首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
The role of intersegmental dynamics during rapid limb oscillations   总被引:4,自引:0,他引:4  
The interactive dynamic effects of muscular, inertial and gravitational moments on rapid, multi-segmented limb oscillations were studied. Using three-segment, rigid-body equations of motion, hip, knee and ankle intersegmental dynamics were calculated for the steady-state cycles of the paw-shake response in adult spinal cats. Hindlimb trajectories were filmed to obtain segmental kinematics, and myopotentials of flexors and extensors at each of the three joints were recorded synchronously with the ciné film. The segmental oscillations that emerged during the paw-shake response were a consequence of an interplay between active and passive musculotendinous forces, inertial forces, and gravity. During steady-state oscillations, the amplitudes of joint excursions, peak angular velocities, and peak angular accelerations increased monotonically and significantly in magnitude from the proximal joint (hip) to the most distal joint (ankle). In contrast to these kinematic relationships, the maximal values of net moments at the hip and knee were equal in magnitude, but of significantly lower magnitude than the large net moment at the ankle joint. At both the ankle and the knee, the flexor and extensor muscle moments were equal, but at the hip the magnitude of the peak flexor muscle moment was significantly greater than the extensor muscle moment. Muscle moments at the hip not only acted to counterbalance accelerations of the more distal segments, but also acted to maintain the postural orientation of the hindlimb. Large muscle moments at the knee functioned to counterbalance the large inertial moments generated by the large angular accelerations of the paw. At the ankle, the muscle moments dominated the generation of the paw accelerations. At the ankle and the knee, muscle moments controlled limb dynamics by slowing and reversing joint motions, and the active muscle forces contributing to ankle and knee moments were derived from lengthening of active musculotendinous units. In contrast to the more distal joints, the active muscles crossing the hip predominantly shortened as a result of the interplay among inertial forces and gravitational moments. The muscle function and kinetic data explain key features of the complex interactions that occur between central control mechanisms and multi-segmented, oscillating limb segments during the paw-shake response.  相似文献   

2.
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   

3.
Joint moments are of interest because they bear some relation to muscular effort and hence rider performance. The general objective of this study is to explore the relation between joint moments and pedalling rate (i.e. cadence). Joint moments are computed by modelling the leg-bicycle system as a five-bar linkage constrained to plane motion. Using dynamometer pedal force data and potentiometer crank and pedal position data, system equations are solved on a computer to produce moments at the ankle, knee and hip joints. Cadence and pedal forces are varied inversely to maintain constant power. Results indicate that average joint moments vary considerably with changes in cadence. Both hip and knee joints show an average moment which is minimum near 105 rotations min-1 for cruising cycling. It appears that an optimum rotations min-1 can be determined from a mechanical approach for any given power level and bicycle-rider geometry.  相似文献   

4.
Soldiers regularly transport loads weighing >20 kg at slow speeds for long durations. These tasks elicit high energetic costs through increased positive work generated by knee and ankle muscles, which may increase risk of muscular fatigue and decrease combat readiness. This study aimed to determine how modifying where load is borne changes lower-limb joint mechanical work production, and if load magnitude and/or walking speed also affect work production. Twenty Australian soldiers participated, donning a total of 12 body armor variations: six different body armor systems (one standard-issue, two commercially available [cARM1-2], and three prototypes [pARM1-3]), each worn with two different load magnitudes (15 and 30 kg). For each armor variation, participants completed treadmill walking at two speeds (1.51 and 1.83 m/s). Three-dimensional motion capture and force plate data were acquired and used to estimate joint angles and moments from inverse kinematics and dynamics, respectively. Subsequently, hip, knee, and ankle joint work and power were computed and compared between armor types and walking speeds. Positive joint work over the stance phase significantly increased with walking speed and carried load, accompanied by 2.3–2.6% shifts in total positive work production from the ankle to the hip (p < 0.05). Compared to using cARM1 with 15 kg carried load, carrying 30 kg resulted in significantly greater hip contribution to total lower-limb positive work, while knee and ankle work decreased. Substantial increases in hip joint contributions to total lower-limb positive work that occur with increases in walking speed and load magnitude highlight the importance of hip musculature to load carriage walking.  相似文献   

5.
Mechanical analysis of the landing phase in heel-toe running.   总被引:3,自引:0,他引:3  
Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.  相似文献   

6.
Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem.  相似文献   

7.
Eight experienced male cyclists (C), eight well-trained male runners (R), and eight less-trained male noncyclists (LT) were tested under multiple cadence and power output conditions to determine: (1) if the cadence at which lower extremity net joint moments are minimized (cost function cadence) was associated with preferred pedaling cadence (PC), (2) if the cost function cadence increased with increases in power output, and (3) if the association is generalizable across groups differing in cycling experience and aerobic power. Net joint moments at the hip, knee, and ankle were computed from video records and pedal reaction force data using 2-D inverse dynamics. The sum of the average absolute hip, knee, and ankle joint moments defined a cost function at each power output and cadence and provided the basis for prediction of the cadence which minimized net joint moments for each subject at each power output. The cost function cadence was not statistically different from the PC at each power output in all groups. As power output increased, however, the cost function cadence increased for all three subject groups (86 rpm at 100 W, 93 rpm at 150 W, 98 rpm at 200 W, and 96 rpm at 250 W). PC showed little change (R) or a modest decline (C, LT) with increasing power output. Based upon the similarity in the mean data but different trends in the cost function cadence and PC in response to changes in power output as well as the lack of significant correlations between these two variables, it was concluded that minimiking net joint moments is a factor modestly associated with preferred cadence selection.  相似文献   

8.
Saddle position affects mechanical variables during submaximal cycling, but little is known about its effect on mechanical performance during maximal cycling. Therefore, this study relates saddle position to experimentally obtained maximal power output and theoretically calculated moment generating capacity of hip, knee and ankle muscles during isokinetic cycling. Ten subjects performed maximal cycling efforts (5 s at 100 rpm) at different saddle positions varying ± 2 cm around the in literature suggested optimal saddle position (109% of inner leg length), during which crank torque and maximal power output were determined. In a subgroup of 5 subjects, lower limb kinematics were additionally recorded during submaximal cycling at the different saddle positions. A decrease in maximal power output was found for lower saddle positions. Recorded changes in knee kinematics resulted in a decrease in moment generating capacity of biceps femoris, rectus femoris and vastus intermedius at the knee. No differences in muscle moment generating capacity were found at hip and ankle. Based on these results we conclude that lower saddle positions are less optimal to generate maximal power output, as it mainly affects knee joint kinematics, compromising mechanical performance of major muscle groups acting at the knee.  相似文献   

9.
The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.  相似文献   

10.
Robotic lower limb exoskeletons hold significant potential for gait assistance and rehabilitation; however, we have a limited understanding of how people adapt to walking with robotic devices. The purpose of this study was to test the hypothesis that people reduce net muscle moments about their joints when robotic assistance is provided. This reduction in muscle moment results in a total joint moment (muscle plus exoskeleton) that is the same as the moment without the robotic assistance despite potential differences in joint angles. To test this hypothesis, eight healthy subjects trained with the robotic hip exoskeleton while walking on a force-measuring treadmill. The exoskeleton provided hip flexion assistance from approximately 33% to 53% of the gait cycle. We calculated the root mean squared difference (RMSD) between the average of data from the last 15 min of the powered condition and the unpowered condition. After completing three 30-min training sessions, the hip exoskeleton provided 27% of the total peak hip flexion moment during gait. Despite this substantial contribution from the exoskeleton, subjects walked with a total hip moment pattern (muscle plus exoskeleton) that was almost identical and more similar to the unpowered condition than the hip angle pattern (hip moment RMSD 0.027, angle RMSD 0.134, p<0.001). The angle and moment RMSD were not different for the knee and ankle joints. These findings support the concept that people adopt walking patterns with similar joint moment patterns despite differences in hip joint angles for a given walking speed.  相似文献   

11.
Coordination of leg muscles during speed skating   总被引:6,自引:0,他引:6  
Five speed skaters of elite performance level and six speed skaters of trained level were subjected to an inverse dynamical analysis during speed skating. Push-off forces were registered by means of special skates. Myoelectric activity (EMG) of ten leg muscles and cinematographic data were recorded. Linked segment modelling yielded net joint moments and joint powers. The speed skating technique is characterized by a typical horizontal position of the trunk and a suppression of a plantar flexion during the push-off. This technique, necessary to reduce external friction, constrains the transfer of rotation in joints to translation of the mass center of the body. In spite of constrained push-off, the EMG levels of the leg muscles show a proximo-distal temporal order which to a certain extent is comparable to that previously found in an unconstrained vertical jump. This proximo-distal sequence is also reflected by the time courses of the net moment and net power output in hip, knee and ankle joints. The temporal sequence in activation levels of activated muscles is not different between elite and trained speed skaters. The difference in performance level between these groups obviously has an origin in the ability of the elite speed skaters to realise larger net joint moments. Differences in net joint moments and in kinematics result in a higher power output and a lower air frictional force for the elite than for the trained speed skaters.  相似文献   

12.
Lower extremity corrective reactions to slip events.   总被引:7,自引:0,他引:7  
A significant number of injuries in the workplace is attributed to slips and falls. Biomechanical responses to actual slip events determine whether the outcome of a slip will be recovery or a fall. The goal of this study was to examine lower extremity joint moments and postural adjustments for experimental evidence of corrective strategies evoked during slipping in an attempt to prevent falling. Sixteen subjects walked onto a possibly oily vinyl tile floor, while ground reaction forces and body motion were recorded at 350 Hz. The onset of corrective reactions by the body in an attempt to recover from slips became evident at about 25% of stance and continued until about 45% into stance, i.e. on average between 190 and 350 ms after heel contact. These reactions included increased flexion moment at the knee and extensor activity at the hip. The ankle, on the other hand, acted as a passive joint (no net moment) during fall trials. Joint kinematics showed increased knee flexion and forward rotation of the shank in an attempt to bring the foot back towards the body. Once again, the ankle kinematics appeared to play a less dominant role (compared to the knee) in recovery attempts. This study indicates that humans generate corrective reactions to slips that are different than previously reported responses to standing perturbations translating the supporting surface.  相似文献   

13.
Acetabular dysplasia is a known cause of hip osteoarthritis. In addition to abnormal anatomy, changes in kinematics, joint reaction forces (JRFs), and muscle forces could cause tissue damage to the cartilage and labrum, and may contribute to pain and fatigue. The objective of this study was to compare lower extremity joint angles, moments, hip JRFs and muscle forces during gait between patients with symptomatic acetabular dysplasia and healthy controls. Marker trajectories and ground reaction forces were measured in 10 dysplasia patients and 10 typically developing control subjects. A musculoskeletal model was scaled in OpenSim to each subject and subject-specific hip joint centers were determined using reconstructions from CT images. Joint kinematics and moments were calculated using inverse kinematics and inverse dynamics, respectively. Muscle forces and hip JRFs were estimated with static optimization. Inter-group differences were tested for statistical significance (p  0.05) and large effect sizes (d  0.8). Results demonstrated that dysplasia patients had higher medially directed JRFs. Joint angles and moments were mostly similar between the groups, but large inter-group effect sizes suggested some restriction in range of motion by patients at the hip and ankle. Higher medially-directed JRFs and inter-group differences in hip muscle forces likely stem from lateralization of the hip joint center in dysplastic patients. Joint force differences, combined with reductions in range of motion at the hip and ankle may also indicate compensatory strategies by patients with dysplasia to maintain joint stability.  相似文献   

14.
The hypothesis which motivated the work reported in this article was that neglecting pure moments developed between the foot and pedal during cycling leads to a substantial error in computing axial and varus/valgus moments at the knee. To test this hypothesis, a mathematical procedure was developed for computing the three-dimensional knee loads using three-dimensional pedal forces and moments. In addition to data from a six-load-component pedal dynamometer, the model used pedal position and orientation and knee position in the frontal plane to determine the knee joint loads. Experimental data were collected from the right leg of 11 male subjects during steady-state cycling at 90 rpm and 225 W. The mean peak varus knee moment calculated was 15.3 N m and the mean peak valgus knee moment was 11.2 N m. Neglecting the pedal moment about the anterior/posterior axis resulted in an average absolute error of 2.6 N m and a maximum absolute error of 4.0 N m in the varus/valgus knee moment. The mean peak internal and external axial knee moments were 2.8 N m and 2.3 N m, respectively. The average and maximum absolute errors in the axial knee moment for not including the moment about an axis normal to the pedal were found to be 2.6 N m and 5.0 N m, respectively. The results strongly support the use of three-dimensional pedal loads in the computation of knee joint moments out of the sagittal plane.  相似文献   

15.
If the efficiency of human movement patterns could be improved using exercise, this could lead to more effective musculoskeletal disease-injury prevention and rehabilitation programs. It has been suggested that an efficient squat movement pattern emphasizes the use of the large hip extensors instead of the smaller knee extensors. The purpose of this study was to determine whether a counterbalanced squat (CBS) could produce a more hip-dominant and less knee-dominant squat movement pattern as compared with a regular squat (RS). There were 31 recreationally trained college-aged participants (15 male, 16 female) who performed 10 squats (5 CBS and 5 RS), while segment kinematics, ground reaction forces, and muscle (gluteus maximus [GM], quadriceps, hamstrings) electromyographic (EMG) activations were recorded. Peak sagittal plane net joint moments and joint ranges of motion at the hip, knee, and ankle joints along with peak and integrated EMG activation levels for all 3 muscles were compared using analysis of variance (squat type × sex). The results revealed that the CBS increased the hip joint moment and GM activation, while it decreased the knee joint moment and quadriceps activation as compared with the RS. Therefore, the CBS produces a more hip-dominant and less knee-dominant squat movement pattern and could be used in exercise programs aimed at producing more hip-dominant movement patterns.  相似文献   

16.
Research concerning forefoot strike pattern (FFS) versus rearfoot strike pattern (RFS) running has focused on the ground reaction force even though internal joint contact forces are a more direct measure of the loads responsible for injury. The main purpose of this study was to determine the internal loading of the joints for each strike pattern. A secondary purpose was to determine if converted FFS and RFS runners can adequately represent habitual runners with regards to the internal joint loading. Using inverse dynamics to calculate the net joint moments and reaction forces and optimization techniques to estimate muscle forces, we determined the axial compressive loading at the ankle, knee, and hip. Subjects consisted of 15 habitual FFS and 15 habitual RFS competitive runners. Each subject ran at a preferred running velocity with their habitual strike pattern and then converted to the opposite strike pattern. Plantar flexor muscle forces and net ankle joint moments were greater in the FFS running compared to the RFS running during the first half of the stance phase. The average contact forces during this period increased by 41.7% at the ankle and 14.4% at the knee joint during FFS running. Peak ankle joint contact force was 1.5 body weights greater during FFS running (p<0.05). There was no evidence to support a difference between habitual and converted running for joint contact forces. The increased loading at the ankle joint for FFS is an area of concern for individuals considering altering their foot strike pattern.  相似文献   

17.
Cycling power decreases substantially during a maximal cycling trial of just 30 s. It is not known whether movement patterns and joint powers produced at each joint decrease to a similar extent or if each joint exhibits an individual fatigue profile. Changes in movement patterns and/or joint powers associated with overall task fatigue could arise from several different mechanisms or from a complex interplay of these mechanisms. The purpose of this investigation was to determine the changes in movement and power at each joint during a fatiguing cycling trial. Thirteen trained cyclists performed a 30 s maximal cycling trial on an isokinetic cycle ergometer at 120 rpm. Pedal forces and limb kinematics were recorded. Joint powers were calculated using a sagittal plane inverse dynamics model and averaged for the initial, middle, and final three second intervals of the trial, and normalized to initial values. Relative ankle plantar flexion power was significantly less than all other joint actions at the middle interval (51±5% of initial power; p=0.013). Relative ankle plantar flexion power for the final interval (37±3%) was significantly less than the relative knee flexion and hip extension power (p=0.010). Relative knee extension power (41±5%) was significantly less than relative hip extension power (55±4%) during the final three second interval (p=0.045). Knee flexion power (47±5%) did not differ from relative hip extension power (p=0.06). These changes in power were accompanied by a decrease in time spent extending by each joint with fatigue (i.e., decreased duty cycle, p<0.03). While central mechanisms may have played a role across all joints, because the ankle fatigued more than the hip and knee joints, either peripheral muscle fatigue or changes in motor control strategies were identified as the potential mechanisms for joint-specific fatigue during a maximal 30 s cycling trial.  相似文献   

18.
Musculoskeletal modeling and simulations have vast potential in clinical and research fields, but face various challenges in representing the complexities of the human body. Soft tissue artifact from skin-mounted markers may lead to non-physiological representation of joint motions being used as inputs to models in simulations. To address this, we have developed adaptive joint constraints on five of the six degree of freedom of the knee joint based on in vivo tibiofemoral joint motions recorded during walking, hopping and cutting motions from subjects instrumented with intra-cortical pins inserted into their tibia and femur. The constraint boundaries vary as a function of knee flexion angle and were tested on four whole-body models including four to six knee degrees of freedom. A musculoskeletal model developed in OpenSim simulation software was constrained to these in vivo boundaries during level gait and inverse kinematics and dynamics were then resolved. Statistical parametric mapping indicated significant differences (p < 0.05) in kinematics between bone pin constrained and unconstrained model conditions, notably in knee translations, while hip and ankle flexion/extension angles were also affected, indicating the error at the knee propagates to surrounding joints. These changes to hip, knee, and ankle kinematics led to measurable changes in hip and knee transverse plane moments, and knee frontal plane moments and forces. Since knee flexion angle can be validly represented using skin mounted markers, our tool uses this reliable measure to guide the five other degrees of freedom at the knee and provide a more valid representation of the kinematics for these degrees of freedom.  相似文献   

19.
This study aimed to understand how players coordinate the multi-joint control strategies of the rear and target legs to satisfy the lower extremity and whole-body mechanical objectives during the golf swing when hitting shots with different clubs. Highly skilled golf players (n = 10) performed golf swings with a 6-iron and a driver. Joint kinetics were calculated using ground reaction forces and segment kinematics to determine net joint moments (NJMs) during the interval of interest within the downswing. Between club difference in NJMs and 3D support moments were compared across the group and within a player. Although player-specific multi-joint control strategies arose, players generally increased target leg ankle, knee, and hip NJMs when hitting with the driver while maintaining the relative contribution to the 3D support moment. Multi-joint control strategies used to control the target and rear legs were found to be different, yet the majority of the 3D support moment was produced by NJMs about an axis perpendicular to the leg planes. These results emphasize the importance of recognizing how an individual player coordinates multi-joint control from each leg, and highlights the need to design interventions that are player and leg specific to aid in improving player performance.  相似文献   

20.
Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号