Frontal plane dynamics of the centre of mass during quadrupedal locomotion on a split-belt treadmill.

Our previous study of cat locomotion demonstrated that lateral displacements of the centre of mass (COM) were strikingly similar to those of human walking and resembled the behaviour of an inverted pendulum (Park et al. 2019 J. Exp. Biol.222, 14. (doi:10.1242/jeb.198648)). Here, we tested the hypothesis that frontal plane dynamics of quadrupedal locomotion are consistent with an inverted pendulum model. We developed a simple mathematical model of balance control in the frontal plane based on an inverted pendulum and compared model behaviour with that of four cats locomoting on a split-belt treadmill. The model accurately reproduced the lateral oscillations of cats' COM vertical projection. We inferred the effects of experimental perturbations on the limits of dynamic stability using data from different split-belt speed ratios with and without ipsilateral paw anaesthesia. We found that the effect of paw anaesthesia could be explained by the induced bias in the perceived position of the COM, and the magnitude of this bias depends on the belt speed difference. Altogether, our findings suggest that the balance control system is actively involved in cat locomotion to provide dynamic stability in the frontal plane, and that paw cutaneous receptors contribute to the representation of the COM position in the nervous system.

Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses.

There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization-based models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters.

Swing- and support-related muscle actions differentially trigger human walk-run and run-walk transitions.

There has been no consistent explanation as to why humans prefer changing their gait from walking to running and from running to walking at increasing and decreasing speeds, respectively. This study examined muscle activation as a possible determinant of these gait transitions. Seven subjects walked and ran on a motor-driven treadmill for 40s at speeds of 55, 70, 85, 100, 115, 130 and 145% of the preferred transition speed. The movements of subjects were videotaped, and surface electromyographic activity was recorded from seven major leg muscles. Resultant moments at the leg joints during the swing phase were calculated. During the swing phase of locomotion at preferred running speeds (115, 130, 145%), swing-related activation of the ankle, knee and hip flexors and peaks of flexion moments were typically lower (P<0.05) during running than during walking. At preferred walking speeds (55, 70, 85%), support-related activation of the ankle and knee extensors was typically lower during stance of walking than during stance of running (P<0.05). These results support the hypothesis that the preferred walk-run transition might be triggered by the increased sense of effort due to the exaggerated swing-related activation of the tibialis anterior, rectus femoris and hamstrings; this increased activation is necessary to meet the higher joint moment demands to move the swing leg during fast walking. The preferred run-walk transition might be similarly triggered by the sense of effort due to the higher support-related activation of the soleus, gastrocnemius and vastii that must generate higher forces during slow running than during walking at the same speed.

Analysis of muscle coordination strategies in cycling.

The functional significance of the stereotypical muscle activation patterns used in skilled multi-joint tasks is not well understood. Optimization methods could provide insight into the functional significance of muscle coordination. The purpose of this study was to predict muscle force patterns during cycling by pushing and pulling the pedal using different optimization criteria and compare the predictions with electromyographic (EMG) patterns. To address the purpose of the study, 1) the contribution of muscle length and velocity changes to EMG-muscle force relationships during cycling was examined by comparing joint moments calculated from EMG and inverse dynamics, 2) patterns of individual muscle forces during cycling of five subjects were predicted using 13 different optimization criteria, and 3) the properties of the criterion with the best performance in predicting the normalized EMG were used to explain the features and functional significance of muscle coordination in cycling. It was shown that the criterion that minimizes the sum of muscle stresses cubed demonstrated the best performance in predicting the relative magnitude and patterns of muscle activation. Based on this criterion, it was suggested that the functional significance of muscle coordination strategy in cycling may be minimization of fatigue and/or perceived effort.

Coordination of two- and one-joint muscles: functional consequences and implications for motor control.

The purpose of this paper is three-fold: (a) to summarize available data on coordination of major two- and one-joint muscles in multijoint tasks and identify basic features of muscle coordination, (b) to demonstrate that there may exist an optimization criterion that predicts essential features of electromyographic activity of individual muscles in a variety of tasks, and (c) to address the functional consequences of the observed muscle coordination and underlying mechanisms of its control. The analysis of the literature revealed that basic features of muscle coordination are similar among different voluntary motor tasks and reflex responses. It is demonstrated that these basic features of coordination of one- and two-joint muscles in two-dimensional tasks are qualitatively predicted by minimizing the sum of muscle stresses cubed. Functional consequences of the observed coordination of one- and two-joint muscles are (a) reduction of muscle force as well as stress, mechanical and metabolic energy expenditure, muscle fatigue, and perceived effort; (b) a spring-like behavior of a multi-joint limb during maintenance of an equilibrium posture; and (c) energy transfer between joints via two-joint muscles. A conceptual scheme of connections between motoneuron pools of one- and two-joint muscles, which accounts for the observed muscle coordination, is proposed. An important part of this scheme is the force-dependent inhibition and excitation from two-joint to one-joint synergists and antagonists, respectively.

Coordination of two-joint rectus femoris and hamstrings during the swing phase of human walking and running.

It has been hypothesized previously that because a strong correlation was found between the difference in electromyographic activity (EMG) of rectus femoris (RF) and hamstrings (HA; EMG(RF)-EMG(HA)) and the difference in the resultant moments at the knee and hip (Mk-Mh) during exertion of external forces on the ground by the leg, input from skin receptors of the foot may play an important role in the control of the distribution of the resultant moments between the knee and hip by modulating activation of the two-joint RF and HA. In the present study, we examined the coordination of RF and HA during the swing phase of walking and running at different speeds, where activity of foot mechanoreceptors is not modulated by an external force. Four subjects walked at speeds of 1.8 m/s and 2.7 m/s and ran at speeds of 2.7 m/s and 3.6 m/s on a motor-driven treadmill. Surface EMG of RF, semimembranosus (SM), and long head of biceps femoris (BF) and coordinates of the four leg joints were recorded. An inverse dynamics analysis was used to calculate the resultant moments at the ankle, knee, and hip during the swing phase. EMG signals were rectified and low-pass filtered to obtain linear envelopes and then shifted in time to account for electromechanical delay between EMG and joint moments. During walking and running at all studied speeds, mean EMG envelope values of RF were statistically (P<0.05) higher in the first half of the swing (or at hip flexion/knee extension combinations of joint moments) than in the second half (or at hip extension/knee flexion combinations of joint moments). Mean EMG values of BF and SM were higher (P<0.05) in the second half of the swing than in the first half. EMG and joint moment peaks were substantially higher (P<0.05) in the swing phase of walking at 2.7 m/s than during the swing phase of running at the same speed. Correlation coefficients calculated between the differences (EMG(RF)-EMG(HA)) and (Mk-Mh), taken every 1% of the swing phase, were higher than 0.90 for all speeds of walking and running. Since the close relationship between EMG and joint moments was obtained in the absence of an external force applied to the foot, it was suggested that the observed coordination of RF and HA can be regulated without a stance-specific modulation of cutaneous afferent input from the foot. The functional role of the observed coordination of RF and HA was suggested to reduce muscle fatigue.

Is coordination of two-joint leg muscles during load lifting consistent with the strategy of minimum fatigue?

The purpose of this study was to examine if strong correlations reported for a back lift task between activity (EMG) of two-joint rectus femoris (RF), hamstrings (HA), and gastrocnemius (GA) and the difference in the joint moments could be predicted by minimizing an objective function of minimum fatigue. Four subjects lifted barbell weights (9 and 18 kg) using a back lift technique at three speeds normal, slow, and fast. Recorded ground reaction forces and coordinates of the leg joints were used to calculate the resultant joint moments. Surface EMG of five muscles crossing the knee joint were also recorded. Forces of nine muscles were calculated using static optimization and a minimum fatigue criterion. Relationships (i) (RF EMG-HA EMG) vs (knee moment hip moment) and (ii) GA EMG vs. (ankle moment knee moment) were closely related (coefficients of determination were typically 0.9 and higher). Qualitatively similar relationships were predicted by minimizing fatigue. Gastrocnemius and hamstrings had the agonistic action at both joints they cross during load lifting, and their activation and predicted forces increased with increasing flexion knee moments and extension ankle and hip moments. The rectus femoris typically had the antagonistic action at the knee and hip, and its activation and predicted force were low. Patterns of predicted muscle forces were qualitatively similar to the corresponding EMG envelopes (except in phases of low joint moments where accuracy of determining joint moments was presumably poor). It was suggested that muscle coordination in load lifting is consistent with the strategy of minimum muscle fatigue.

Forces of individual cat ankle extensor muscles during locomotion predicted using static optimization.

In order to test the principles of the control of synergistic muscles that were proposed in the literature, forces of cat soleus (SO), gastrocnemius (GA), and plantaris (PL) measured during locomotion were compared with the corresponding forces predicted using different optimization criteria. Forces of cat SO, GA, and PL, and the corresponding cat kinematics were recorded simultaneously using E-shaped force transducers and high-speed video, respectively. Measurements were obtained from three cats walking and trotting on a treadmill at five nominal speeds ranging from 0.4 to 1.8 m s-1. Muscle forces were predicted using static optimization and a musculoskeletal model of the cat hindlimb consisting of three segments (foot, shank, and thigh) and three muscles (SO, GA, and PL). Six optimization criteria which had been proposed in the literature were tested. Linear criteria based on the principles of minimum muscle force and stress predicted forces during the stance phase with an average normalized error of 59-322%. Three other criteria--minimization of the sum of the relative muscle forces squared, minimization of the sum of the muscle stresses cubed, and minimization of the upper bound for all of the muscle stresses-showed a better performance: (i) the average error was 43-119% and (ii) the correlation coefficient calculated between the predicted and actual forces exceeded 0.9 for all three muscles. A criterion that was based on the principle of minimum fatigue and accounted for the percentage of slow-twitch fibers in the muscles, had the lowest average error (26-52%). The high correlation (0.97-0.99) between the measured forces and forces predicted by using the minimum fatigue criterion suggested that force sharing among SO, GA, and PL during cat locomotion may be the same for a given set of joint moments and muscle moment arms. It was concluded that static optimization with the appropriate criterion can predict muscle forces adequately for specific movement conditions.

Mechanical power and work of cat soleus, gastrocnemius and plantaris muscles during locomotion: possible functional significance of muscle design and force patterns.

Electrical activity, forces, power and work of the soleus (SO), the gastrocnemius (GA) and the plantaris (PL) muscles were measured during locomotion in the cat in order to study the functional role of these ankle extensor muscles. Forces and electrical activity (EMG) of the three muscles were measured using home-made force transducers and bipolar, indwelling wire electrodes, respectively, for walking and trotting at speeds of 0.4 to 1.8 m s-1 on a motor-driven treadmill. Video records and a geometrical model of the cat hindlimb were used for calculating the rates of change in lengths of the SO, GA and PL muscles. The instantaneous maximum possible force that can be produced by a muscle at a given fibre length and the rate of change in fibre length (termed contractile abilities) were estimated for each muscle throughout the step cycle. Fibre lengths of the SO, GA and PL were calculated using a planar, geometrical muscle model, measured muscle forces and kinematics, and morphological measurements from the animal after it had been killed. Mechanical power and work of SO, GA and PL were calculated for 144 step cycles. The contribution of the positive work done by the ankle extensor muscles of one hindlimb to the increase of the total mechanical energy of the body (estimated from values in the literature) increased from 4-11% at speeds of locomotion of 0.4 and 0.8 m s-1 to 7-16% at speeds of 1.2 m s-1 and above. The relative contributions of the negative and positive work to the total negative and positive work done by the three ankle extensor muscles increased for GA, decreased for SO and remained about the same for PL, with increasing speeds of locomotion. At speeds of 0.4-0.8 m s-1, the positive work normalized to muscle mass was 7.5-11.0 J kg-1, 1.9-3.0 J kg-1 and 5.3-8.4 J kg-1 for SO, GA and PL, respectively. At speeds of 1.2-1.8 m s-1, the corresponding values were 9.8-16.7 J kg-1, 6.0-10.7 J kg-1 and 13.4-25.0 J kg-1. Peak forces of GA and PL increased and peak forces of SO did not change substantially with increasing speeds of locomotion. The time of decrease of force and the time of decrease of power after peak values had been achieved were much shorter for SO than the corresponding times for GA and PL at fast speeds of locomotion. The faster decrease in the force and power of SO compared with GA and PL was caused by the fast decrease of the contractile abilities and the activation of SO. The results of this study suggest that the ankle extensor muscles play a significant role in the generation of mechanical energy for locomotion.

Transfer of mechanical energy between ankle and knee joints by gastrocnemius and plantaris muscles during cat locomotion.

The purposes of this study were (1) to define and estimate the direction and amount of the energy transfer between the knee and ankle through gastrocnemius (GA) and plantaris (PL) muscles during cat locomotion, and (2) to test the assumption that the force and activity patterns of soleus (SO), GA, and PL are mechanically and physiologically advantageous for providing the transfer of energy between these joints. The direction, amount and rate of the energy transfer through a two-joint muscle were defined using a theoretical analysis of movements in two adjacent joints spanned by the two-joint muscle. The energy transferred between the ankle and the knee was calculated using the time integration of the difference between the power developed by the moments of SO, GA, and PL at the ankle joint and the total power of these muscles. The total power of SO, GA, and PL muscles, and the power of their movements about the ankle and knee, were obtained using the experimentally determined muscle forces, the rates of change in muscle length, and the angular velocities at the knee and ankle which were calculated from the kinematics and the geometry of the cat hindlimb. Muscular forces and hindlimb kinematics of the cats were recorded during normal walking and trotting on a treadmill at speeds of 0.4, 0.8, 1.2, 1.5, and 1.8 ms-1 using 'E'-shaped tendon transducers and high-speed video, respectively. It was found that during the early phase of support, there was a transfer of mechanical energy from the ankle to the knee through GA and PL. During the late phase of support, mechanical energy was transferred from the knee to the ankle. The amount of energy transferred increased with increasing speeds of locomotion. The energy transferred from the ankle to the knee was 3-60 mJ (7-22% of the negative work done by the moments of SO, GA, and PL at the ankle), and the energy transferred from the knee to the ankle was 10-67 mJ (7-14% of the positive work done by the moments of SO, GA, and PL at the ankle). The results of this study suggest that the activation and the forces of one-joint SO and multi-joint GA and PL are organized in such a way as to fit the features of the design of these ankle extensor muscles in order to provide locomotion efficiently. For example, the decrease in the contractile abilities of SO during the late phase of support at fast speeds of locomotion may be compensated for by the transfer of energy from the knee to the ankle through GA and PL. The design of GA and PL (a high percentage of fast-twitch muscle fibers, large angles of pinnation and short length of the fibers, long tendons, and the location about the ankle and knee joints) seems to be well suited for transferring mechanical energy between the ankle and knee at fast speeds of locomotion. Because of the design of GA and PL, their contractile abilities remain close to the maximum at fast speeds of locomotion. The design of GA and PL allows for extension of the ankle joint through the action of the knee extensor muscles during knee extension with a relatively small change in length of GA and PL.

Comparison of mechanical energy expenditure of joint moments and muscle forces during human locomotion.

The mechanical energy expenditures (MEEs) of two human lower extremity models with different sources of mechanical energy - (1) muscles and (2) joint moments - were compared theoretically. Sources of mechanical energy producing movement of Model 1 were eight muscle, three of which were two-joint muscles. Sources of mechanical energy producing movement of Model 2 were net moments at its joints. These sources of mechanical energy were substituted by 11 one-joint muscles, with the assumption that antagonistic muscles did not produce force. Because of this assumption, summed MEE of all joint moments and all one-joint muscles of Model 2 were the same. It was shown that during the same movement the model with two-joint muscles could spend less mechanical energy than the model without two-joint muscles. This economy of mechanical energy realized by two-joint muscles was possible if (i) signs of the muscle powers which were produced by the two-joint muscle at both joints were opposite, (ii) moments produced by that muscle at each of the two joints had the same direction as the net joint moments at these joints, and (iii) muscles crossing these two joints from the opposite side did not produce force. Realization of these three conditions during human locomotion was checked experimentally. Electrical activity of eight lower extremity muscles of ten subjects was measured during treadmill walking and running. Based on this information, the periods where the muscles produce force were estimated. Moments and their power at joints of the lower extremity of two subjects performing walking and running were calculated using kinematics and ground reaction force measurements, and an inverse dynamics approach. It was shown that MEE of models with different sources of mechanical energy appeared to be different during certain periods of the swing phase. However, the magnitude of this difference was probably relatively small.

Role of the muscle belly and tendon of soleus, gastrocnemius, and plantaris in mechanical energy absorption and generation during cat locomotion.

The functional significance of tendons, and the differences in tendon properties among synergistic muscles, is not well established for normal locomotion. Previous studies have suggested that tendons may store mechanical energy during the early phase of support, and then release this energy during the late phase of support. The storage and release of mechanical energy by tendons may modify the velocity of shortening and elongation and the power produced by the muscle belly and the fibers, and may influence the metabolic cost of locomotion. The aims of this study were (1) to estimate the amount of negative and positive work done by the tendon and the muscle belly of the cat soleus (SO), gastrocnemius (GA), and plantaris (PL), and (2) to determine the relative contribution of the elastic energy stored in the tendons to the total mechanical work done by these three muscles during walking and trotting. Forces of SO, GA, and PL muscles were measured using standard force transducers in three cats walking and trotting at speeds of 0.4-1.8 ms-1 on a motor-driven treadmill. Video records and a geometrical model of the cat hindlimb were used for calculating length of the muscle-tendon complexes of SO, GA, and PL during locomotion. Instantaneous lengths of the tendons of SO, GA, and PL during a step cycle were estimated from the stress-strain properties, the effective lengths, the cross-sectional areas, and the instantaneous forces of the tendons. Stress-strain properties for the tendons were obtained experimentally from one animal. The length of the belly was defined as the difference between the muscle-tendon complex length and the tendon length. Mechanical power of the tendon and the muscle belly was calculated as the product of the measured muscle force and the calculated rates of change in tendon and muscle belly lengths, respectively. Mechanical power and work of the tendons and bellies of SO, GA, and PL were calculated for 144 step cycles. During a step cycle, peak negative and peak positive velocities as well as peak powers of the muscle-tendon complexes of SO, GA, and PL were typically higher than those of the muscle bellies. Positive work done by the muscle-tendon complexes exceeded the positive work done by the muscle bellies. GA and PL tendons stored more mechanical energy than the SO tendon. The contributions of the elastic energy stored in the tendons to the positive work done by the muscle-tendon complexes decreased with increasing speeds of locomotion for two of the three cats studied and did not change for the third one. These contributions equaled 50-21%, 30-14%, and 25-18% for the three cats, respectively. The results of this study suggest that energy absorption and release by the tendons of cat SO, GA, and PL make up a substantial part of the total energy absorbed and generated by the corresponding muscle-tendon complexes.

Force-sharing between cat soleus and gastrocnemius muscles during walking: explanations based on electrical activity, properties, and kinematics.

Studying force sharing between synergistic muscles can be useful for understanding the functional significance of musculoskeletal redundancy and the mechanisms underlying the control of synergistic muscles. The purpose of this study was to quantify and explain force sharing between cat soleus (SO) and gastrocnemius (GA) muscles, and changes in force sharing, as a function of integrated electrical activity (IEMG), contractile and mechanical properties, and kinematics of the muscles for a variety of locomotor conditions. Forces in SO and GA were measured using standard tendon force transducers of the 'buckle' type, and EMGs were recorded using bipolar, indwelling fine wire electrodes. Muscle tendon and fiber lengths, as well as the corresponding velocities, were derived from the hindlimb kinematics, anthropometric measurements, and a muscle model. In order to describe force- and IEMG-sharing between SO and GA, SO force vs GA force and SO IEMG vs GA IEMG plots were constructed. Force- and IEMG-sharing curves had a loop-like shape. Direction of formation of the loop was typically counterclockwise for forces and clockwise for IEMG; that is, forces of GA reached the maximum and then decreased faster relative to forces of SO, and IEMG of SO reached the maximum and then decreased faster relative to IEMG of GA. With increasing speeds of locomotion, the width of the force-sharing loops tended to decrease, and the width of the IEMG-sharing loops increased. Peak forces in GA muscle and peak IEMGs in SO and GA muscles tended to increase with increasing speeds of locomotion, whereas peak SO forces remained nearly constant for all activities. Because of these changes in the peak forces and IEMGs of SO and GA, the slope of the force-sharing loop decreased, and the slope of the IEMG-sharing loop did not change significantly with increasing speeds of locomotion. Length changes and velocities of SO and GA increased with the speed of locomotion and were similar in absolute magnitude for both muscles at a given speed. However, SO tended to work consistently closer than GA to the optimal length for all activities. The normalized velocities of elongation and shortening of SO fibers were consistently larger than those of GA, and the differences in these velocities increased as the speed of locomotion increased.(ABSTRACT TRUNCATED AT 400 WORDS)

Variations in force-time histories of cat gastrocnemius, soleus and plantaris muscles for consecutive walking steps.

Force-sharing among muscles during locomotion has been studied experimentally using 'representative' or 'average' step cycles. Mathematical approaches aimed at predicting individual muscle forces during locomotion are based on the assumption that force-sharing among muscles occurs in a consistent and unique way. In this study, we quantify normal variations in muscular force-time histories for step cycles executed at a given nominal speed, so that we can appreciate what it means to analyze 'representative' or 'average' step cycles and can evaluate whether these normal variations in muscular force-time histories are random or may be associated with variations in the kinematics of consecutive step cycles. Forces in gastrocnemius, soleus and plantaris muscles were measured for step cycles performed at a constant nominal speed in freely moving cats. Gastrocnemius forces were always larger than peak plantaris or soleus forces. Also, peak gastrocnemius forces typically occurred first after paw contact, followed by peak soleus and then peak plantaris forces. Furthermore, it was found that variations in muscular force-time histories were substantial and were systematically related to step-cycle durations. The results of this study suggest that findings based on 'representative' or 'average' step cycles for a given nominal speed of locomotion should be viewed cautiously and that variations in force-sharing among muscles are systematically related to variations in locomotor kinematics.

Tendon action of two-joint muscles: transfer of mechanical energy between joints during jumping, landing, and running.

The amount of mechanical energy transferred by two-joint muscles between leg joints during squat vertical jumps, during landings after jumping down from a height of 0.5 m, and during jogging were evaluated experimentally. The experiments were conducted on five healthy subjects (body height, 1.68-1.86 m; and mass, 64-82 kg). The coordinates of the markers on the body and the ground reactions were recorded by optical methods and a force platform, respectively. By solving the inverse problem of dynamics for the two-dimensional, four-link model of a leg with eight muscles, the power developed by the joint (net muscular) moments and the power developed by each muscle were determined. The energy transferred by two-joint muscles from and to each joint was determined as a result of the time integration of the difference between the power developed at the joint by the joint moment, and the total power of the muscles serving a given joint. It was shown that during a squat vertical jump and in the push-off phase during running, the two-joint muscles (rectus femoris and gastrocnemius) transfer mechanical energy from the proximal joints of the leg to the distal ones. At landing and in the shock-absorbing phase during running, the two-joint muscles transfer energy from the distal to proximal joints. The maximum amount of energy transferred from the proximal joints to distal ones was equal to 178.6 +/- 45.7 J (97.1 +/- 27.2% of the work done by the joint moment at the hip joint) at the squat vertical jump. The maximum amount of energy transferred from the distal to proximal joints was equal to 18.6 +/- 4.2 J (38.5 +/- 36.4% of work done by the joint moment at the ankle joint) at landing. The conclusion was made that the one-joint muscles of the proximal links compensate for the deficiency in work production of the distal one-joint muscles by the distribution of mechanical energy between joints through the two-joint muscles. During the push-off phase, the muscles of the proximal links help to extend the distal joints by transferring to them a part of the generated mechanical energy. During the shock-absorbing phase, the muscles of the proximal links help the distal muscles to dissipate the mechanical energy of the body.