Human hopping on damped surfaces: strategies for adjusting leg mechanics

Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.     

Weinbergina,a xiphosuran arthropod from the devonian hunsrück slate

Weinbergina is the first synziphosurid in which ventral appendages have been found. It is so far unique among chelicerates in having six pairs of prosomal legs in addition to the chelicerae. This indicates that the pregeni tal segment with the last pair of walking legs, corresponding to the chilaria ofLimulus, must be counted with the prosoma. The first interpretation of the opisthosomal appendages is given. They appear to be plate-like and to combine the presence of lamellar gills of limulid type with flattened spines (so called gill filaments) of trilobitomorph type.Weinbergina apparently was adapted for a life on soft substrate but not for burrowing.     

Purification and localization of p10, a novel protein that increases in nymphal regenerating legs of Periplaneta americana (American cockroach).

Content of a protein with a molecular mass of 10 kDa (p10) was found to increase significantly in regenerating legs of the American cockroach (Periplaneta americana). This protein was purified to homogeneity from a homogenate of regenerating legs. Partial amino acid sequencing indicated that p10 is a novel protein. Immunoblotting showed that its content in regenerating legs was 30 times that in normal legs, and decreased significantly when leg regeneration was complete. An immunofluorescence study revealed that p10 localizes exclusively on the external side of newly formed epidermis of regenerating legs.     

A model of bipedal locomotion on compliant legs.

Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.     

An Experimental Study on the Gait Patterns and Kinematics of Chinese Mitten Crabs

Despite the many studies on eight-legged animals and the importance of their mechanics of terrestrial locomotion, the mechanical energy of crabs in voluntary locomotion on uneven, unpredictable terrain surfaces has received little attention thus far. In this paper, motion video images of Chinese mitten crab (Eriocheir sinensis Milne-Edwards) locomotion on five types of terrains were recorded using a high-speed three-dimensional (3D) recording video system. The typical variables of locomotion such as gait patterns, duty factor, mechanical energy of the mass center, mass-specific rate of the total mechanical power of the mass center, and percentage recovery, were analyzed. Results show that the Chinese mitten crab uses random gaits instead of the alternating tetrapod gait with the increasing terrain roughness. The duty factors of the rows of the leading legs are greater for all terrains than those of the rows of the trailing legs. On smooth terrain, the duty factors of the rows of the trailing legs are greater than that on rough terrains. Kinematic measurements and calculations reveal that similar to mammals, birds, and arthropods, the Chinese mitten crab uses two fundamental gaits to save mechanical energy: the inverted pendulum gait and the bouncing gait. The bouncing gait is the main pattern of mechanical energy conservation. The low probability of injury and energy expenditure due to adaptations to various terrains induce the Chinese mitten crab to modify the mass-specific rate of the total mechanical power of the mass center. The statistical results of percentage recovery also reveal that the Chinese mitten crab has lower energy recovery efficiency over rough terrains compared with smooth terrains.     

Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadruped

Limb design is well conserved among quadrupeds, notably, the knees point forward (i.e. cranial inclination of femora) and the elbows point back (i.e. caudal inclination of humeri). This study was undertaken to examine the effects of joint orientation on individual leg forces and centre of mass dynamics. Steady-speed trotting was simulated in two quadrupedal models. Model I had the knee and elbow orientation of a quadruped and model II had a reversed leg configuration in which knees point back and elbows point forward. The model's legs showed directional compliance determined by the orientation of the knee/elbow. In both models, forward pointing knees/elbows produced a propulsive force bias, while rearward pointing knees/elbows produced a braking force bias. Hence, model I showed the same pattern of hind-leg propulsion and fore-leg braking observed in trotting animals. Simulations revealed minimal pitch oscillations during steady-speed trotting of model I, but substantially greater and more irregular pitch oscillations of model II. The reduced pitch oscillation of model I was a result of fore-leg and hind-leg forces that reduced pitching moments during early and late stance, respectively. This passive mechanism for reducing pitch oscillations was an emergent property of directionally compliant legs with the fore-hind configuration of model I. Such intrinsic stability resulting from mechanical design can simplify control tasks and lead to more robust running machines.     

Within-season reproductive and somatic energy allocation in a freshwater clam,Anodonta piscinalis

The effect of a change in the environment on reproductive and somatic energy allocation in an iteroparous freshwater clam Anodonta piscinalis was studied at different time of the seasonal reproductive cycle. Environmental change was produced by reciprocal transplant experiments among sites of varying productivity. In addition, clams were caged at high density to reduce the availability of resources. Transplanting females before fertilization (from May to June), or during the early development of the brood (from July to August) had no detectable effect on reproductive output. Early-season environment, however, affected body mass and percent fat content of females from two populations. This suggests that maintaining the level of reproductive allocation when resources are reduced early in the season leads to lower allocation to somatic growth and biochemical storage. Transplanting females late in the season (from September to November) had a substantial effect on reproductive output and body mass, but not on fat content, suggesting that late in the season allocation to biochemical energy storage is important. Hence, late in the season reproductive allocation may be adjusted to prevailing conditions in preparation for winter. Indeed, over-wintering site had a significant effect on percent fat content, body mass and shell growth when females were kept in a new environment from September to March. Variation among transplant sites in female body mass matched the estimated productivity of the sites, suggesting that it occurred in response to differences in the productivity of the habitats. The results emphasize the importance of taking seasonal changes in the priorities of energy allocation and the seasonality of reproductive processes into account when developing or testing models of optimal energy allocation.     

Form in the context of function: Fundamentals of an energy effective striding walk,the role of the plantigrade foot and its expected size

What morphological and functional factors allow for the unique and characteristic upright striding walk of the hominin lineage? Predictive models of locomotion that arise from considering mechanisms of energy loss indicate that collision-like losses at the transition between stance limbs are important determinants of bipedal gait. Theoretical predictions argue that these collisional losses can be reduced by having “functional extra legs” which are physically the heel and the toe part of a single anatomical foot. The ideal spacing for these “functional legs” are up to a quarter of a stride length, depending on the model employed. We evaluate the foot in the context of the dynamics of a bipedal system and compare predictions of optimal foot size against empirical data from modern humans, the Laetoli footprint trackways, and chimpanzees walking bipedally. The dynamics-based modeling approach provides substantial insight into how, and why, walking works as it does, even though current models are too simple to make predictions at a level adequate to anticipate specific morphology except at the most general level.     

Effect of strength training and the practice of Alpine skiing on bone mass density, growth, body composition, and the strength and power of the legs of adolescent skiers

This work examines the influence of practicing strength training and Alpine skiing over 2 years on bone mineral density (BMD), growth, body composition, and the strength and power of the legs of adolescent skiers. The study subjects were 20 adolescent skiers (10 girls and 10 boys) and 19 sedentary adolescents (9 girls and 10 boys), all 13-16 years of age. The BMDs of the lumbar column (L2-L4) and hip (neck of the femur, trochanter, and Ward's triangle) were determined by dual x-ray photon absorptiometry at the beginning and end of the experimental period. The increase in height and the percentage fat and muscular masses of the subjects were also recorded, as was their ability to jump (countermovement jump [CMJ]), their leg strength and power (squat test), and their leg anaerobic power (continuous jump test [CMJ15″]). No significant differences were seen in the increase in height, body weight, or percentage fat mass between the skiers and sedentary subjects, although the boy skiers showed a significant increase in percentage muscular mass (p < 0.05) compared to the sedentary boys. The improvement in the values of the different CMJ variables was significantly greater among the boy skiers than among the sedentary boys (p < 0.001-0.01). The same was true for the girls (p < 0.001), except for CMJ15″. The skiers experienced a significantly greater increase in L2-L4 BMD than the sedentary subjects (boys p < 0.05; girls p < 0.01). These results suggest that Alpine skiing combined with rational strength training involves no special risk for the physical development of young people, has a positive effect on the power and the percentage of muscle mass in the legs, and helps to have a higher bone density in the lumbar spine (L2-L4).     

Relationships between legs bone mineral density, anthropometry and jumping height in prepubertal children

The aim of this study was to determine how the legs bone mineral density (BMD) is influenced by anthropometry and vertical jumping height in prepubertal children. In total, 64 8-11-year-old schoolchildren (27 boys and 37 girls) were studied. All children were at Tanner stage 1. The subjects' height and body mass were measured and BMI calculated. The following anthropometric parameters directly connected with leg were measured: skinfolds--front thigh and medial calf girths--gluteal, thigh, mid-thigh, calf and ankle; lengths--iliospinale height, trochanterion height, trochanteriontibiale laterale, tibiale-laterale height and tibiale mediale-spyrion tibiale; and breadths--biiliocristal, foot length and biepicondylar femur. Total body and legs fat mass and fat %, lean body mass (LBM) and both legs BMD were measured by DXA. Maximal jumping height was measured on the contact mat. Stepwise multiple regression analysis indicated that body height in boys (54.6%; R2 x 100) and body mass in girls (57.3%) were the most important basic anthropometric parameters that influenced BMD in legs. From the measured skinfolds, that of the front thigh characterized legs BMD by 24.9-35.6%. From the girths, the most important parameter to characterize legs BMD was that of calf (50.0-59.1%). Tibiale laterale height was the only length parameter which was highly related with legs BMD (51.1-54.5%). Biepicondylar femur was the most important breadth parameter which characterized legs BMD (51.0-54.8%). Femur breadth and tibiale-laterale height were selected (68.7%) in boys, and tibiale-laterale height and front thigh skinfold thickness (66.0%) in girls when all measured leg anthropometric parameters were analyzed together. From the body composition parameters, the most important parameter to characterize legs BMD was legs LBM (48.9-59.5%). Jumping height did not correlate with legs BMD in any studied groups. In summary, the present study demonstrated that legs LBM together with tibiale-laterale height are the main predictors of legs BMD in prepubertal children.     

A model analysis of internal loads, energetics, and effects of wobbling mass during the whole-body vibration

The internal loads, energetics, and the effects of wobbling mass during the whole-body vibration are studied in terms of analysis and comparison of two models: one is a system of four degrees-of-freedom with rigid and wobbling masses in both lower body and upper body (Model A), while the other one (Model B) is a system of three degrees-of-freedom with a rigid upper body and is otherwise identical to Model A. The main findings are the following: (1) The wobbling mass in the upper body is able to reduce the total internal load on the rigid mass of the upper body considerably. (2) "Partial" internal loads on a certain part of the body may be even larger than the total load on the same part of the body because of the phase differences among the partial loads. Therefore, a full consideration of safety during the whole-body vibration has to take not only the total, but also all the partial internal loads into account. (3) The fluctuation of power input and the fluctuation of mechanical energy could be much larger than the fluctuation of dissipation rate. (4) For frequencies higher than the resonance frequency range, the amplitude of the oscillation of the centre of mass of the body is so reduced that only the change of elastic potential energy dominates in the change of mechanical energy. Thus, a simple picture of energy flow is obtained as follows: for approximately one half of the oscillation period, the energy flows from the vibrator into the human body and is mainly stored in the muscle-tendon system, while for the remaining approximate half of the period, the energy flows from the muscle-tendon system back to the vibrator with a slightly smaller amount because a small part of the flown-in energy has been dissipated.     

ADAPTATION, CONSTRAINT, AND COMPROMISE IN AVIAN POSTNATAL DEVELOPMENT

1. This paper discusses factors that influence the evolution of growth rate and determine its variation among species of birds. Growth rate is related to evolutionary fitness through the use of time, energy, and nutrients. In addition, balances between factors favouring rapid growth and those favouring slow growth may be investigated directly by experiment and by comparative observation. 2. David Lack (1968) proposed that the growth rate of the young is the optimum balance between selection for rapid growth to reduce the vulnerable period of development and selection for slow growth to reduce the energy requirements of the young. 3. To test Lack's hypothesis, the growth rates of birds, estimated by fitting sigmoid equations to curves relating weight to age, were surveyed widely from the literature. Among all species examined, growth rate was inversely related to adult weight. Among birds of similar size, most variation in growth rate was related to the degree of maturity of the neonate. Altricial chicks, which depend upon their parents for food and warmth, grow more rapidly than precocial chicks, which are self-sufficient shortly after hatching. Lack's hypothesis, which predicts a direct relationship between growth rate and mortality rate, was not supported. 4. I propose that the key to understanding variation in growth rate among birds lies in the balance between rate of cell proliferation or cell growth, on one hand, and acquisition of mature function, on the other. This idea is consistent with principles of cellular and developmental biology. It is supported by comparisons of (a) the neonates of different species, (b) the individual over the course of the developmental period, and (c) tissues whose use is acquired at different stages of development, wherein more mature individuals or tissues grow more slowly than those with less developed function. 5. Species of birds that are classified as semi-precocial develop precocially but grow rapidly. Although these seemingly violate the general rule relating growth rate to precocity, a closer inspection of their development reveals that they too support the rule. In the Common Tern, the legs, which are the key organ in precocial development, grow at the expected slow rate. The body as a whole grows rapidly because the growth increment of the legs is small and their growth is completed quickly. 6. Growth rates of precocial birds do not decrease abruptly at hatching. This points more to gradual tissue differentiation than to the pattern of procurement and allocation of energy as the primary control for growth rate. 7. Precocious development is favoured when the chicks are capable of self-feeding or when food supplies are distant from the next site and travelling time between one and the other is long. Precocity of the neonates frees both parents to feed at a distant food source. 8. Some species having diets with low levels of protein or other nutrients may grow slowly in order to match nutrient requirements to their availability in the diet. This pattern is indicated especially among the Procellariiformes, which feed an oily diet to their young, and also among tropical fruit-eating birds. 9. Some tropical, pelagically-feeding sea-birds that rear only one offspring at a time may not be able to procure food sufficient to support rapid chick growth. Alternative explanations for slow growth among these species include difficulty in obtaining essential nutrients and more precocious development of activity than in related species having more rapid growth.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Experimental Studies and Dynamics Modeling Analysis of the Swimming and Diving of Whirligig Beetles (Coleoptera: Gyrinidae)

Whirligig beetles (Coleoptera, Gyrinidae) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle''s legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots.     

Mechanics of posture and gait of some large dinosaurs

Dimensions of dinosaur bones and of models of dinosaurs have been used as the basis for calculations designed to throw light on the posture and gaits of dinosaurs.
Estimates of the masses of some dinosaurs, obtained from the volumes of models, are compared with previous estimates. The positions of dinosaurs' centres of mass, derived from models, show that some large quadrupedal dinosaurs supported most of their weight on their hind legs and were probably capable of rearing up on their hind legs.
Distributions of bending moments along the backs of large dinosaurs are derived from measurements on models. The tensions required in epaxial muscles to enable Diplodocus to stand are calculated. It is likely that the long neck of this dinosaur was supported by some structure running through the notches in the neural spines of its cervical and dorsal vertebrae. The nature of this hypothetical structure is discussed.
An attempt is made to reconstruct the walking gait of sauropod dinosaurs, from the pattern of footprints in fossil tracks.
The dimensions of dinosaur leg bones are compared to predictions for mammals of equal body mass, obtained by extrapolation of allometric equations. Their dimensions are also used to calculate a quantity which is used as an indicator of strength in bending. Comparisons with values for modern animals lead to speculations about the athletic performance of dinosaurs.
Estimates of pressures exerted on the ground by the feet of dinosaurs are used in a discussion of the ability of dinosaurs to walk over soft ground.     

Apolipoprotein structural organization in high density lipoproteins: belts, bundles, hinges and hairpins

PURPOSE OF REVIEW: To summarize recent advances towards an understanding of the three-dimensional structures of the apolipoprotein components of HDL with a specific focus on high resolution models of apolipoprotein A-I. RECENT FINDINGS: Since the primary sequence was first reported, various models have been advanced for the structure of apolipoprotein A-I, the major protein constituent of HDL, in its lipid-free and lipid-bound forms. Unfortunately, the generation of experimental data capable of distinguishing among the competing models has lagged far behind. However, recent experimental strategies, including X-ray crystallography, applications of resonance energy transfer and mass spectrometry, have combined with sophisticated theoretical approaches to develop three-dimensional structural models of apolipoprotein A-I with previously unavailable resolution. SUMMARY: The recent synergy of sophisticated computer modeling techniques with hard experimental data has generated new models for apolipoprotein A-I in certain subclasses of HDL produced in vitro. The challenge now is to adapt and test these models in the more complex forms of HDL isolated directly from human plasma.     

The simplest walking model: stability, complexity, and scaling.

We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.     

Coordination in vertical jumping

The present study was designed to investigate for vertical jumping the relationships between muscle actions, movement pattern and jumping achievement. Ten skilled jumpers performed jumps with preparatory countermovement. Ground reaction forces and cinematographic data were recorded. In addition, myoelectric activity (EMG) was recorded from seven leg muscles. EMG-signals were rectified and low-pass filtered to obtain EMG-levels. The latter, which were assumed to reflect activation levels, rose to a plateau in the sequence m. semitendinosus, long head of m. biceps femoris, m. gluteus maximus, m. vastus medialis, m. rectus femoris, m. soleus, m. gastrocnemius. It was attempted to link the EMG-pattern to the purpose of the push-off, namely to maximize the effective energy (Ey) of the mass center of the body (MCB). The term Ey designates the sum of the potential energy of MCB and the kinetic energy due to the vertical velocity of MCB. One of the requirements for maximization of Ey is that the mono-articular extensor muscles release as much energy as possible before toe-off occurs. It is argued that this requirement can only be satisfied if the vertical velocity differences between the proximal and distal ends of body segments reach their peaks in a sequence. The sequence that is realized by the pattern of muscular activation is upper body, upper legs, lower legs, feet. Another important requirement is that the mechanical energy released by the muscles is optimally used. This requirement can be satisfied by transportation of energy via the biarticular m. rectus femoris and m. gastrocnemius.     

Locomotion and bone strength of the white rhinoceros, Ceratotherium simum

Measurements have been made, of lengths and of geometric properties of cross-sections, of the long bones of the legs of a young white rhinoceros of about 750 kg body mass. These are considered in conjunction with data from film of white rhinoceros trotting and galloping. The stresses developed in the bones in running are rather low, in comparison with other large mammals, suggesting that rhinoceros skeletons may be built to unusually high factors of safety. The long, relatively straight legs of elephants (whose bones experience higher stresses) are contrasted with the shorter, less straight legs of the other graviportal mammals.