Mechanical Energy Changes Research Articles

하프 빈야사 요가 수련 전·후의 역학적 에너지 변화 - 신체분절의 에너지 기여도 및 최고무게중심과 분절 에너지의 상관관계를 중심으로 -

The purpose of this study was to investigate change of mechanical energy before and after training of half vinyasa yoga. Thirteen subjects (height: <TEX>$163.4{\pm}3.9$</TEX> cm, body mass: <TEX>$54.9{\pm}7.3$</TEX> kg, age: <TEX>$20.0{\pm}0.49$</TEX> yrs) participated in this experiment. The motions of half vnyasa yoga were captured with Vicon system and parameters were calculated with Visual-3D. After training of half vinyasa yoga, the mechanical energies of body segments were increased and increments of mechanical energies in the lower segments were greater than the upper segments. The phase increments of mechanical energies increased phase 1, phase 2, and phase 3 in order. After training of half vinyasa yoga, phase contributions of body segments were similar before training of half vinyasa yoga. The contribution of mechanical energy on trunk segment in body was the greatest contribution of upper segments; also that of mechanical energy on thigh segment in body was the greatest contribution of lower segments. Before training, the coefficient of correlation between vertical center of gravity (CoGz) and mechanical energy of phase 3 was a -.559, but after training, the coefficient of correlation between CoGz and mechanical energy of phase 2 was a .587. These findings suggest that the training of half vinyasa yoga may be increasing the mechanical energies of body segments.

Change in the Mechanical Energy of the Body Center of Mass in Hemiplegic Gait after Continuous Use of a Plantar Flexion Resistive Ankle-foot Orthosis

[Purpose] The aim of this study was to investigate the changes in mechanical energy due to continuous use of a plantar flexion resistive ankle-foot orthosis (AFO) of subjects with chronic hemiplegia. [Subjects and Methods] The subjects were 5 hemiplegic patients using AFOs without a plantar flexion resistive function in their daily lives. We analyzed the gait of the subjects using a 3D motion capture system under three conditions: patients’ use of their own AFOs; after being fitted with a plantar flexion resistive AFO; and after continuous use of the device. The gait efficiency was determined by calculating the mutual exchange of kinetic and potential energy of the center of mass. [Results] An increased exchange rate of the kinetic and potential energy was found for all subjects. A larger increase of energy exchange was shown on the non-paralyzed side, and after continuous use of the plantar flexion resistive AFO. [Conclusion] We found that continuous use of a plantar flexion resistive AFO increased the rate of mutual exchange between kinetic energy and potential energy. The change in the rate was closely related to the role of the non-paretic side, showing that the subjects needed a certain amount of time to adapt to the plantar flexion resistive AFO.

Mechanical output in jumps of marmosets (Callithrix jacchus)

In this study we determined the mechanical output of common marmosets (Callithrix jacchus) during jumping. Vertical ground reaction forces were measured in 18 animals while they jumped from an instrumented crossbar to a crossbar located 70 cm higher. From the vertical force time histories, we calculated the rate of change of mechanical energy of the centre of mass (dE/dt). The mean value of dE/dt during the push-off amounted to 51.8±6.2 W kg(-1) body mass, and the peak value to 116.4±17.6 W kg(-1) body mass. We used these values in combination with masses of leg muscles, determined in two specimens, to estimate mean and peak values of dE/dt of 430 and 970 W kg(-1) muscle, respectively. These values are higher than values reported in the literature for jumps of humans and bonobos, but smaller than those of jumps of bushbabies. Surprisingly, the mean value of dE/dt of 430 W kg(-1) muscle was close to the maximal power output of 516 W kg(-1) muscle reported in the literature for isokinetic contractions of rat medial gastrocnemius, one of the fastest mammalian muscles. Further study of the force-velocity relationship of muscle tissue of small primates is indicated.

Protein Shape Change Has a Major Effect on the Gating Energy of a Mechanosensitive Channel

Increasing experimental evidence has shown that membrane protein functionality depends on molecular composition of cell membranes. However, the origin of this dependence is not fully understood. It is reasonable to assume that specific lipid-protein interactions are important, yet more generic effects due to mechanical properties of lipid bilayers likely play a significant role too. Previously it has been demonstrated using models for elastic properties of membranes and lateral pressure profiles of lipid bilayers that the mechanical properties of a lipid bilayer can contribute as much as ∼10 kBT to the free energy difference associated with a change in protein conformational state. Here, we extend those previous approaches to a more realistic model for a large mechanosensitive channel (MscL). We use molecular dynamics together with the MARTINI model to simulate the open and closed states of MscL embedded in a DOPC bilayer. We introduce a procedure to calculate the mechanical energy change in the channel gating using a three-dimensional pressure distribution inside a membrane, computed from the molecular dynamics simulations. We decompose the mechanical energy to terms associated with area dilation and shape contribution. Our results highlight that the lateral pressure profile of a lipid bilayer together with the shape change in gating can induce a contribution of ∼30 kBT on the gating energy of MscL. This contribution arises largely from the interfacial tension between hydrophobic and hydrophilic regions in a lipid bilayer.

Age-related changes in mechanical and metabolic energy during typical gait

The purpose of the study was to investigate and report age-related changes in walking energy expenditure using different methods of energy estimation. For 81 children and 16 adults (3–35 years) energy expenditure was investigated by using the following methods: analysis of energy changes of the centre of body mass (external and internal mechanical work), sum of segmental energies, sum of net joint work and gross and net metabolic cost, as well as net non-dimensional oxygen cost. Different methods of energy estimation not only show different outcome results but also different age-related changes. Significant changes were found for negative net joint work, external mechanical work and recovery as well as sum of segmental energies, until 9, 11 and 19 years respectively. Positive net joint work showed no differences between age groups and the differences for internal work did not suggest development. Metabolic energy showed significant changes until adult age. Gross cost decreases with increasing age in children and, although more gradually, still in adolescents. Net and net non-dimensional cost shows a more constant decrease with increasing age until adulthood. Therefore, the choice of estimation method and the use of age-related reference data when evaluating young patients should be carefully considered. For interpretation of oxygen consumption in children the use of net is superior to gross cost, but even after net non-dimensional normalization, age-related reference data should be used.

Dynamics of goat distal hind limb muscle–tendon function in response to locomotor grade

The functional roles of the lateral gastrocnemius (LG), medial gastrocnemius (MG) and superficial digital flexor (SDF) muscle-tendon units (MTUs) in domestic goats (N=6) were studied as a function of locomotor grade, testing the hypothesis that changes in distal limb muscle work would reflect changes in mechanical work requirements while goats walked or trotted on the level, 15 deg. decline and 15 deg. incline. As steep terrain-adapted animals, changes in muscle work output are expected to be particularly important for goats. In vivo muscle-tendon forces, fascicle length changes and muscle activation were recorded via tendon force buckles, sonomicrometry and electromyography to evaluate the work performance and elastic energy recovery of the three distal MTUs. These recordings confirmed that fascicle strain and force within goat distal hind limb muscles are adjusted in response to changes in mechanical work demand associated with locomotor grade. In general, muscle work was modulated most consistently by changes in fascicle strain, with increased net shortening (P<0.001) observed as goats switched from decline to level to incline locomotion. Peak muscle stresses increased as goats increased speed from a walk to a trot within each grade condition (P<0.05), and also increased significantly with grade (P<0.05 to P<0.01). Due to the increase in net fascicle shortening and muscle force, net muscle work per cycle also increased significantly (P<0.05 to P<0.005) as goats switched from decline to level to incline conditions (LG work: 20 mJ to 56 mJ to 209 mJ; MG work: -7 mJ to 34 mJ to 179 mJ; SDF work: -42 mJ to 14 mJ to 71 mJ, at a 2.5 ms(-1) trot). Although muscle work was modulated in response to changes in grade, the amount of work produced by these three distal pennate muscles was small (being <3%) in comparison with the change in mechanical energy required of the limb as a whole. Elastic energy recovery in the SDF and gastrocnemius (GA) tendons was substantial across all three grades, with the SDF tendon recovering 2.4 times more energy, on average, than the GA tendon. In parallel with the increase in muscle-tendon force, tendon energy recovery also increased as goats increased speed and changed gait, reaching the highest levels when goats trotted on an incline at 2.5 ms(-1) (GA: 173 mJ; SDF: 316 mJ). In general, tendon elastic energy exceeded net muscle work across all grade and gait conditions. These results demonstrate, for the first time in a quadruped, similar findings to those observed in ankle extensor muscles in humans, wallabies, turkeys and guinea fowl, suggesting that distal muscle-tendon architecture more generally favors a design for economic force production and tendon elastic energy recovery, with the majority of limb work during incline or decline running performed by larger proximal muscles.

Muscle work is biased toward energy generation over dissipation in non-level running

This study tested the hypothesis that skeletal muscles generate more mechanical energy in gait tasks that raise the center of mass compared to the mechanical energy they dissipate in gait tasks that lower the center of mass despite equivalent changes in total mechanical energy. Thirteen adults ran on a 10° decline and incline surface at a constant average velocity. Three-dimensional (3D) joint powers were calculated from ground force and 3D kinematic data using inverse dynamics. Joint work was calculated from the power curves and assumed to be due to skeletal muscle–tendon actuators. External work was calculated from the kinematics of the pelvis through the gait cycle. Incline vs. decline running was characterized with smaller ground forces that operated over longer lever arms causing larger joint torques and work from these torques. Total lower extremity joint work was 28% greater in incline vs. decline running (1.32 vs. −1.03 J/kg m, p<0.001). Total lower extremity joint work comprised 86% and 71% of the total external work in incline (1.53 J/kg m) and decline running (−1.45 J/kg m), which themselves were not significantly different ( p<0.180). We conjectured that the larger ground forces in decline vs. incline running caused larger accelerations of all body tissues and initiated a greater energy-dissipating response in these tissues compared to their response in incline running. The runners actively lowered themselves less during decline stance and descended farther as projectiles than they lifted themselves during incline stance and ascended as projectiles. These data indicated that despite larger ground forces in decline running, the reduced displacement during downhill stance phases limited the work done by muscle contraction in decline compared to incline running.

The landing–take-off asymmetry of human running is enhanced in old age

The landing-take-off asymmetry of running was thought to derive from, or at least to be consistent with, the physiological property of muscle to resist stretching (after landing) with a force greater than it can develop during shortening (before take-off). In old age, muscular force is reduced, but the deficit in force is less during stretching than during shortening. The greater loss in concentric versus eccentric strength with aging led us to hypothesize that older versus younger adults would increase the landing-take-off asymmetry in running. To test this hypothesis, we measured the within-step changes in mechanical energy of the centre of mass of the body in old and young subjects. The difference between the peaks in kinetic energy attained during the fall and during the lift of the centre of mass is greater in the old subjects. The difference between the time to lift and accelerate the centre of mass (positive work) and to absorb the same amount of energy during the downward displacement (negative work) is also greater in the old subjects. Both these findings imply a difference in force between stretching and shortening during the bounce, which is greater in the old subjects than in the young subjects. This is qualitatively consistent with the more asymmetric force-velocity relation found in aged muscle and supports, even if does not prove, the hypothesis that the landing-take-off asymmetry in running derives from the different response of muscle to stretching and shortening.

Dissociation Between Oxygen Uptake Drift During Severe Exercise And Changes In Running Mechanics

PURPOSE: The purpose of this study was to examine the relationship between changes in total mechanical energy (ME) and oxygen consumption during treadmill running in the severe intensity domain. METHODS: Seven subjects (3 males, 4 females) volunteered for this study (mean age ±SD = 25.4 ± 2.5 yrs; mass = 66.6 ±7.0 kg). After a separate familiarization session, subjects performed an incremental treadmill test to exhaustion (1% grade, speed increment = 0.5 mph per minute) from which the ventilatory threshold, respiratory compensation threshold, and peak VO2 were determined. On a subsequent day, subjects performed a constant speed treadmill run at a speed above the respiratory compensation threshold but below the speed at VO2 peak. During this run, gas exchange data was continuously recorded. In addition, 3-D kinematic data was captured over a 10 second epoch every 30 seconds using an 8-camera Motion Analysis system at 120 Hz. The total ME was calculated using the no transfer approach for a 13 segment anthropometric model. The total ME was calculated for each epoch was normalized to J/kg/m. After removing the first minute of the run data, both VO2 and ME were regressed against time within each subject. The slopes of the individual regressions were analyzed by constructing 95% confidence intervals around the mean slopes. In addition, the correlation between the VO2 and ME slopes was calculated. RESULTS: The mean ME slope was .0093 + 0.04 J/kg/m per min (95% CI = −0.26 − 0.045) and the mean VO2 slope was 74.3 + 94.8 mlO2 per min (95% CI = −13.4 - 161.9). The correlation between the ME and VO2 slopes was negative (r=−0.75, p =0.03), although was likely driven by the leverage associated with one subject with both the largest VO2 slope and the most negative ME slope. CONCLUSIONS: The results do not support the hypothesis that increases in oxygen consumption during severe intensity running at a constant speed are driven by changes in total mechanical energy.

Time-scale invariances in preseismic electromagnetic radiation, magnetization and damage evolution of rocks

Abstract. We investigate the time-scale invariant changes in electromagnetic and mechanical energy releases prior to a rock failure or a large earthquake. The energy release processes are caused by damage evolutions such as crack propagation, motion of charged dislocation, area-enlargement of sheared asperities and repetitive creep-rate changes. Damage mechanics can be used to represent the time-scale invariant evolutions of both brittle and plastic damages. Irreversible thermodynamics applied to the damage mechanics reveals that the damage evolution produces the variations in charge, dipole and electromagnetic signals in addition to mechanical energy release, and yields the time-scale invariant patterns of Benioff electromagnetic radiation and cumulative Benioff strain-release. The irreversible thermodynamic framework of damage mechanics is also applicable to the seismo-magnetic effect, and the time-scale invariance is recognized in the remanent magnetization change associated with damage evolution prior to a rock failure.

Muscles do more positive than negative work in human locomotion.

Muscle work during level walking and ascent and descent ramp and stairway walking was assessed in order to explore the proposition that muscles perform more positive than negative work during these locomotion tasks. Thirty four healthy human adults were tested while maintaining a constant average walking velocity in the five gait conditions. Ground reaction force and sagittal plane kinematic data were obtained during the stance phases of these gaits and used in inverse dynamic analyses to calculate joint torques and powers at the hip, knee and ankle. Muscle work was derived as the area under the joint power vs time curves and was partitioned into positive, negative and net components. Dependent t-tests were used to compare positive and negative work in level walking and net joint work between ascent and descent gaits on the ramp and stairs (P<0.010). Total negative and positive work in level walking was -34 J and 50 J, respectively, with the difference in magnitude being statistically significant (P<0.001). Level walking was therefore performed with 16 J of net positive muscle work per step. The magnitude of the net work in ramp ascent was 25% greater than the magnitude of net work in ramp descent (89 vs -71 J m(-1), P<0.010). Similarly, the magnitude of the net work in stair ascent was 43% greater than the magnitude of net work in stair descent (107 vs -75 J step(-1), P<0.000). We identified three potential causes for the reduced negative vs positive work in these locomotion tasks: (1) the larger magnitude of the accelerations induced by the larger ground reaction forces in descending compared to ascending gaits elicited greater energy dissipation in non-muscular tissues, (2) the ground reaction force vector was directed closer to the joint centers in ramp and stair descent compared to ascent, which reduced the load on the muscular tissues and their energy dissipating response, and (3) despite the need to produce negative muscle work in descending gaits, both ramp and stair descent also had positive muscle work to propel the lower extremity upward and forward into the swing phase movement trajectory. We used these data to formulate two novel hypotheses about human locomotion. First, level walking requires muscles to generate a net positive amount of work per gait cycle to overcome energy losses by other tissues. Second, skeletal muscles generate more mechanical energy in gait tasks that raise the center of mass compared to the mechanical energy they dissipate in gait tasks that lower the center of mass, despite equivalent changes in total mechanical energy.

Ability of the planar spring–mass model to predict mechanical parameters in running humans

The planar spring–mass model is a simple mathematical model of bouncing gaits, such as running, trotting and hopping. Although this model has been widely used in the study of locomotion, its accuracy in predicting locomotor mechanics has not been systematically quantified. We determined the percent error of the model in predicting 10 locomotor parameters in running humans by comparing the model predictions to experimental data from humans running in normal gravity and simulated reduced gravity. We tested the hypotheses that the model would overestimate horizontal impulse and the change in mechanical energy of the centre of mass (COM) during stance. The model provided good predictions of stance time, vertical impulse, contact length, duty factor, relative stride length and relative peak force. All predictions of these parameters were within 20% of measured values and at least 90% of predictions of each parameter were within 10% of measured values (median absolute errors: <7%). This suggests that the model incorporates all features of running humans that have a significant influence upon these six parameters. As simulated gravity level decreased, the magnitude of the errors in predicting each of these parameters either decreased or stayed constant, indicating that this is a good model of running in simulated reduced gravity. As hypothesised, horizontal impulse and change in mechanical energy of the COM during stance were overestimated (median absolute errors: 43.6% and 26.2%, respectively). Aerial time and peak vertical COM displacement during stance were also systematically overestimated (median absolute errors: 17.7% and 22.9%, respectively). Care should be taken to ensure that the model is used only to investigate parameters which it can predict accurately. It would be useful to extend this analysis to other species and gaits.

EFFECT OF WHEEL CAMBER ON MECHANICAL ENERGY AND POWER FLOW ANALYSIS OF THE UPPER EXTREMITY IN WHEELCHAIR PROPULSION

INTRODUCTION The wheel camber is an important parameter that affects wheelchair exercise. It has been suggested that minimization of energy cost is a primary determinant for selection of rear-wheel camber. Limited studies have taken into account the mechanical energy and power flow of upper extremity during wheelchair propulsion. In this study, we investigated the rates of change of mechanical energy (mechanical power) and power flow of upper limb for 0o and 15o wheel camber to see the effects of the wheel camber. We examined the difference between these two powers estimates to find the guidelines for the configuration of wheelchairs. The results may provide more insight of the metabolic difference between the different wheelchair cambers.

The landing–take-off asymmetry in human running

In the elastic-like bounce of the body at each running step the muscle-tendon units are stretched after landing and recoil before take-off. For convenience, both the velocity of the centre of mass of the body at landing and take-off, and the characteristics of the muscle-tendon units during stretching and recoil, are usually assumed to be the same. The deviation from this symmetrical model has been determined here by measuring the mechanical energy changes of the centre of mass of the body within the running step using a force platform. During the aerial phase the fall is greater than the lift, and also in the absence of an aerial phase the transduction between gravitational potential energy and kinetic energy is greater during the downward displacement than during the lift. The peak of kinetic energy in the sagittal plane is attained thanks to gravity just prior to when the body starts to decelerate downwards during the negative work phase. In contrast, a lower peak of kinetic energy is attained, during the positive work phase, due to the muscular push continuing to accelerate the body forwards after the end of the acceleration upwards. Up to a speed of 14 km h(-1) the positive external work duration is greater than the negative external work duration, suggesting a contribution of muscle fibres to the length change of the muscle-tendon units. Above this speed, the two durations (<0.1 s) are similar, suggesting that the length change is almost totally due to stretch-recoil of the tendons with nearly isometrically contracting fibres.

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.

Centre of mass movement and mechanical energy fluctuation during gallop locomotion in the Thoroughbred racehorse

During locomotion cyclical interchange between different forms of mechanical energy enhances economy; however, 100% efficiency cannot be achieved and ultimately some mechanical work must be performed de novo. There is a metabolic cost associated with fluctuations in mechanical energy, even in the most efficient animals. In this study we investigate the exchanges between different forms of mechanical energy involved in high-speed gallop locomotion in Thoroughbred race horses during over-ground locomotion using innovative, mobile data collection techniques. We use hoof-mounted accelerometers to capture foot contact times, a GPS data logger to monitor speed and an inertial sensor mounted over the dorsal spinous processes of the fourth to sixth thoracic vertebrae (the withers) of the horse to capture trunk movement with six degrees of freedom. Trunk movement data were used to estimate the movement of the centre of mass (CoM). Linear (craniocaudal, mediolateral and dorsoventral) and rotational (roll, pitch and heading) kinematic parameters (displacement, velocity and acceleration) were calculated for seven horses at gallop speeds ranging from 7 to 17 m s(-1) during their regular training sessions. These were used to estimate external mechanical energy (potential energy and linear kinetic energy of the CoM) as well as selected components of internal energy (angular kinetic energy). Elastic energy storage in the limbs was estimated from duty factor, sine wave assumptions and published leg stiffness values. External mechanical energy changes were dominated by changes in craniocaudal velocity. Potential energy change, which was in phase with craniocaudal energy during the front limb stances, was small. Elastic energy storage in the limbs was small compared to the overall amplitude of fluctuation of external mechanical energy. Galloping at high speeds does not therefore fit classical spring mass mechanics.

Experimentally Based Investigations on the Degradation-Process of Concrete Under Cyclic Load

In concrete structures fatigue can become relevant, when the construction is exposed to cyclic loads. For consideration of accompanying degradation processes also a large scatter of such variations have to be considered. For validation of already developed simulating models the mechanical degradation processes of concrete resulting from cyclic loads were studied experimentally within various cyclic tests on drilled cores. The attention was focused on the changes in the relevant properties of plain concrete. The main aim of these investigations was to get quantitative information about the changes in mechanical strength, stiffness and fracture energy caused by microcracks in the concrete structure during uniaxial cyclic loads. It could be proved, that during some few thousands of load-cycles microcracking already takes place to some extent, which mainly can be detected by changes in the dynamic E-modulus. However, it could also be determined, that the results measured in some repetition tests are varying within a large scatter.

Characterization of Watermarks Formed in Nano-Carpet Effect

In the spreading of a water droplet on an aligned silicon nanorod array surface, a precursor rim was detected moving ahead of the contact line. In this process, nanorods were bundled by the capillary force to form clusters, and a watermark developed on the surface after water evaporated. The size of the watermark, R(p)max, corresponding to the maximum radius of the precursor rim, followed a simple power law relationship with the volume of water droplet omega, R(p)max proportional to omega(beta). The scaling exponent beta increased when the nanorod height decreased, but all in the vicinity of 1/3. This behavior was attributed to the competition of evaporation and spreading of a water droplet during the spreading process. The size of the bundled nanorod cluster formed by the capillary force not only depended on the nanorod height but also on the location in the watermark. The cluster size almost remained as a constant near the center, and then it decreased with the distance from the center. This phenomenon can be qualitatively interpreted through the change of the total free energy during the precursor invading the nanorod array, by considering the contribution from the mechanical energy change due to the bending and clustering of nanorods.

Tuataras and salamanders show that walking and running mechanics are ancient features of tetrapod locomotion.

The lumbering locomotor behaviours of tuataras and salamanders are the best examples of quadrupedal locomotion of early terrestrial vertebrates. We show they use the same walking (out-of-phase) and running (in-phase) patterns of external mechanical energy fluctuations of the centre-of-mass known in fast moving (cursorial) animals. Thus, walking and running centre-of-mass mechanics have been a feature of tetrapods since quadrupedal locomotion emerged over 400 million years ago. When walking, these sprawling animals save external mechanical energy with the same pendular effectiveness observed in cursorial animals. However, unlike cursorial animals (that change footfall patterns and mechanics with speed), tuataras and salamanders use only diagonal couplet gaits and indifferently change from walking to running mechanics with no significant change in total mechanical energy. Thus, the change from walking to running is not related to speed and the advantage of walking versus running is unclear. Furthermore, lumbering mechanics in primitive tetrapods is reflected in having total mechanical energy driven by potential energy (rather than kinetic energy as in cursorial animals) and relative centre-of-mass displacements an order of magnitude greater than cursorial animals. Thus, large vertical displacements associated with lumbering locomotion in primitive tetrapods may preclude their ability to increase speed.

In vivo mechanical properties of the human Achilles tendon during one-legged hopping

Compliant tendons act as energy stores, which benefit the energetics and power output of a muscle-tendon unit. However the compliance of tendon and the material properties may vary between individuals and hence alter the energy storing capacity of the tendon. We aimed to determine the in vivo Achilles tendon (AT) stress and strain during one-legged hopping and hence the contribution of elastic recoil to mechanical energy changes. We simultaneously measured the length of the Achilles tendon from the muscle-tendon junction to the insertion on the calcaneous and the approximate AT force in ten male participants. The position of the muscle-tendon junction was determined using ultrasound images that were projected into three-dimensional space. Achilles tendon force was measured using inverse dynamics. The results demonstrated that one-legged hopping elicited high tendon strains and that the force-length relationship of the whole tendon is relatively linear, particularly at high strains. The stiffness, elastic modulus and hysteresis varied across the population (inter-quartile range of 145-231 N mm-1, 0.67-1.07 GPa and 17-35%, respectively). These values are within the reported biological range. An average of 38 J of energy was recovered from the elastic recoil of the tendon, which contributes 16% of the total average mechanical work of the hop (254 J). The high strains measured here (average peak strain was 8.3%) and in other studies may be possible due to the complex architecture of the Achilles tendon; however, prolonged hopping may well cause tendon damage. In conclusion, the properties of the elastic Achilles tendon can contribute significantly to the total mechanical work of the body during one-legged hopping; however, individual variation in the properties of the tendon vary the energy storing capacity of this structure.