a complex series of events which allowed the arms to build up energy early in the jump and transfer it to the rest of the body during the later stages of the jump. This energy came from the shoulder and elbow joints as well as from extra work done at the hip. This energy was used to (i) increase the kinetic and potential energy of the arms at take-off, (ii) store and release energy from the muscles and tendons around the ankle, knee and hip joint, and (iii) ‘pull’ on the body through an upward force acting on the trunk at the shoulder. It was concluded that none of the prevailing theories exclusively explains the enhanced performance in the arm swing jump, but rather the enhanced performance is based on several mechanisms operating together.  相似文献   

11.
Kinematic variables of the vertical jump (jumping height, jump phase durations and joint angles) were measured on 39 male physical education students. In addition, kinetic parameters of the hip and knee extensors, and of the plantar flexors (maxima voluntary force and its rate of development) were recorded on the same subjects, in isometric conditions. The results demonstrated significant positive correlations between kinetic parameters of the active muscle groups and jumping height (r = 0.217-0.464). The dominant effect on these correlations was due to the knee extensors. Correlations between these parameters and the duration of the jump phases were much weaker. Correlation coefficients between kinetic parameters and limb angles in the lowest body position showed that fast force production in one muscle group was related to a significant decrease in the joint angles of distant body segments. Multiple correlation coefficients between leg extensor parameters and kinematic variables (ranging between 0.256 for the duration of the counter-movement phase and 0.616 for jump height) suggested that kinetic parameters could explain more than a quarter of the variability of this complex human movement. Therefore, the conclusion was drawn that an extended set of measurements of the relevant musculo-skeletal system parameters could predict a considerable amount of the variability of human movement. However, high correlation coefficients between the same kinetic parameters of different muscle groups suggest that not all active muscle groups have to be included in the measurements.  相似文献   

12.
A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas—which determine the maximum force deliverable by the muscles—constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.  相似文献   

13.
The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.  相似文献   

14.
The purpose of this study was to investigate the effects of static stretching of the gastrocnemius muscle on maximal vertical jump performance using electromyographic activity (EMG) of the gastrocnemius musculature to record muscle activation during vertical jump performance. Fourteen healthy adults (8 men and 6 women) aged 18-34 years, who were familiar with the vertical jumping task and had no lower extremity injuries or any bone or joint disorders within the past year, served as participants for this study. After a brief warm-up, participants performed the following sequence: (a) three baseline maximal vertical jump trials, (b) 15 minutes of quiet sitting and three 30-second bilateral static stretches of the gastrocnemius muscles, and (c) 3 maximal vertical jump trials. Jump height data were collected using the Kistler force plate, while muscle activity was recorded during the jumping and stretching trials using a Noraxon telemetry EMG unit. Vertical jump height data as well as EMG values were averaged for the 3 trials and analyzed using paired t-tests for pre- and poststretching (alpha = 0.05). Vertical jump height was 5.6% lower when poststretch heights were compared with prestretch heights (t = -4.930, p < 0.005). Gastrocnemius EMG was 17.9% greater when the EMG during poststretch jumps was compared with prestretch jumps (t = 2.805, p < 0.02). The results from this study imply that, despite increased gastrocnemius muscle activity, static stretching of the gastrocnemius muscles had a negative effect on maximal jumping performance. The practical importance concerns coaches and athletes, who may want to consider the potential adverse effects of performing static stretching of the gastrocnemius muscles only before a jumping event, as jump height may be negatively affected. Future research is required to identify the mechanisms that affect vertical jump performance.  相似文献   

15.
Jumping is an important performance component of many sporting activities. A number of training modalities have been used to enhance jumping performance including plyometrics. The positive effects of plyometric training on jumping performance are a function of the stretch-shortening cycle phenomenon. However, there has been little research on the effects of the surface on jumping performance. This study examined the effects of performing 2 different plyometric exercises, depth jump (DJ) and counter movement jump (CMJ), on noncompliant (ground) and compliant (mini-trampoline) surfaces. Male participants (N = 20; age = 21.8 +/- 3.8 years; height = 184.6 +/- 7.6 cm; mass = 83.6 +/- 8.2 kg) randomly performed 10 CMJ and 10 DJ on compliant and noncompliant surfaces. Kinematic data were determined via 2-dimensional high-speed video. There were significant (p < 0.05) differences in DJ and CMJ joint and segment range of movement for ankle, knee, hip and trunk, indicating less crouch when the participants performed plyometric exercises on the compliant surface.  相似文献   

16.
This study aimed to investigate the kinematic and kinetic changes when resistance is applied in horizontal and vertical directions, produced by using different percentages of body weight, caused by jumping movements during a dynamic warm-up. The group of subjects consisted of 35 voluntary male athletes (19 basketball and 16 volleyball players; age: 23.4 ± 1.4 years, training experience: 9.6 ± 2.7 years; height: 177.2 ± 5.7 cm, body weight: 69.9 ± 6.9 kg) studying Physical Education, who had a jump training background and who were training for 2 hours, on 4 days in a week. A dynamic warm-up protocol containing seven specific resistance movements with specific resistance corresponding to different percentages of body weight (2%, 4%, 6%, 8%, 10%) was applied randomly on non consecutive days. Effects of different warm-up protocols were assessed by pre-/post- exercise changes in jump height in the countermovement jump (CMJ) and the squat jump (SJ) measured using a force platform and changes in hip and knee joint angles at the end of the eccentric phase measured using a video camera. A significant increase in jump height was observed in the dynamic resistance warm-up conducted with different percentages of body weight (p < 0.05). On the other hand, no significant difference in different percentages of body weight states was observed (p > 0.05). In jump movements before and after the warm-up, while no significant difference between the vertical ground reaction forces applied by athletes was observed (p > 0.05), in some cases of resistance, a significant reduction was observed in hip and knee joint angles (p < 0.05). The dynamic resistance warm-up method was found to cause changes in the kinematics of jumping movements, as well as an increase in jump height values. As a result, dynamic warm-up exercises could be applicable in cases of resistance corresponding to 6-10% of body weight applied in horizontal and vertical directions in order to increase the jump performance acutely.  相似文献   

17.
The purpose of this study was to investigate the correlations between biomechanical outcome measures and weightlifting performance. Joint kinematics and kinetics of the hip, knee, and ankle were calculated while 10 subjects performed a clean at 85% of 1 repetition maximum (1RM). Kinematic and kinetic time-series patterns were extracted with principal components analysis. Discrete scores for each time-series pattern were calculated and used to determine how each pattern was related to body mass-normalized 1RM. Two hip kinematic and 2 knee kinetic patterns were significantly correlated with relative 1RM. The kinematic patterns captured hip and trunk motions during the first pull and hip joint motion during the movement transition between the first and second pulls. The first kinetic pattern captured a peak in the knee extension moment during the second pull. The second kinetic pattern captured a spatiotemporal shift in the timing and amplitude of the peak knee extension moment. The kinematic results suggest that greater lift mass was associated with steady trunk position during the first pull and less hip extension motion during the second-knee bend transition. Further, the kinetic results suggest that greater lift mass was associated with a smaller knee extensor moments during the first pull, but greater knee extension moments during the second pull, and an earlier temporal transition between knee flexion-extension moments at the beginning of the second pull. Collectively, these results highlight the importance of controlled trunk and hip motions during the first pull and rapid employment of the knee extensor muscles during the second pull in relation to weightlifting performance.  相似文献   

18.
Although it is known that an arm swing can enhance the performance in vertical jumping, the mechanisms through which this enhancement occurs are not yet clearly described. The purpose of this study was to examine how arm swing affects the lower extremity torque, power and work in vertical jumping and to gain an insight into the mechanisms that enable the arm swing to increase jump height. Five subjects maximally performed two types of vertical squat jumps with (SJA) and without (SJ) an arm swing from a force platform. All performances were videotaped with a high-speed video camera (200 Hz). The jump heights, joint torques, power and work were calculated by combining kinematic and kinetic data. It was confirmed that arm swing enhanced the jump height significantly (p<0.01). The work by the hip and by the ankle was significantly augmented by arm swing (p<0.05 and p<0.01, respectively). However, the work by the knee was significantly smaller in SJA (p<0.05). The total work by the three lower extremity joints (ankle, knee and hip) was significantly larger in SJA (p<0.05). The increase of the lower extremity work by the arm swing (31.4 J) was about twice as large as the work done by the shoulder and elbow in SJA (16.3 J). It was concluded that the increment of jump height resulted mainly from the increase of the lower extremity work, which is considered to have been brought about by the additional load on the lower extremity due to the arm swing.  相似文献   

19.
To evaluate lower-limb explosive strength with respect to lifetime athletic activity, we measured vertical jumping height on a contact mat in former male runners (n = 28). soccer players (n = 31), weightlifters (n = 29) and shooters (n = 29) (age range 45 68 years). There were no statistically significant age-adjusted sport-group differences in jumping height, but differences by sport were evident among the subgroup of athletes without hip or knee osteoarthritis (n = 65) (P < 0.05). Thus, sports that increased jumping height also predisposed to lower-limb osteoarthritis. After adjustment for age and sport, the subjects without osteoarthritis jumped higher than those with osteoarthritis (n = 33) (P < 0.01). In a multiple linear regression analysis, age, reported hip and knee disability, and knee pain reduced jumping height. Hours spent in team-training during the past 12 months and the hours spent during their lifetime in power training were associated with improved vertical jumping height and together explained 41% of the difference among the subjects. The ability to jump even among athletes with hip or knee osteoarthritis would suggest that former elite athletes possess advanced lower limb muscle function.  相似文献   

20.
The purpose of this study was to examine the co-activation of the rectus femoris (RF) and biceps femoris (BF) during drop jumping exercises using the co-contraction index (CI). Ten trained male long jumpers performed drop jumps from 20 cm (DJ20), 40 cm (DJ40) and 60 cm (DJ60) on a force platform. Surface electromyographic (EMG) activity of the RF and BF, vertical ground reaction force data and knee joint angular displacement and angular velocities were recorded and normalized as percentage of maximum isometric values. The CI was calculated for the pre-contact, braking and propulsive phases of the jump using four methods: (1) by dividing the double integrated antagonistic activity by the sum of the RF and BF EMG; (2) by finding the amount of overlap between the linear envelopes of the agonist and antagonist muscles and dividing by the number of data points; (3) by calculating the co-contraction at any instant point of time; and (4) by dividing the BF integrated activity by the total registered muscle activity around the knee. The CI ranged from 13.03+/-9.33 to 70.80+/-25.81%, depending on the estimation method used. A two-way analysis of variance (ANOVA) indicated that the CI was not affected by drop jumping height (p>0.05) while it was significantly higher (p<0.05) in the pre-contact phase compared to the braking and propulsion phases. The CI can be useful when examining muscle co-activation using EMG measurements in drop jumps. However, the conclusions on muscle co-activation depend on the equation used to estimate CI and therefore a commonly accepted method is necessary.  相似文献   

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