The Degrees of Freedom Problem in Human Standing Posture: Collective and Component Dynamics

The experiment was setup to investigate the coordination and control of the degrees of freedom (DFs) of human standing posture with particular reference to the identification of the collective and component variables. Subjects stood in 3 postural tasks: feet side by side, single left foot quiet stance and single left foot stance with body rocking at the ankle joint in the sagittal plane. All three postural tasks showed very high coherence (∼1) of center of pressure (COP) - center of mass (COM) in the low frequency range. The ankle and hip coherence was mid range (∼.5) with the tasks having different ankle/hip compensatory cophase patterns. The findings support the view that the in-phase relation of the low frequency components of the COP-COM dynamic is the collective variable in the postural tasks investigated. The motions of the individual joints (ankle, knee, hip, neck) and couplings of pair wise joint synergies (e.g., ankle-hip) provide a supporting cooperative role to the preservation of the collective variable in maintaining the COM within the stability region of the base of support (BOS) and minimizing the amount of body motion consistent with the task constraint.     

Simulated movement termination for balance recovery: can movement strategies be sought to maintain stability in the presence of slipping or forced sliding?

Slipping during various kinds of movement often leads to potentially dangerous incidents of falling. The purpose of this study was to determine whether there was evidence to support the theory that movement strategies could be used by individuals to regain stability during an episode of slipping and whether forced sliding from a moving platform accurately simulated the effect of slipping on stability and balance. A single-link-plus-foot biomechanical model was used to mathematically simulate base of support (BOS) translation and body segment rotation during movement termination in sagittal plane. An optimization routine was used to determine region of stability [defined at given COM locations as the feasible range of horizontal velocities of the center of mass (COM) of human subject that can be reduced to zero with respect to the BOS while still allowing the COM to traverse within the BOS limits]. We found some 30% overlap in the region of stability for slipping and non-slipping conditions. This finding supports the theory that movement strategies can be sought for restoring stability and balance even if slipping unexpectedly occurs. We also found that forced sliding produces effects on stability that are similar to those of slipping, indicated by over 50% overlap in the regions of stability for the two conditions. In addition, forced sliding has distinctive effects on stability, including a "shift" of the region of stability extended beyond the BOS in the direction of sliding. These findings may provide quantifiable guidance for balance training aimed at reducing fall incidents under uncertain floor surface conditions.     

Age-related differences in muscle power during single-step balance recovery

The purpose of this study was to investigate age-related differences in muscle power during a surrogate task of trip recovery. Participants included 10 healthy young men (19-23 years old) and 10 healthy older men (65-83). The task involved releasing participants from a forward-leaning posture. After release, participants attempted to recover their balance using a single step of the right foot. Muscle power at the hip, knee, and ankle of the stepping limb were determined from the product of joint angular velocity and joint torque. Muscle powers during balance recovery followed a relatively consistent pattern in both young and older men, and showed effects of both lean and age. Interestingly, the effects of age did not always involve smaller peak power values in the older men as expected from the well-documented loss of muscle power with aging. Older men exhibited smaller peak muscle power at the knee and larger peak muscle power at the ankle and hip compared to young men. The increases in muscle power at the ankle and hip may result from a neuromuscular adaptation aimed at improving balance recovery ability by compensating for the age-related loss of muscle function.     

Biomechanical analysis of movement strategies in human forward trunk bending. II. Experimental study

 The large mass of the human upper trunk, its elevated position during erect stance, and the small area limited by the size of the feet, stress the importance of equilibrium control during trunk movements. The objective of the present study was to perform a biomechanical analysis of fast forward trunk movements in order to understand the coordination between movement and posture. The analysis is based on a comparison between experimentally observed bending and hypothetical “optimal bending” performed on an infinitely narrow support, as presented in a companion paper. The experimental data were obtained from 16 subjects who performed fast forward bending while standing on a wide platform or on a narrow beam. The analysis is performed by decomposition of the movement into three dynamically independent components, each representing a movement along one of the three eigenvectors of the motion equation. The eigenmovements are termed “hip”, “ankle”, and “knee” eigenmovements, according to the dominant joint. The experimentally observed movement is characterized mainly by the hip and ankle eigenmovements, whereas the knee eigenmovement is negligible. Similarly to the “optimal bending” the ankle eigenmovement starts earlier and lasts longer than the hip eigenmovement. An early forward acceleration of the center of gravity in the ankle eigenmovement is caused by anticipatory changes in the ankle joint torque. This clarifies the role of the early tibialis anterior burst and/or soleus inhibition usually observed in electromyographic recordings during forward bending. The results suggest that the hip and the ankle eigenmovements can be treated as independently controlled motion units aimed at functionally different behavioral goals: the bending per se and postural adjustment. It is proposed that the central nervous system has to control these motion units sequentially in order to perform the movement and maintain equilibrium. It is also suggested that the hip and ankle eigenmovements can be regarded as a biomechanical background for the hip and ankle strategies introduced by Horak and Nashner (1986) on the basis of electromyographic recordings and kinematic patterns in response to postural perturbations. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Thresholds for step initiation induced by support-surface translation: a dynamic center-of-mass model provides much better prediction than a static model

The need to initiate a step in order to recover balance could, in theory, be predicted by a static model based solely on displacement of the center of mass (COM) with respect to the base of support (BOS), or by a dynamic model based on the interaction between COM displacement and velocity. The purpose of this study was to determine whether the dynamic model provides better prediction than the static model regarding the need to step in response to moving-platform perturbation. The COM phase plane trajectories were determined for 10 healthy young adults for trials where the supporting platform was translated at three different acceleration levels in anterior and posterior directions. These trajectories were compared with the thresholds for step initiation predicted by the static and dynamic COM models. A single-link-plus-foot biomechanical model was employed to mathematically simulate termination of the COM movement, without stepping, using the measured platform acceleration as the input. An optimization routine was used to determine the stability boundaries in COM state space so as to establish the dynamic thresholds where a compensatory step must be initiated in order to recover balance. In the static model, the threshold for step initiation was reached if the COM was displaced beyond the BOS limits. The dynamic model showed substantially better accuracy than the static model in predicting the need to step in order to recover balance: 71% of all stepping responses predicted correctly by the dynamic model versus only 11% by the static model. These results support the proposition that the central nervous system must react to and control dynamic effects, i.e. COM velocity, as well as COM displacement in order to maintain stability with respect to the existing BOS without stepping.     

Predicted threshold against backward balance loss in gait

The purpose of this study was to determine the minimum forward center of mass (COM) velocity required to prevent backward loss of balance in gait as function of the initial COM position. We hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing. To investigate this issue, we constructed a seven-link, nine-degree-of-freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions: (1) the posture at the beginning of swing phase (i.e., at toe-off), and (2) symmetric bipedal standing. In particular, for a range of possible COM positions posterior to the base of support (BOS), simulated annealing was used to search for the minimum velocity that could carry the COM into the BOS and avoid backward loss of balance. We found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing. In general, the minimal COM velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing, and the difference could approach 30% or more when the COM started 0.5 and 1.0 foot-lengths behind the BOS. These discrepancies suggest that simpler biomechanical models, while being more efficient and easier to employ, may not always be adequate for exploring stability limits of humans.     

Age-related changes in posture response under a continuous and unexpected perturbation

Aging is a critical factor to influence the functional performance during daily life. Without an appropriate posture control response when experiencing an unexpected external perturbation, fall may occur. A novel six-degree-of freedom platform with motion control protocol was designed to provide a real-life simulation of unexpected disturbance in order to discriminate the age-related changes of the balance control and the recovery ability. Twenty older adults and 20 healthy young adults participated in the study. The subjects stood barefoot on the novel movable platform, data of the center of mass (COM) excursion, joint rotation angle and electromyography (EMG) were recorded and compared. The results showed that the older adults had similar patterns of joint movement and COM excursion as the young adults during the balance reactive-recovery. However, larger proximal joint rotation in elderly group induced larger COM sway envelop and therefore loss of the compensatory strategy of posture recovery. The old adults also presented a lower muscle power. In order to keep an adequate joint stability preventing from falling, the EMG activity was increased, but the asymmetric pattern might be the key reason of unstable postural response. This novel design of moveable platform and test protocol comprised the computerized dynamic posturography (CDP) demonstrate its value to assess the possible sensory, motor, and central adaptive impairments to balance control and could be the training tool for posture inability person.     

Gait posture estimation using wearable acceleration and gyro sensors

A method for gait analysis using wearable acceleration sensors and gyro sensors is proposed in this work. The volunteers wore sensor units that included a tri-axis acceleration sensor and three single axis gyro sensors. The angular velocity data measured by the gyro sensors were used to estimate the translational acceleration in the gait analysis. The translational acceleration was then subtracted from the acceleration sensor measurements to obtain the gravitational acceleration, giving the orientation of the lower limb segments. Segment orientation along with body measurements were used to obtain the positions of hip, knee, and ankle joints to create stick figure models of the volunteers. This method can measure the three-dimensional positions of joint centers of the hip, knee, and ankle during movement. Experiments were carried out on the normal gait of three healthy volunteers. As a result, the flexion–extension (F–E) and the adduction–abduction (A–A) joint angles of the hips and the flexion–extension (F–E) joint angles of the knees were calculated and compared with a camera motion capture system. The correlation coefficients were above 0.88 for the hip F–E, higher than 0.72 for the hip A–A, better than 0.92 for the knee F–E. A moving stick figure model of each volunteer was created to visually confirm the walking posture. Further, the knee and ankle joint trajectories in the horizontal plane showed that the left and right legs were bilaterally symmetric.     

Predicted threshold against forward and backward loss of balance for perturbed walking

The biomechanical mechanisms of loss of balance have been studied before for slip condition but have not been investigated for arbitrary perturbation profiles under non-slip conditions in sagittal plane. This study aimed to determine the thresholds of center of mass (COM) velocity and position relative to the base of support (BOS) that predict forward and backward loss of balance during walking with a range of BOS perturbations. Perturbations were modeled as sinusoidal BOS motions in the vertical or anterior-posterior direction or as sagittal rotation. The human body was modeled using a seven-link model. Forward dynamics alongside with dynamic optimization were used to find the thresholds of initial COM velocity for each initial COM position that would predict forward or backward loss of balance. The effects of perturbation frequency and amplitude on these thresholds were modeled based on the simulation data. Experimental data were collected from 15 able-bodied individuals and three individuals with disability during perturbed walking. The simulation results showed similarity with the stability region reported for slip and non-slip conditions. The feasible stability region shrank when the perturbation frequency and amplitude increased, especially for larger initial COM velocities. 89.5% (70.9%) and 82.4% (68.2%) of the measured COM position and velocity combinations during low (high) perturbations were located inside the simulated limits of the stability region, for able-bodied and disabled individuals, respectively. The simulation results demonstrated the effects of different perturbation levels on the stability region. The obtained stability region can be used for developing rehabilitative programs in interactive environments.     

Predicted threshold against backward balance loss following a slip in gait

The purpose of this study was to use a 7-link, moment-actuated human model to predict, at liftoff of the trailing foot in gait, the threshold of the center of mass (COM) velocity relative to the base of support (BOS) required to prevent backward balance loss during single stance recovery from a slip. Five dynamic optimization problems were solved to find the minimum COM velocities that would allow the simulation to terminate with the COM above the BOS when the COM started 0.25, 0.5, 0.75, 1.0, and 1.25 foot lengths behind the heel of the stance foot (i.e., behind the BOS). The initial joint angles of the model were based on averaged data from experimental trials. Foot-ground contact was modeled using 16 visco-elastic springs distributed under the stance foot. Slipping was modeled by setting the sliding coefficient of friction of these springs to 0.02. The forward velocity of the COM necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non-slip conditions. The predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking. In all trials in which a subject's COM had a velocity below the predicted threshold, the subject's recovery foot landed posterior to the slipping foot as predicted. Finally, combining experimental data with optimization, we verified that the 7-link model could more accurately predict gait stability than a 2-link model.     

Posturographic analysis through markerless motion capture without ground reaction forces measurement

The ability of the central nervous system to control posture and balance has been used with increasing frequency for the diagnosis and/or treatment evaluation of various neuromuscular diseases. Typically this analysis (Posturographic Analysis) is based on tracking the motion of the center of mass (COM) during quiet standing, however direct measurement of the COM has been commonly approximated using the movement of the center of pressure (COP). The purpose of this study was to apply and validate a new method to track the COM (center of mass) and COP (center of pressure) from a visual hull measured using a markerless motion capture (MMC) method. The method was tested by comparing the calculation of the COP from direct measurements of the COP. The deviations between the methods, below 2 mm, were small relative to the average range of movement guaranteeing a satisfactory signal to noise ratio. This new method requires only kinematic data through MMC method and without the need of a force plate can identify the influence of individual body segments to motion of the COM.     

Lower limb kinematics in individuals with chronic low back pain during walking

Several investigators have suggested the presence of a link between Chronic Low Back Pain (CLBP) and lower limbs kinematics that can contribute to functional limitations and disability. Moreover, CLBP has been connected to postural and structural asymmetry. Understanding the movement pattern of lower extremities and its asymmetry during walking can provide a basis for examination and rehabilitation in people with CLBP. The present study focuses on lower limbs kinematics in individuals with CLBP during walking. Three-dimensional movements of the pelvic, hip, knee and ankle joints were tracked using a seven-camera Qualysis motion capture system. Functional dada analysis (FDA) was applied for the statistical analysis of pelvic and lower limbs motion patterns in 40 participants (20 CLBP and 20 controls). The CLBP group showed significantly different hip motion pattern in the transvers plane, altered knee and ankle motion pattern in the sagittal plane on the dominant side and different hip motion pattern in the transvers and frontal planes on the non-dominant side in comparison with the control group over the stance phase. In terms of symmetry, in the CLBP group, hip and knee moved through a significantly different motion patterns in the transvers plane on the dominant side in comparison with the non-dominant side. In the control group, knee moved through a significantly different motion pattern in the transvers plane on the dominant side in comparison with the non-dominant side. In conclusion, low back pain lead to altered movement patterns of the main joints of lower limbs especially on the dominant side during stance phase. Therefore, care should be taken to examine dominant lower limb movement pattern in CLBP to make a better clinical decision.     

Physical sensor difference-based method and virtual sensor difference-based method for visual and quantitative estimation of lower limb 3D gait posture using accelerometers and magnetometers

An approach using a physical sensor difference-based algorithm and a virtual sensor difference-based algorithm to visually and quantitatively confirm lower limb posture was proposed. Three accelerometers and two MAG(3)s (inertial sensor module) were used to measure the accelerations and magnetic field data for the calculation of flexion/extension (FE) and abduction/adduction (AA) angles of hip joint and FE, AA and internal/external rotation (IE) angles of knee joint; then, the trajectories of knee and ankle joints were obtained with the joint angles and segment lengths. There was no integration of acceleration or angular velocity for the joint rotations and positions, which is an improvement on the previous method in recent literature. Compared with the camera motion capture system, the correlation coefficients in five trials were above 0.91 and 0.92 for the hip FE and AA, respectively, and higher than 0.94, 0.93 and 0.93 for the knee joint FE, AA and IE, respectively.     

Recovery of walking speed and symmetrical movement of the pelvis and lower extremity joints after unilateral THA

In 17 patients with unilateral hip disease who underwent total hip arthroplasty (THA), the gait was analyzed preoperatively and 1, 3, 6, and 12 months after unilateral THA using a Vicon system to assess the recovery of walking speed and symmetrical movement of the hip, knee, ankle, and pelvis. The walking speed of these patients reached that of normal Japanese persons by 12 months after surgery. Walking speed was correlated with the range of hip motion on the operated side at 1 month postoperatively, and was correlated with the hip joint extension moment of force on both sides from 3 to 6 months after surgery. Before THA, asymmetry was observed in the range of the hip motion, maximum hip flexion, maximum hip extension, maximum knee flexion, as well as in pelvic obliquity, pelvic tilt, and pelvic rotation. There were no differences of the stride length or step length between both sides throughout the observation period. The preoperative range of hip flexion on the operated side during a gait cycle (21.3+/-7.9 degrees ) was significantly smaller than on the non-operated side (46.7+/-7.1 degrees ), and the difference between sides was still significant at 12 months after surgery (35.1+/-6.2 degrees on the operated side and 43.6+/-5.7 degrees on the non-operated side). The majority (74%) of the difference in hip motion range during this period was due to the difference in maximum extension of the hip. The increase in the range of pelvic tilt and the range of motion of the opposite hip showed an inverse correlation with the range of motion of the operated hip, suggesting a compensatory preoperative role. However, this correlation became insignificant after 6 months postoperatively. Asymmetry of the range of hip motion persisted at 12 months after THA in patients with unilateral coxoarthropathy during free level walking, while the operation normalized the spatial asymmetry of other joints and the walking speed prior to the recovery of hip motion.     

Adaptive control of center of mass (global) motion and its joint (local) origin in gait

Dynamic gait stability can be quantified by the relationship of the motion state (i.e. the position and velocity) between the body center of mass (COM) and its base of support (BOS). Humans learn how to adaptively control stability by regulating the absolute COM motion state (i.e. its position and velocity) and/or by controlling the BOS (through stepping) in a predictable manner, or by doing both simultaneously following an external perturbation that disrupts their regular relationship. Post repeated-slip perturbation training, for instance, older adults learned to forward shift their COM position while walking with a reduced step length, hence reduced their likelihood of slip-induced falls. How and to what extent each individual joint influences such adaptive alterations is mostly unknown. A three-dimensional individualized human kinematic model was established. Based on the human model, sensitivity analysis was used to systematically quantify the influence of each lower limb joint on the COM position relative to the BOS and the step length during gait. It was found that the leading foot had the greatest effect on regulating the COM position relative to the BOS; and both hips bear the most influence on the step length. These findings could guide cost-effective but efficient fall-reduction training paradigm among older population.     

Cross-correlations of center of mass and center of pressure displacements reveal multiple balance strategies in response to sinusoidal platform perturbations

Compared to static balance, dynamic balance requires a more complex strategy that goes beyond keeping the center of mass (COM) within the base of support, as established by the range of foot center of pressure (COP) displacement. Instead, neuromechanics must accommodate changing support conditions and inertial effects. Therefore, because they represent body's position and changes in applied moments, relative COM and COP displacements may also reveal dynamic postural strategies. To investigate this concept, kinetics and kinematics were recorded during three 12 cm, 1.25 Hz, sagittal perturbations. Forty-one individual trials were classified according to averaged cross-correlation lag between COM and COP displacement (lag(COM:COP)) and relative head-to-ankle displacement (Δ(head)/Δ(ankle)) using a k-means analysis. This process revealed two dominant patterns, one for which the lag(COM:COP) was positive (Group 1 (n=6)) and another for which it was negative (Group 2 (n=5)) . Group 1 (G1) absorbed power from the platform over most of the cycle, except during transitions in platform direction. Conversely, Group 2 (G2) participants applied power to the platform to maintain a larger margin between COM and COP position and also had larger knee flexion and ankle dorsiflexion, resulting in a lower stance. By the third repetition, the only kinematic differences were a slightly larger G2 linear knee displacement (p=0.008) and an antiphasic relationship of pelvis (linear) and trunk (angular) displacements. Therefore, it is likely that the strategy differences were detected by including COP in the initial screening method, because it reflects the pattern of force application that is not detectable by tracking body movements.     

Physical sensor difference-based method and virtual sensor difference-based method for visual and quantitative estimation of lower limb 3D gait posture using accelerometers and magnetometers

An approach using a physical sensor difference-based algorithm and a virtual sensor difference-based algorithm to visually and quantitatively confirm lower limb posture was proposed. Three accelerometers and two MAG³s (inertial sensor module) were used to measure the accelerations and magnetic field data for the calculation of flexion/extension (FE) and abduction/adduction (AA) angles of hip joint and FE, AA and internal/external rotation (IE) angles of knee joint; then, the trajectories of knee and ankle joints were obtained with the joint angles and segment lengths. There was no integration of acceleration or angular velocity for the joint rotations and positions, which is an improvement on the previous method in recent literature. Compared with the camera motion capture system, the correlation coefficients in five trials were above 0.91 and 0.92 for the hip FE and AA, respectively, and higher than 0.94, 0.93 and 0.93 for the knee joint FE, AA and IE, respectively.     

An investigation of rugby scrimmaging posture and individual maximum pushing force

Although rugby is a popular contact sport and the isokinetic muscle torque assessment has recently found widespread application in the field of sports medicine, little research has examined the factors associated with the performance of game-specific skills directly by using the isokinetic-type rugby scrimmaging machine. This study is designed to (a) measure and observe the differences in the maximum individual pushing forward force produced by scrimmaging in different body postures (3 body heights x 2 foot positions) with a self-developed rugby scrimmaging machine and (b) observe the variations in hip, knee, and ankle angles at different body postures and explore the relationship between these angle values and the individual maximum pushing force. Ten national rugby players were invited to participate in the examination. The experimental equipment included a self-developed rugby scrimmaging machine and a 3-dimensional motion analysis system. Our results showed that the foot positions (parallel and nonparallel foot positions) do not affect the maximum pushing force; however, the maximum pushing force was significantly lower in posture I (36% body height) than in posture II (38%) and posture III (40%). The maximum forward force in posture III (40% body height) was also slightly greater than for the scrum in posture II (38% body height). In addition, it was determined that hip, knee, and ankle angles under parallel feet positioning are factors that are closely negatively related in terms of affecting maximum pushing force in scrimmaging. In cross-feet postures, there was a positive correlation between individual forward force and hip angle of the rear leg. From our results, we can conclude that if the player stands in an appropriate starting position at the early stage of scrimmaging, it will benefit the forward force production.     

Empirical evaluation of gastrocnemius and soleus function during walking

Distinguishing gastrocnemius and soleus muscle function is relevant for treating gait disorders in which abnormal plantarflexor activity may contribute to pathological movement patterns. Our objective was to use experimental and computational analysis to determine the influence of gastrocnemius and soleus activity on lower limb movement, and determine if anatomical variability of the gastrocnemius affected its function. Our hypothesis was that these muscles exhibit distinct functions, with the gastrocnemius inducing limb flexion and the soleus inducing limb extension. To test this hypothesis, the gastrocnemius or soleus of 20 healthy participants was electrically stimulated for brief periods (90 ms) during mid- or terminal stance of a random gait cycle. Muscle function was characterized by the induced change in sagittal pelvis, hip, knee, and ankle angles occurring during the 200 ms after stimulation onset. Results were corroborated with computational forward dynamic gait models, by perturbing gastrocnemius or soleus activity during similar portions of the gait cycle. Mid- and terminal stance gastrocnemius stimulation induced posterior pelvic tilt, hip flexion and knee flexion. Mid-stance gastrocnemius stimulation also induced ankle dorsiflexion. In contrast mid-stance soleus stimulation induced anterior pelvic tilt, knee extension and plantarflexion, while late-stance soleus stimulation induced relatively little change in motion. Model predictions of induced hip, knee, and ankle motion were generally in the same direction as those of the experiments, though the gastrocnemius? results were shown to be quite sensitive to its knee-to-ankle moment arm ratio.     

Quantitative evaluation of the major determinants of human gait

Accurate knowledge of the isolated contributions of joint movements to the three-dimensional displacement of the center of mass (COM) is fundamental for understanding the kinematics of normal walking and for improving the treatment of gait disabilities. Saunders et al. (1953) identified six kinematic mechanisms to explain the efficient progression of the whole-body COM in the sagittal, transverse, and coronal planes. These mechanisms, referred to as the major determinants of gait, were pelvic rotation, pelvic list, stance knee flexion, foot and knee mechanisms, and hip adduction. The aim of the present study was to quantitatively assess the contribution of each major gait determinant to the anteroposterior, vertical, and mediolateral displacements of the COM over one gait cycle. The contribution of each gait determinant was found by applying the concept of an ‘influence coefficient’, wherein the partial derivative of the COM displacement with respect to a prescribed determinant was calculated. The analysis was based on three-dimensional measurements of joint angular displacements obtained from 23 healthy young adults walking at slow, normal and fast speeds. We found that hip flexion, stance knee flexion, and ankle-foot interaction (comprised of ankle plantarflexion, toe flexion and the displacement of the center of pressure) are the major determinants of the displacements of the COM in the sagittal plane, while hip adduction and pelvic list contribute most significantly to the mediolateral displacement of the COM in the coronal plane. Pelvic rotation and pelvic list contribute little to the vertical displacement of the COM at all walking speeds. Pelvic tilt, hip rotation, subtalar inversion, and back extension, abduction and rotation make negligible contributions to the displacements of the COM in all three anatomical planes.