scholarly journals Mechanical work rate minimization and freely chosen stride frequency of human walking: a mathematical model

1992 ◽  
Vol 170 (1) ◽  
pp. 19-34 ◽  
Author(s):  
A. E. Minetti ◽  
F. Saibene
Keyword(s):  
Mathematical Model ◽  
Work Rate ◽  
The Body ◽  
Mechanical Work ◽  
Stride Frequency ◽  
External Work ◽  
High Speeds ◽  
Theoretical Predictions ◽  
Work Done ◽  
Good Agreement

The interplay between the work done to move the body centre of mass with respect to the environment (external work) and the work done to move the limbs with respect to the body (internal work) has been shown experimentally partially to determine the freely chosen stride frequency during walking. A mathematical model that estimates the two components of the mechanical work is proposed. The model, according to the criterion of work rate minimization (both positive and positive plus negative), is able to predict the natural stride frequency as a function of the average progression speed. The adequacy of the model and the validity of the assumptions have been checked against measurements of natural stride frequency in 11 subjects walking on a treadmill at several speeds (range 1–3 m s-1). Comparison with theoretical predictions shows good agreement with the minimization of positive work rate at low speeds, while at high speeds the stride frequency is better explained by the model for minimum positive plus negative work rate.

External work in walking

1963 ◽  
Vol 18 (1) ◽  
pp. 1-9 ◽  
Author(s):  
G. A. Cavagna ◽  
F. P. Saibene ◽  
R. Margaria
Keyword(s):  
Inertial Force ◽  
Center Of Gravity ◽  
The Body ◽  
External Work ◽  
High Speeds ◽  
Moving Body ◽  
Vertical Displacements ◽  
Lateral Displacements ◽  
Work Done ◽  
Static Contractions

From records obtained from a triple accelerometer applied to the trunk of a subject the displacements of the trunk in vertical, forward, and lateral directions have been calculated. With motion pictures taken simultaneously, displacements of the center of gravity within the body were measured. From these data the external mechanical work of walking was calculated. The sum of work for vertical and for forward displacements of the center of gravity of the body gives the total external work; energy for the lateral displacements was negligible. Total external work appears to be lower than that calculated from the vertical displacements alone, because work done in lifting is partly sustained by the inertial force of the forward-moving body. Total external work reaches a highest value (0.1 kcal/km kg) at the most economical speed of walking, 4 km/hr, which corresponds to an energy consumption of 0.48 kcal/km kg. At this speed the internal work appears negligible; it amounts to appreciable entities at very low speeds because of the static contractions of the muscles, and at high speeds because of considerable stiffening of the limbs and movements not involving a displacement of the center of gravity. Submitted on May 25, 1962

scholarly journals Mechanical determinants of the minimum energy cost of gradient running in humans.

1994 ◽  
Vol 195 (1) ◽  
pp. 211-225 ◽  
Author(s):  
A E Minetti ◽  
L P Ardigò ◽  
F Saibene
Keyword(s):  
Human Subjects ◽  
Minimum Energy ◽  
Metabolic Cost ◽  
The Body ◽  
Mechanical Work ◽  
Stride Frequency ◽  
Centre Of Mass ◽  
Negative Part ◽  
External Work ◽  
Level Running

The metabolic cost and the mechanical work of running at different speeds and gradients were measured on five human subjects. The mechanical work was partitioned into the internal work (Wint) due to the speed changes of body segments with respect to the body centre of mass and the external work (Wext) due to the position and speed changes of the body centre of mass in the environment. Wext was further divided into a positive part (W+ext) and a negative part (W-ext), associated with the energy increases and decreases, respectively, over the stride period. For all constant speeds, the most economical gradient was -10.6 +/-0.5% (S.D., N = 5) with a metabolic cost of 146.8 +/- 3.8 ml O2 kg-1 km-1. At each gradient, there was a unique W+ext/W-ext ratio (which was 1 in level running), irrespective of speed, with a tendency for W-ext and W+ext to disappear above a gradient of +30% and below a gradient of -30%, respectively. Wint was constant within each speed from a gradient of -15% to level running. This was the result of a nearly constant stride frequency at all negative gradients. The constancy of Wint within this gradient range implies that Wint has no role in determining the optimum gradient. The metabolic cost C was predicted from the mechanical experimental data according to the following equation: [formula: see text] where eff- (0.80), eff+ (0.18) and effi (0.30) are the efficiencies of W-ext, W+ext and Wint, respectively, and el- and el+ represent the amounts of stored and released elastic energy, which are assumed to be 55J step-1. The predicted C versus gradient curve coincides with the curve obtained from metabolic measurements. We conclude that W+ext/W-ext partitioning and the eff+/eff- ratio, i.e. the different efficiency of the muscles during acceleration and braking, explain the metabolic optimum gradient for running of about -10%.

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

2001 ◽  
Vol 124 (2) ◽  
pp. 398-405 ◽  
Author(s):  
S. Yoshimoto ◽  
S. Oshima ◽  
S. Danbara ◽  
T. Shitara
Keyword(s):  
High Speed ◽  
Water Pressure ◽  
Rotating Shaft ◽  
Pressurized Water ◽  
High Speeds ◽  
Theoretical Predictions ◽  
The Stability ◽  
Stability Of Water ◽  
Spiral Grooves ◽  
Good Agreement

In this paper, the stability of water-lubricated, hydrostatic, conical bearings with spiral grooves for high-speed spindles is investigated theoretically and experimentally. In these bearing types, pressurized water is first fed to the inside of the rotating shaft and then introduced into spiral grooves through feeding holes located at one end of each spiral groove. Therefore, water pressure is increased due to the effect of the centrifugal force at the outlets of the feeding holes, which results from shaft rotation. In addition, water pressure is also increased by the viscous pumping effect of the spiral grooves. The stability of the proposed bearing is theoretically predicted using the perturbation method, and calculated results are compared with experimental results. It was consequently found that the proposed bearing is very stable at high speeds and theoretical predictions show good agreement with experimental data.

Energy expenditure while performing gymnastic-like motion in spacelab during spaceflight: case study

2006 ◽  
Vol 31 (5) ◽  
pp. 631-634 ◽  
Author(s):  
Masahiro Kaneko ◽  
Kazuki Miyatsuji ◽  
Satoru Tanabe
Keyword(s):  
Energy Expenditure ◽  
Control Subject ◽  
Center Of Mass ◽  
Mechanical Efficiency ◽  
Video Camera ◽  
The Body ◽  
Mechanical Work ◽  
Whole Body ◽  
Total Power ◽  
External Work

To estimate energy cost of a gymnastic-like exercise performed by an astronaut during spaceflight (cosmic exercise), energy expenditure was determined by measuring mechanical work done around the center of mass (COM) of the body. The cosmic exercise, which consisted of whole-body flexion and extension, was performed during a spaceflight and recorded with a video camera. By analyzing the videotape, the internal mechanical work (Wint) against inertia load of the body segments was calculated. To compare how human muscles work on Earth, a motion similar to the cosmic exercise was performed by a control subject who had a physique similar to that of the astronaut. The total mechanical power of the astronaut was determined to be about 119 W; although the control subject showed a similar total power value, half of the power was external work (Wext) against gravitational load. By assuming a mechanical efficiency of 0.25, the energy expenditure was estimated to be 476 W or 7.7 W/kg, which is equivalent to that expended during fast walking and half of that used during moderate-speed running. Our results suggest that this form of cosmic exercise is appropriate for astronauts in space and can be performed safely, as there are no COM shifts while floating in a spacecraft and no vibratory disturbance.

MODELING SELECTION AND EXTINCTION MECHANISMS OF BIOLOGICAL SYSTEMS

2011 ◽  
Vol 22 (07) ◽  
pp. 669-686 ◽  
Author(s):  
ADIL AMIRJANOV
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Biological Systems ◽  
Selection Mechanism ◽  
Evolutionarily Stable Strategies ◽  
Animal Group ◽  
Theoretical Predictions ◽  
Evolutionarily Stable ◽  
Good Agreement

In this paper, the behavior of a genetic algorithm is modeled to enhance its applicability as a modeling tool of biological systems. A new description model for selection mechanism is introduced which operates on a portion of individuals of population. The extinction and recolonization mechanism is modeled, and solving the dynamics analytically shows that the genetic drift in the population with extinction/recolonization is doubled. The mathematical analysis of the interaction between selection and extinction/recolonization processes is carried out to assess the dynamics of motion of the macroscopic statistical properties of population. Computer simulations confirm that the theoretical predictions of described models are in good approximations. A mathematical model of GA dynamics was also examined, which describes the anti-predator vigilance in an animal group with respect to a known analytical solution of the problem, and showed a good agreement between them to find the evolutionarily stable strategies.

A mathematical model of body kinematics in swimming tadpoles

1993 ◽  
Vol 71 (2) ◽  
pp. 407-413 ◽  
Author(s):  
W. M. Oxner ◽  
J. Quinn ◽  
M. E. DeMont
Keyword(s):  
Mathematical Model ◽  
Resonant Frequency ◽  
The Body ◽  
Numerical Techniques ◽  
Cross Sectional ◽  
Finite Dimensional ◽  
Straight Line ◽  
Locomotor Muscles ◽  
Variable Moment ◽  
Good Agreement

A mathematical model is described that predicts the body kinematics of tadpoles swimming in a straight line at constant velocity. The model is a forced beam with a variable moment of inertia and cross-sectional area. The beam is free at both ends and forced cyclically at the position that corresponds to the base of the tail in a real animal. This forcing regime simulates the real contraction of locomotor muscles. Finite-dimensional numerical techniques were used to approximate the solution. The lowest predicted fundamental frequency of vibration should be the resonant frequency of vibration of the tadpole. The predicted resonant frequency and the observed swimming frequencies were in good agreement.

scholarly journals Kinematics of male Eupalaestrus weijenberghi (Araneae, Theraphosidae) locomotion on different substrates and inclines

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7748 ◽  
Author(s):  
Valentina Silva-Pereyra ◽  
C Gabriel Fábrica ◽  
Carlo M. Biancardi ◽  
Fernando Pérez-Miles
Keyword(s):  
The Body ◽  
Mechanical Work ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Time Lags ◽  
External Work ◽  
Gait Patterns ◽  
Unit Distance ◽  
Body Segments ◽  
Gait Parameters

Background The mechanics and energetics of spider locomotion have not been deeply investigated, despite their importance in the life of a spider. For example, the reproductive success of males of several species is dependent upon their ability to move from one area to another. The aim of this work was to describe gait patterns and analyze the gait parameters of Eupalaestrus weijenberghi (Araneae, Theraphosidae) in order to investigate the mechanics of their locomotion and the mechanisms by which they conserve energy while traversing different inclinations and surfaces. Methods Tarantulas were collected and marked for kinematic analysis. Free displacements, both level and on an incline, were recorded using glass and Teflon as experimental surfaces. Body segments of the experimental animals were measured, weighed, and their center of mass was experimentally determined. Through reconstruction of the trajectories of the body segments, we were able to estimate their internal and external mechanical work and analyze their gait patterns. Results Spiders mainly employed a walk-trot gait. Significant differences between the first two pairs and the second two pairs were detected. No significant differences were detected regarding the different planes or surfaces with respect to duty factor, time lags, stride frequency, and stride length. However, postural changes were observed on slippery surfaces. The mechanical work required for traversing a level plane was lower than expected. In all conditions, the external work, and within it the vertical work, accounted for almost all of the total mechanical work. The internal work was extremely low and did not rise as the gradient increased. Discussion Our results support the idea of considering the eight limbs functionally divided into two quadrupeds in series. The anterior was composed of the first two pairs of limbs, which have an explorative and steering purpose and the posterior was more involved in supporting the weight of the body. The mechanical work to move one unit of mass a unit distance is almost constant among the different species tested. However, spiders showed lower values than expected. Minimizing the mechanical work could help to limit metabolic energy expenditure that, in small animals, is relatively very high. However, energy recovery due to inverted pendulum mechanics only accounts for only a small fraction of the energy saved. Adhesive setae present in the tarsal, scopulae, and claw tufts could contribute in different ways during different moments of the step cycle, compensating for part of the energetic cost on gradients which could also help to maintain constant gait parameters.

scholarly journals How zebrafish turn: analysis of pressure force dynamics and mechanical work

2020 ◽  
Vol 223 (16) ◽  
pp. jeb223230
Author(s):  
Robin Thandiackal ◽  
George V. Lauder
Keyword(s):  
The Body ◽  
Mechanical Work ◽  
Body Region ◽  
Fish Locomotion ◽  
Force Dynamics ◽  
Negative Work ◽  
Image Velocimetry ◽  
Work Done ◽  
Swimming Kinematics ◽  
Posterior Body Region

ABSTRACTWhereas many fishes swim steadily, zebrafish regularly exhibit unsteady burst-and-coast swimming, which is characterized by repeated sequences of turns followed by gliding periods. Such a behavior offers the opportunity to investigate the hypothesis that negative mechanical work occurs in posterior regions of the body during early phases of the turn near the time of maximal body curvature. Here, we used a modified particle image velocimetry (PIV) technique to obtain high-resolution flow fields around the zebrafish body during turns. Using detailed swimming kinematics coupled with body surface pressure computations, we estimated fluid–structure interaction forces and the pattern of forces and torques along the body during turning. We then calculated the mechanical work done by each body segment. We used estimated patterns of positive and negative work along the body to evaluate the hypothesis (based on fish midline kinematics) that the posterior body region would experience predominantly negative work. Between 10% and 20% of the total mechanical work was done by the fluid on the body (negative work), and negative work was concentrated in the anterior and middle areas of the body, not along the caudal region. Energetic costs of turning were calculated by considering the sum of positive and negative work and were compared with previous metabolic estimates of turning energetics in fishes. The analytical workflow presented here provides a rigorous way to quantify hydrodynamic mechanisms of fish locomotion and facilitates the understanding of how body kinematics generate locomotor forces in freely swimming fishes.

scholarly journals The power of cycling

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Steve Stannard ◽  
Paul Macdermaid ◽  
Matthew Miller
Keyword(s):  
Physiological Stress ◽  
Work Rate ◽  
Training Intensity ◽  
External Work ◽  
Cycling Exercise ◽  
Technological Advances ◽  
External Power ◽  
Relationship Of ◽  
Work Done ◽  
The Relationship

<p>One of the advantages of cycling exercise is that the rider is interfaced to a machine, and this exercise can be easily metered. Recent technological advances have made this metering easier and cheaper such that riders, sports scientists and coaches are able to record the external work done, and thus the net rate of mechanical work (power) during training and racing. Since external power is related to performance, the power requirements of competition can be observed and the training intensity can be prescribed. However, the ability to closely scrutinize power during training brings about a number of issues which need to be addressed. These issues include the accuracy and reliability of the meter, the relationship of the external work rate to the total physiological stress, and how training prescription through analysis by power may change the athlete-coach relationship. </p>

Force platforms as ergometers

1975 ◽  
Vol 39 (1) ◽  
pp. 174-179 ◽  
Author(s):  
G. A. Cavagna
Keyword(s):  
Body Weight ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Force Plate ◽  
Vertical Displacement ◽  
The Body ◽  
Mechanical Work ◽  
Vertical Force ◽  
External Work ◽  
Total Mechanical Energy

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.

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