Mechanical Energy Fluctuations Research Articles

Asymmetric bipedal locomotion--an adaptive response to incomplete spinal injury in the chick.

The purpose of this study was to compare the asymmetric gait induced by unilateral spinal cord injury in chicks with asymmetric gaits of other bipeds and quadrupeds. After lateral hemisection of the left thoracic spinal cord, kinetic (ground reaction forces) and kinematic (distance and timing) data were recorded as chicks moved overground unrestrained. Ground reaction forces were analyzed to obtain the mechanical energy changes throughout the stride. Kinematic measurements were obtained over a range of speeds to determine the velocity-dependent characteristics of the gait. Hemisected chicks adopted an asymmetric hopping gait in which the animals hopped from the right leg (contralateral to the lesion) onto the left (ipsilateral) leg but then fell forward onto the right leg. Mechanical energy fluctuations throughout a single stride (i.e., two steps) approximated the oscillations that occur during a single walking step of control animals. When examined over a range of velocities, asymmetries in limb timing remained constant, but distance measurements such as step length became more symmetric as speed increased. The results show that, after spinal hemisection, adaptations of the remaining neural circuitry permitted the production of a locomotor pattern that, in addition to providing effective support and propulsion, incorporated some of the energy-conserving mechanisms of the normal walk. Adjustment of this novel locomotor pattern for different velocities further demonstrates the flexibility of locomotor circuitry. Comparisons with other studies shows that this gait shares some temporal and energetic features with asymmetric gaits of several bipedal species, including humans. In particular, hemisected chicks and some hemiplegic humans adopt an asymmetric gait in which maximum energy recovery occurs during the stance of the affected limb; these similarities probably relate to common mechanical constraints imposed on bipedal forms of terrestrial locomotion.

Similarity in multilegged locomotion: Bouncing like a monopode

Despite impressive variation in leg number, length, position and type of skeleton, similarities of legged, pedestrian locomotion exist in energetics, gait, stride frequency and ground-reaction force. Analysis of data available in the literature showed that a bouncing, spring-mass, monopode model can approximate the energetics and dynamics of trotting, running, and hopping in animals as diverse as cockroaches, quail and kangaroos. From an animal's mechanical-energy fluctuation and ground-reaction force, we calculated the compression of a virtual monopode's leg and its stiffness. Comparison of dimensionless parameters revealed that locomotor dynamics depend on gait and leg number and not on body mass. Relative stiffness per leg was similar for all animals and appears to be a very conservative quantity in the design of legged locomotor systems. Differences in the general dynamics of gait are based largely on the number of legs acting simultaneously to determine the total stiffness of the system. Four- and six-legged trotters had a greater whole body stiffness than two-legged runners operating their systems at about the same relative speed. The greater whole body stiffness in trotters resulted in a smaller compression of the virtual leg and a higher natural frequency and stride frequency.

Mechanics of six-legged runners

Six-legged pedestrians, cockroaches, use a running gait during locomotion. The gait was defined by measuring ground reaction forces and mechanical energy fluctuations of the center of mass in Blaberus discoidalis (Serville) as they travelled over a miniature force platform. These six-legged animals produce horizontal and vertical ground-reaction patterns of force similar to those found in two-, four- and eight-legged runners. Lateral forces were less than half the vertical force fluctuations. At speeds between 0.08 and 0.66 ms-1, horizontal kinetic and gravitational potential energy changes were in phase. This pattern of energy fluctuation characterizes the bouncing gaits used by other animals that run. Blaberus discoidalis attained a maximum sustainable stride frequency of 13 Hz at 0.35 ms-1, the same speed and frequency predicted for a mammal of the same mass. Despite differences in body form, the mass-specific energy used to move the center of mass a given distance (0.9 J kg-1m-1) was the same for cockroaches, ghost crabs, mammals, and birds. Similarities in force production, stride frequency and mechanical energy production during locomotion suggest that there may be common design constraints in terrestrial locomotion which scale with body mass and are relatively independent of body form, leg number and skeletal type.

Locomotion Energetics of the Ghost Crab: II. Mechanics of the Centre of Mass During Walking and Running

ABSTRACT Terrestrial locomotion involving appendages has evolved independently in vertebrates and arthropods. Differences in the mechanical design of the locomotor apparatus could impose constraints on the energetics of locomotion. The mechanical energy fluctuations of the centre of mass of an arthropod, the ghost crab Ocvpode quadrata (Fabricius), were examined by integrating the ground reaction forces exerted during sideways locomotion. Crabs used a pendulum-type energy exchange mechanism during walking, analogous to an egg rolling end over end, with the same effectiveness as birds and mammals. Moreover, ghost crabs were found to have two running gaits. A switch from a slow to a fast run occurred at the same speed and stride frequency predicted for the trot-gallop transition of a quadrupedal mammal of the same body mass. In addition, the mass-specific mechanical energy developed over a unit distance was independent of speed and was within the limits measured for birds and mammals. Despite the obvious differences in mechanical design between crabs and mammals, energy-conserving mechanisms and the efficiency of locomotion were remarkably similar. These similarities may result from the fact that the muscles that generate forces during terrestrial locomotion have relatively conservative mechanical and energetic properties.

Stabilization of stokes pulse energies in the nonlinear regime of stimulated Raman scattering

An experimental study of quantum mechanical pulse energy fluctuations in stimulated Raman scattering from hydrogen is presented. The probability density function P( W) for Stokes pulse energy W is measured for highly transient scattering in both the linear and nonlinear gain regimes. While large pulse energy fluctuations (100%) occur in the linear gain regime, the fluctuations are reduced to about 20% in the nonlinear regime where the laser pulse is depleted significantly. The results are in excellent agreement with the theoretical predictions of Lewenstein.

Optimum walking techniques for quadrupeds and bipeds

A new theory is presented which describes quadrupedal as well as bipedal walking. It avoids errors which occurred in previous theories by evaluating separately the work done by each leg instead of deriving net work from mechanical energy fluctuations. It takes particular account of two parameters, the duty factor β (the fraction of the stride for which each foot is on the ground) and a parameter q which defines the time course of the force on each foot. It shows that for any given speed there is an optimum (β,q) which minimizes the energy cost of locomotion. These (β,q) are only a little different for bipeds and quadrupeds except near the critical speed at which the optimum moves abruptly from walking (high β) to running (low β). Walking men use (β, q) close to the theoretical optima, but with slightly higher q. Walking dogs and sheep use q which are lower than the optimum values except at very low speeds. Some of the energy which would otherwise be required for locomotion may be saved by storage of elastic strain energy in tendons etc. This mechanism is more effective in running than in fast walking, which may be why men change from walking to running at lower speeds than the inelastic theory suggests.

The American upper Ordovician standard; XV, Clay mineralogy of insoluble residues from Cincinnatian limestones, Hamilton County, Ohio

ABSTRACT Clays included in the insoluble residue from 35 limestones (biomicrosparrudites) collected from the Kope and Fairview Formations in Hamilton County, Ohio were qualitatively and quantitatively analyzed to determine possible variations which might reflect changes in source during deposition of these lithic units. Illite and chlorite-vermiculite are the only clay groups identified. Illite comprises from 75 to 99 percent of the total clay fraction and averages 95 to 93 percent with the Kope and Fairview limestones respectively. No significant change in the clay percentages within insoluble residues occur across the Kope-Fairview contact, nor is there any obvious correlation between the clay percentages and mechanical energy fluctuations which occur within these two formations. These resul s suggest no significant variation concerning the source(s) of these clays during Kope and Fairview sedimentation.