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1.
Our purpose was to compare joint loads between habitual rearfoot (hRF) and habitual mid/forefoot strikers (hFF), rearfoot (RFS) and mid/forefoot strike (FFS) patterns, and shorter stride lengths (SLs). Thirty-eight hRF and hFF ran at their normal SL, 5% and 10% shorter, as well as with the opposite foot strike. Three-dimensional ankle, knee, patellofemoral (PF) and hip contact forces were calculated. Nearly all contact forces decreased with a shorter SL (1.2–14.9% relative to preferred SL). In general, hRF had higher PF (hRF-RFS: 10.8 ± 1.4, hFF-FFS: 9.9 ± 2.0 BWs) and hip loads (axial hRF-RFS: ?9.9 ± 0.9, hFF-FFS: ?9.6 ± 1.0 BWs) than hFF. Many loads were similar between foot strike styles for the two groups, including axial and lateral hip, PF, posterior knee and shear ankle contact forces. Lateral knee and posterior hip contact forces were greater for RFS, and axial ankle and knee contact forces were greater for FFS. The tibia may be under greater loading with a FFS because of these greater axial forces. Summarising, a particular foot strike style does not universally decrease joint contact forces. However, shortening one’s SL 10% decreased nearly all lower extremity contact forces, so it may hold potential to decrease overuse injuries associated with excessive joint loads.  相似文献   

2.
ABSTRACT

This study aimed to explore the plantar loading variables between habitual rearfoot strike (RFS) and non-rearfoot strike (NRFS) during running. 78 healthy males participated in this study (41 RFS, 37 NRFS). In-shoe pressure sensors were used to measure plantar loading while the participants were running on a 15 m indoor runway with their preferred foot strike pattern (FSP) at 12.0 ± 5% km/h. Results indicate that force and pressure parameters were much higher in the rearfoot and midfoot regions during RFS running and relatively greater in forefoot region during NRFS running. However, compared with NRFS running, the contact area, maximum force and force-time-integrals during RFS running on total foot were 21.44% (P < 0.001, ES = 2.29), 13.99% (P = 0.006, ES = 0.64) and 21.27% (P < 0.001, ES = 0.85) higher, respectively. Total foot peak pressure and pressure-time-integral between two FSPs were similar. Higher loads in the rearfoot region may transmit to the knee joint and result in patellofemoral joint injuries. NRFS runners’ higher loads in forefoot seem to be ralated to metatarsal stress fractures and compensatory damage to the Achilles tendon. Therefore, runners should choose proper FSPs according to their unique physical conditions.  相似文献   

3.
BackgroundInvestigations of running gait among barefoot and populations have revealed a diversity of foot strike behaviors, with some preferentially employing a rearfoot strike (RFS) as the foot touches down while others employ a midfoot strike (MFS) or forefoot strike (FFS). Here, we report foot strike behavior and joint angles among traditional Hadza hunter-gatherers living in Northern Tanzania.MethodsHadza adults (n = 26) and juveniles (n = 14) ran at a range of speeds (adults: mean 3.4 ± 0.7 m/s, juveniles: mean 3.2 ± 0.5 m/s) over an outdoor trackway while being recorded via high-speed digital video. Foot strike type (RFS, MFS, or FFS) and hind limb segment angles at foot strike were recorded.ResultsHadza men preferentially employed MFS (86.7% of men), while Hadza women and juveniles preferentially employed RFS (90.9% and 85.7% of women and juveniles, respectively). No FFS was recorded. Speed, the presence of footwear (sandals vs. barefoot), and trial duration had no effect on foot strike type.ConclusionUnlike other habitually barefoot populations which prefer FFS while running, Hadza men preferred MFS, and Hadza women and juveniles preferred RFS. Sex and age differences in foot strike behavior among Hadza adults may reflect differences in running experience, with men learning to prefer MFS as they accumulate more running experience.  相似文献   

4.
The aim of this study was to determine if selected kinematic measures (foot strike index [SI], knee contact angle and overstride angle) were different between aquatic treadmill (ATM) and land treadmill (LTM) running, and to determine if these measures were altered during LTM running as a result of 6 weeks of ATM training. Acute effects were tested using 15 competitive distance runners who completed 1 session of running on each treadmill type at 5 different running speeds. Subsequently, three recreational runners completed 6 weeks of ATM training following a single-subject baseline, intervention and withdrawal experiment. Kinematic measures were quantified from digitisation of video. Regardless of speed, SI values during ATM running (61.3 ± 17%) were significantly greater (P = 0.002) than LTM running (42.7 ± 23%). Training on the ATM did not change (pre/post) the SI (26 ± 3.2/27 ± 3.1), knee contact angle (165 ± 0.3/164 ± 0.8) or overstride angle (89 ± 0.4/89 ± 0.1) during LTM running. Although SI values were different between acute ATM and LTM running, 6 weeks of ATM training did not appear to alter LTM running kinematics as evidenced by no change in kinematic values from baseline to post intervention assessments.  相似文献   

5.
The purpose of this study was to investigate the interaction of foot strike and common speeds on sagittal plane ankle and knee joint kinetics in competitive rear foot strike (RFS) runners when running with a RFS pattern and an imposed forefoot strike (FFS) pattern. Sixteen competitive habitual male RFS runners ran at two different speeds (i.e. 8 and 6?min?mile?1) using their habitual RFS and an imposed FFS pattern. A repeated measures analysis of variance was used to assess a potential interaction between strike pattern and speed for selected ground reaction force (GRF) variables and, sagittal plane ankle and knee kinematic and kinetic variables. No foot strike and speed interaction was observed for any of the kinetic variables. Habitual RFS yielded a greater loading rate of the vertical GRF, peak ankle dorsiflexor moment, peak knee extensor moment, peak knee eccentric extensor power, peak dorsiflexion and sagittal plane knee range of motion compared to imposed FFS. Imposed FFS yielded greater maximum vertical GRF, peak ankle plantarflexor moment, peak ankle eccentric plantarflexor power and sagittal plane ankle ROM compared to habitual RFS. Consistent with previous literature, imposed FFS in habitual RFS reduces eccentric knee extensor and ankle dorsiflexor involvement but produce greater eccentric ankle plantarflexor action compared to RFS. These acute differences between strike patterns were independent of running speeds equivalent to typical easy and hard training runs in competitive male runners. Current findings along with previous literature suggest differences in lower extremity kinetics between habitual RFS and imposed FFS running are consistent among a variety of runner populations.  相似文献   

6.
Ankle taping is commonly used to prevent ankle sprains. However, kinematic assessments investigating the biomechanical effects of ankle taping have provided inconclusive results. This study aimed to determine the effect of ankle taping on the external ankle joint moments during a drop landing on a tilted surface at 25°. Twenty-five participants performed landings on a tilted force platform that caused ankle inversion with and without ankle taping. Landing kinematics were captured using a motion capture system. External ankle inversion moment, the angular impulse due to the medio-lateral and vertical components of ground reaction force (GRF) and their moment arm lengths about the ankle joint were analysed. The foot plantar inclination relative to the ground was assessed. In the taping condition, the foot plantar inclination and ankle inversion angular impulse were reduced significantly compared to that of the control. The only component of the external inversion moment to change significantly in the taped condition was a shortened medio-lateral GRF moment arm length. It can be assumed that the ankle taping altered the foot plantar inclination relative to the ground, thereby shortening the moment arm of medio-lateral GRF that resulted in the reduced ankle inversion angular impulse.  相似文献   

7.
Purpose. We aimed to determine the effect of speed-induced changes in foot contact patterns on the vertical instantaneous loading rate (VILR). We hypothesized that transition runners, i.e. runners that shift towards a mid- (MF) or forefoot contact pattern (FF) when running speed increases, show smaller increases in VILR than non-transition runners, i.e. runners that remain with a rearfoot contact pattern (RF).

Methods. Fifty-two male and female runners ran overground at 3.2, 4.1, 5.1 and 6.2?m?s?1. Ground reaction forces, lower limb sagittal plane knee and ankle kinematics and plantar pressures were recorded. Multi-level linear regression models were used to assess differences between transition and non-transition runners.

Results. Non-transition runners experienced larger speed-induced increases in VILR (48.6?±?2.6?BW?s?1 per m?s?1) than transition runners (–1.4?±?7.6?BW?s?1 per m?s?1). Transition runners showed higher VILRs and a more flat foot touch down at the same pre-transition speed than non-transition runners.

Conclusion. When running speed increases, some runners transition towards more anterior foot contact patterns. This reduces or even eliminates the speed-induced increase in VILR. This result is especially the case for those RF runners who already have relatively high VILRs and flat foot positioning at slower running speeds.  相似文献   

8.
研究背景:现有研究文献尚无有关在着地过程中不同表面倾斜度和踝关节护具效应的运动学、动力学和地面反作用力的综合数据。通过对比25°斜面和平面的着地以及使用和不使用踝关节护具情况下来检测踝关节的生物力学特性。研究方法: 11名健康受试者[年龄:(24.6±3.5)岁,身高:(24.6±0.10)m,质量:(65.6±14.9)kg)参与本次研究。受试者在4个动态运动条件下各进行5五次实验:从0.45米高处垂直下落至25°的斜面(IS)或平面(FS)上,使用或不使用半刚性踝关节护具,同时采集三维运动学和测力台地面反作用力数据。利用2×2(表面X踝关节护具)的重复测量方差分析来评估选定的变量。研究结果:与平面着地相比,斜面着地造成较小的垂直和内侧地面反作用力峰值。研究还发现踝关节背曲运动范围、着地角度和背曲速度、最大外翻与跖曲角速度提高,但产生了更大内翻角度和运动范围、着地内翻速度和最大跖曲力矩。踝关节护具在斜面着地时减少了达到地面反作用力第二垂直峰值的时间、着地角度、背曲速度、最大外翻和跖曲速度,但增加了跖曲力矩的最大值。研究结论:斜面增加踝关节额状面的运动范围和踝关节负荷。但是,就斜面着地而言,踝关节护具对踝关节额状面的运动范围和踝关节负荷的影响是相当有限的。  相似文献   

9.
ABSTRACT

Ankle sprains are the most common injury in regular badminton players and usually occur at the end of a match or training. The purpose of the present study was to examine the influence of fatigue produced by badminton practice on the lower limb biomechanics of badminton players. It was hypothesized that fatigue induces ankle kinematic and lower leg muscle activity changes which may increase the risk of ankle sprain. Ankle kinematics, ankle kinetics and muscles activities of 17 regular badminton players were recorded during lateral jumps before and after an intense badminton practice session. Post-fatigue, ankle inversion at foot strike and peak ankle inversion increased (+2.6°, p = 0.003 and +2.5°, p = 0.005, respectively). EMG pre-activation within 100 ms before foot landing significantly decreased after fatigue for soleus (?23.4%, p = 0.031), gastrocnemius lateralis (?12.2%, p = 0.035), gastrocnemius medialis (?23.3%, p = 0.047) and peroneus brevis (?17.4%, p = 0.036). These results demonstrate impaired biomechanics of badminton players when fatigue increases, which may cause a greater risk of experiencing an ankle sprain injury.  相似文献   

10.
The purpose of this study was to determine the foot strike patterns (FSP), rearfoot position at initial contact (RPic, i.e., No INV/EVE) and foot rotation in children in relation to age. A total of 932 children aged 3 to 16 years participated in this study. A sagittal and frontal-plane video was recorded using a high-speed camcorder to analyse these variables. There is a significant increase (p < 0.001) of rearfoot strike patterns (RFS) prevalence in relation to age; e.g. preschool children (3–6 years old) displayed an RFS prevalence 46.65% and the adolescent population(15–16 years old) an RFS prevalence 92.20%. The total RFS prevalence in all samples was 69.25%. There was a significant reduction (p < 0.001) of prevalence of RPic in relation to age groups; preschool children displayed a prevalence of RPic 60.37% and the adolescent population 10%. There was a significant reduction (p < 0.001) of prevalence of no foot rotation in relation to age groups; preschool children displayed a prevalence of no foot rotation 48.95% and the adolescent population 13.55%. In conclusion, FSP in children are influenced by age. It is noteworthy that the RFS prevalence of children is lower in comparison to the adult population.  相似文献   

11.
BackgroundThis study presents a kinematic analysis of an acute lateral ankle sprain incurred during a televised badminton match. The kinematics of this injury were compared to those of 19 previously reported cases in the published literature.MethodsFour camera views of an acute lateral ankle sprain incurred during a televised badminton match were synchronized and rendered in 3-dimensional animation software. A badminton court with known dimensions was built in a virtual environment, and a skeletal model scaled to the injured athlete's height was used for skeletal matching. The ankle joint angle and angular velocity profiles of this acute injury were compared to the summarized findings from 19 previously reported cases in the published literature.ResultsAt foot strike, the ankle joint was 2° everted, 33° plantarflexed, and 18° internally rotated. Maximum inversion of 114° and internal rotation of 69° was achieved at 0.24 s and 0.20 s after foot strike, respectively. After the foot strike, the ankle joint moved from an initial position of plantarflexion to dorsiflexion—from 33° plantarflexion to 53° dorsiflexion (range = 86°). Maximum inversion, dorsiflexion, and internal rotation angular velocity were 1262°/s, 961°/s, and 677°/s, respectively, at 0.12 s after foot strike.ConclusionA forefoot landing posture with a plantarflexed and internally rotated ankle joint configuration could incite an acute lateral ankle sprain injury in badminton. Prevention of lateral ankle sprains in badminton should focus on the control and stability of the ankle joint angle during forefoot landings, especially when the athletes perform a combined lateral and backward step.  相似文献   

12.
This study presents the kinematics and plantar pressure characteristics of eight elite national-level badminton athletes and eight recreational college-level badminton players while performing a right-forward lunge movement in a laboratory-simulated badminton court. The hypothesis was that recreational players would be significantly different from elite players in kinematics and plantar pressure measures. Vicon® motion capture and Novel® insole plantar pressure measurement were simultaneously taken to record the lower extremity kinematics and foot loading during stance. Recreational players showed significantly higher peak pressure in the lateral forefoot (P = 0.002) and force time integral in the lateral forefoot (P = 0.013) and other toes (P = 0.005). Elite athletes showed higher peak pressure in the medial forefoot (P = 0.003), hallux (P = 0.037) and force time integral in the medial forefoot (P = 0.009). The difference in landing techniques for the lunge step between elite athletes and recreational players was observed with peak ankle eversion (?38.2°±2.4° for athletes and ?11.1°±3.9° for players, P = 0.015); smaller knee range of motion in the coronal and transverse planes, with differences in peak knee adduction (28.9°±6.8° for athletes and 15.7°±6.2° for players, P = 0.031); peak knee internal rotation (20.3°±1.3° for athletes and 11.8°±3.2° for players, P = 0.029) and peak hip flexion (77.3°±4.1° for athletes and 91.3°±9.3° for players, P = 0.037).  相似文献   

13.
The effect of textured insoles on kinetics and kinematics of overground running was assessed. 16 male injury-free-recreational runners attended a single visit (age 23?±?5 yrs; stature 1.78?±?0.06 m; mass 72.6?±?9.2?kg). Overground 15-m runs were completed in flat, canvas plimsolls both with and without textured insoles at self-selected velocity on an indoor track in an order that was balanced among participants. Average vertical loading rate and peak vertical force (Fpeak) were captured by force platforms. Video footage was digitised for sagittal plane hip, knee and ankle angles at foot strike and mid stance. Velocity, stride rate and length and contact and flight time were determined. Subjectively rated plantar sensation was recorded by visual scale. 95% confidence intervals estimated mean differences. Smallest worthwhile change in loading rate was defined as standardised reduction of 0.54 from a previous comparison of injured versus non-injured runners. Loading rate decreased (?25 to ?9.3?BW?s?1; 60% likely beneficial reduction) and plantar sensation was increased (46–58?mm) with the insole. Fpeak (?0.1 to 0.14?BW) and velocity (?0.02 to 0.06?m?s?1) were similar. Stride length, flight and contact time were lower (?0.13 to ?0.01 m; ?0.02 to?0.01?s; ?0.016 to ?0.006?s) and stride rate was higher (0.01–0.07 steps?s?1) with insoles. Textured insoles elicited an acute, meaningful decrease in vertical loading rate in short distance, overground running and were associated with subjectively increased plantar sensation. Reduced vertical loading rate could be explained by altered stride characteristics.  相似文献   

14.
This study investigated the three-dimensional (3-D) pedaling kinematics using a noncircular chainring system and a conventional system. Five cyclists pedaled at their preferred cadence at a workload of 300 W using two crank systems. Flexion/extension of the hip, knee and ankle as well as shank rotation, foot adduction/abduction, and pedal angle were measured. Joint range of motion (ROM) and angular displacements were compared between the systems. Sagittal plane ROM was significantly greater (P < 0.05) at the hip (noncircular system = 39 ± 3°; conventional system = 34 ± 4°) the knee (noncircular system = 69 ± 4°; conventional system = 57 ± 10°), and ankle (noncircular system = 21 ± 2°; conventional system = 19 ± 4°) resulting in greater pedal ROM (noncircular system = 43 ± 3°; conventional system = 37 ± 5°) while using the noncircular system. Shank rotation ROM was significantly lower (P < 0.05) while using the noncircular chainring (noncircular system = 10 ± 1°; conventional system = 14 ± 1°). These results support a significant effect of the noncircular chainring system on pedaling kinematics during submaximal exercise.  相似文献   

15.
BackgroundForefoot strike (FFS) and rearfoot strike (RFS) runners differ in their kinematics, force loading rates, and joint loading patterns, but the timing of their muscle activation is less clear.MethodsForty recreational and highly trained runners ran at four speeds barefoot and shod on a motorized treadmill. “Barefoot” runners wore thin, five-toed socks and shod runners wore neutral running shoes. Subjects were instructed to run comfortably at each speed with no instructions about foot strike patterns.ResultsEleven runners landed with an FFS when barefoot and shod and eleven runners landed with an RFS when barefoot and shod. The 18 remaining runners shifted from an FFS when barefoot to an RFS when shod (shifters). Shod shifters ran with a lower stride frequency and greater stride length than all other runners. All FFS runners landed with more plantarflexed ankles and more vertical lower legs at the beginning of stance compared to RFS runners. FFS runners activated their plantarflexor muscles 11% earlier and 10% longer than RFS runners.ConclusionThis earlier and longer relative activation of the plantarflexors likely enhances the capacity for the passive structures of the foot and ankle to store elastic energy, and may also enhance the performance of the active muscle by increasing the storage of elastic strain energy in the cross-bridges and activated titin.  相似文献   

16.
The purpose of this study was to investigate the kinematic and metabolic effects of running on an irregular surface. We also examined how altering the frontal plane foot angle (inversion/eversion) at contact using real-time visual feedback would affect these other variables. Sixteen participants completed three running bouts lasting 5–7 minutes each on an irregular surface (IS) treadmill, a traditional smooth surface (SS) treadmill, and on SS while receiving visual feedback of the frontal plane foot angle at contact (SSF) with a goal of matching IS foot angle on SS. Frontal plane foot angle increased 40% from IS to SS (IS: 8.4 ± 4.09°, SS: 11.8 ± 4.52°, < 0.0001, ES 1.40). Knee flexion angle at contact decreased 33% from IS to SS (IS: 9.2 ± 4.88°, SS: 6.2 ± 5.03°, < 0.0001, ES 1.30). Rate of oxygen consumption decreased by 10% from IS to SS (IS: 37.9 ± 5.68 ml·kg?1·min?1, SS: 34.1 ± 5.07 ml·kg?1·min?1, P < 0.0001, ES 3.05). PSD of leg accelerations decreased by 38% (IS: 0.17 ± 0.07 g2/Hz, SS: 0.106 ± 0.05 g2/Hz, < 0.000, ES 1.69). Frontal plane foot angle decreased by 14% from SS to SSF (SS: 11.8 ± 4.52°, SSF: 10.1 ± 4.42°, P = 0.027. ES 0.62) but did not result in significant changes in any other variables. There were no significant differences in shock attenuation between any conditions (IS: ?9.8 ± 2.26 dB, SS: ?9.5 ± 3.12 dB, SSF: ?9.9 ± 2.62 dB, P = 0.671). Running with greater eversion on the irregular surface may be an attempt by runners to reduce the perceived potential of an inversion ankle sprain. As a partial compensation for the decreased foot angle, runners increased knee flexion. This maintained shock attenuation but increased the rate of oxygen consumption. Altering the foot angle at contact using feedback on the SS caused the knee angle at contact to increase, but did not change shock attenuation or metabolic cost.  相似文献   

17.
Despite the growing interest in minimalist shoes, no studies have compared the efficacy of different types of minimalist shoe models in reproducing barefoot running patterns and in eliciting biomechanical changes that make them differ from standard cushioned running shoes. The aim of this study was to investigate the acute effects of different footwear models, marketed as “minimalist” by their manufacturer, on running biomechanics. Six running shoes marketed as barefoot/minimalist models, a standard cushioned shoe and the barefoot condition were tested. Foot–/shoe–ground pressure and three-dimensional lower limb kinematics were measured in experienced rearfoot strike runners while they were running at 3.33 m · s?1 on an instrumented treadmill. Physical and mechanical characteristics of shoes (mass, heel and forefoot sole thickness, shock absorption and flexibility) were measured with laboratory tests. There were significant changes in foot strike pattern (described by the strike index and foot contact angle) and spatio-temporal stride characteristics, whereas only some among the other selected kinematic parameters (i.e. knee angles and hip vertical displacement) changed accordingly. Different types of minimalist footwear models induced different changes. It appears that minimalist footwear with lower heel heights and minimal shock absorption is more effective in replicating barefoot running.  相似文献   

18.
Abstract

High ground reaction forces during the front foot contact phase of the bowling action are believed to be a major contributor to the high prevalence of lumbar stress fractures in fast bowlers. This study aimed to investigate the influence of front leg technique on peak ground reaction forces during the delivery stride. Three-dimensional kinematic data and ground reaction forces during the front foot contact phase were captured for 20 elite male fast bowlers. Eight kinematic parameters were determined for each performance, describing run-up speed and front leg technique, in addition to peak force and time to peak force in the vertical and horizontal directions. There were substantial variations between bowlers in both peak forces (vertical 6.7 ± 1.4 body weights; horizontal (braking) 4.5 ± 0.8 body weights) and times to peak force (vertical 0.03 ± 0.01 s; horizontal 0.03 ± 0.01 s). These differences were found to be linked to the orientation of the front leg at the instant of front foot contact. In particular, a larger plant angle and a heel strike technique were associated with lower peak forces and longer times to peak force during the front foot contact phase, which may help reduce the likelihood of lower back injuries.  相似文献   

19.
Abstract

The objective of this study was to compare the three-dimensional lower extremity running kinematics of young adult runners and elderly runners. Seventeen elderly adults (age 67–73 years) and 17 young adults (age 26–36 years) ran at 3.1 m · s?1 on a treadmill while the movements of the lower extremity during the stance phase were recorded at 120 Hz using three-dimensional video. The three-dimensional kinematics of the lower limb segments and of the ankle and knee joints were determined, and selected variables were calculated to describe the movement. Our results suggest that elderly runners have a different movement pattern of the lower extremity from that of young adults during the stance phase of running. Compared with the young adults, the elderly runners had a substantial decrease in stride length (1.97 vs. 2.23 m; P = 0.01), an increase in stride frequency (1.58 vs. 1.37 Hz; P = 0.002), less knee flexion/extension range of motion (26 vs. 33°; P = 0.002), less tibial internal/external rotation range of motion (9 vs. 12°; P < 0.001), larger external rotation angle of the foot segment (toe-out angle) at the heel strike (?5.8 vs. ?1.0°; P = 0.009), and greater asynchronies between the ankle and knee movements during running. These results may help to explain why elderly individuals could be more susceptible to running-related injuries.  相似文献   

20.
Abstract

The mechanics of cutting movements have been investigated extensively, but few studies have considered the rapid deceleration phase prior to turning which has been linked to muscle damage. This study used accelerometry to examine the influence of turning intensity on the last three steps of a severe turn.

Ten soccer players performed 135° “V” cuts at five different intensities. Resultant decelerations were recorded from a trunk-mounted tri-axial accelerometer. Lower limb kinematics and ground reaction forces (GRF) from the pivot foot-ground contact (FGC) were also monitored.

Average peak trunk decelerations were larger at the two preceding steps (4.37 ± 0.12 g and 4.58 ± 0.11 g) compared to the PIVOT step (4.10 ± 0.09 g). Larger peak joint flexion angular velocities were observed at PRE step (ankle: 367 ± 192 deg.s?1; knee 493 ± 252 deg.s?1) compared to PIVOT step (ankle 255 ± 183 deg.s?1; knee 377 ± 229 deg.s?1). Turn intensity did not influence peak GRF at PIVOT step.

This study highlights the importance of steps prior to turning and their high-frequency loading characteristics. It is suggested that investigations of lower limb loading during turning should include this deceleration phase and not focus solely on pivot FGC.  相似文献   

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