scholarly journals The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
J R Usherwood
Keyword(s):  
Potential Energy ◽  
Industrial Revolution ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Phase Fluctuation ◽  
Vertical Axis ◽  
The Body ◽  
Mechanical Work ◽  
Gravitational Potential Energy ◽  
Pull Out

Synopsis Animal legs are diverse, complex, and perform many roles. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy. This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only—effectively a wheel-like translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? In order to approach this question, various linkages described during the industrial revolution are considered. Watt’s linkage provides an analogue for sprawled vertebrates that uses diagonal limb support and shows how vertical-axis joints could enable approximately straight-line horizontal translation while demanding minimal mechanical power. An additional vertical-axis joint per leg results in the wall-mounted pull-out monitor arm and would enable translation with zero mechanical work due to weight support, without tipping or toppling. This is consistent with force profiles observed in tortoises. The Peaucellier linkage demonstrates that parasagittal limbs with lateral-axis joints could also achieve the zero-work strategy. Suitably tuned four-bar linkages indicate this is feasibly approximated for flexed, biologically realistic limbs. Where “walking” gaits typically show out of phase fluctuation in center of mass kinetic and gravitational potential energy, and running, hopping or trotting gaits are characterized by in-phase energy fluctuations, the zero limb-work strategy approximated by tortoises would show zero fluctuations in kinetic or potential energy. This highlights that some gaits, perhaps particularly those of animals with sprawled or crouched limbs, do not fit current kinetic gait definitions; an additional gait paradigm, the “zero limb-work strategy” is proposed.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

Mechanics of locomotion in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2177-2188 ◽  
Author(s):  
C T Farley ◽  
T C Ko
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Gravitational Potential Energy ◽  
Lateral Bending ◽  
Walking Gait ◽  
Bending Force

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

scholarly journals Use of Lumbar Point for the Estimation of Potential and Kinetic Mechanical Power in Running

2004 ◽  
Vol 20 (3) ◽  
pp. 324-331 ◽  
Author(s):  
Jean Slawinski ◽  
Véronique Billat ◽  
Jean-Pierre Koralsztein ◽  
Michel Tavernier
Keyword(s):  
Potential Energy ◽  
Constant Velocity ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Video Camera ◽  
The Body ◽  
Motion Analysis System ◽  
The Difference ◽  
Analysis System ◽  
Significant Underestimation

The purpose of this study was to estimate the difference between potential and kinetic mechanical powers in running (Pke, Ppe) calculated from the center of mass and one anatomic point of the body located on the lower part of the runner's back, the “lumbar point.” Six runners undertook a treadmill run at constant velocity and were filmed individually with a video camera (25 Hz). The 3-D motion analysis system, ANIMAN3D, uses a numerical manikin (MAN3D) which compares a voluminal subject (the athlete) directly to the manikin which possesses the same voluminal properties. This analysis system allows the trajectories of the center of mass and the lumbar point to be calculated. Then, from these trajectories, potential and kinetic mechanical powers in running are calculated. The results show that the utilization of the lumbar point rather than the runner's center of mass leads to a significant overestimation of Pkeand a significant underestimation of Ppe(bothp< 0.05). In spite of these differences, however, both methods of calculating Pkeand Ppeare well correlated: respectively,r= 0.92;p≤ 0.01, andr= 0.68;p≤ 0.05. Taking into account that the trajectory of an anatomic point is experimentally easier to access than that of the center of mass, such a point could be used to estimate the evolution of kinetic or potential energy variation in different cases. However, when the lumbar point rather than the center of mass is used to estimate the mechanical energy produced in running, Pkecould appear to be a discriminating parameter, which it is not.

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.

scholarly journals External Mechanical Work in Runners With Unilateral Transfemoral Amputation

2021 ◽  
Vol 9 ◽  
Author(s):  
Hiroto Murata ◽  
Genki Hisano ◽  
Daisuke Ichimura ◽  
Hiroshi Takemura ◽  
Hiroaki Hobara
Keyword(s):  
Sagittal Plane ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Time Integration ◽  
The Body ◽  
Mechanical Work ◽  
External Work ◽  
Transfemoral Amputees ◽  
The Difference ◽  
Underlying Mechanisms

Carbon-fiber running-specific prostheses have enabled individuals with lower extremity amputation to run by providing a spring-like leg function in their affected limb. When individuals without amputation run at a constant speed on level ground, the net external mechanical work is zero at each step to maintain a symmetrical bouncing gait. Although the spring-like “bouncing step” using running-specific prostheses is considered a prerequisite for running, little is known about the underlying mechanisms for unilateral transfemoral amputees. The aim of this study was to investigate external mechanical work at different running speeds for unilateral transfemoral amputees wearing running-specific prostheses. Eight unilateral transfemoral amputees ran on a force-instrumented treadmill at a range of speeds (30, 40, 50, 60, 70, and 80% of the average speed of their 100-m personal records). We calculated the mechanical energy of the body center of mass (COM) by conducting a time-integration of the ground reaction forces in the sagittal plane. Then, the net external mechanical work was calculated as the difference between the mechanical energy at the initial and end of the stance phase. We found that the net external work in the affected limb tended to be greater than that in the unaffected limb across the six running speeds. Moreover, the net external work of the affected limb was found to be positive, while that of the unaffected limb was negative across the range of speeds. These results suggest that the COM of unilateral transfemoral amputees would be accelerated in the affected limb’s step and decelerated in the unaffected limb’s step at each bouncing step across different constant speeds. Therefore, unilateral transfemoral amputees with passive prostheses maintain their bouncing steps using a limb-specific strategy during running.

External, internal and total work in human locomotion.

1995 ◽  
Vol 198 (2) ◽  
pp. 379-393 ◽  
Author(s):  
P A Willems ◽  
G A Cavagna ◽  
N C Heglund
Keyword(s):  
Potential Energy ◽  
Mechanical Energy ◽  
Human Locomotion ◽  
The Body ◽  
Whole Body ◽  
Gravitational Potential Energy ◽  
Total Work ◽  
Centre Of Mass ◽  
Body Segments ◽  
Energy Transfers

The muscle-tendon work performed during locomotion can, in principle, be measured from the mechanical energy of the centre of mass of the whole body and the kinetic energy due to the movements of the body segments relative to the centre of mass of the body. Problems arise when calculating the muscle-tendon work from increases in mechanical energy, largely in correctly attributing these increases either to energy transfer or to muscle-tendon work. In this study, the kinetic and gravitational potential energy of the centre of mass of the whole human body was measured (using a force platform) simultaneously with calculation of the kinetic and potential energy of the body segments due to their movements relative to the body centre of mass (using cinematography) at different speeds of walking and running. Upper and lower boundaries to the total work were determined by including or excluding possible energy transfers between the segments of each limb, between the limbs and between the centre of mass of the body and the limbs. It appears that the muscle-tendon work of locomotion is most accurately measured when energy transfers are only included between segments of the same limb, but not among the limbs or between the limbs and the centre of mass of the whole body.

Mechanics of a rapid running insect: two-, four- and six-legged locomotion

1991 ◽  
Vol 156 (1) ◽  
pp. 215-231 ◽  
Author(s):  
R. J. Full ◽  
M. S. Tu
Keyword(s):  
Periplaneta Americana ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Reaction Force ◽  
Metabolic Cost ◽  
Legged Locomotion ◽  
American Cockroach ◽  
Stride Frequency ◽  
Gravitational Potential Energy ◽  
Vertical Ground Reaction Force

To examine the effects of variation in body form on the mechanics of terrestrial locomotion, we used a miniature force platform to measure the ground reaction forces of the smallest and, relative to its mass, one of the fastest invertebrates ever studied, the American cockroach Periplaneta americana (mass = 0.83 g). From 0.44-1.0 ms-1, P. americana used an alternating tripod stepping pattern. Fluctuations in gravitational potential energy and horizontal kinetic energy of the center of mass were nearly in phase, characteristic of a running or bouncing gait. Aerial phases were observed as vertical ground reaction force approached zero at speeds above 1 ms-1. At the highest speeds (1.0-1.5 ms-1 or 50 body lengths per second), P. americana switched to quadrupedal and bipedal running. Stride frequency approached the wing beat frequencies used during flight (27 Hz). High speeds were attained by increasing stride length, whereas stride frequency showed little increase with speed. The mechanical power used to accelerate the center of mass increased curvilinearly with speed. The mass-specific mechanical energy used to move the center of mass a given distance was similar to that measured for animals five orders of magnitude larger in mass, but was only one-hundredth of the metabolic cost.

Mechanics of six-legged runners

1990 ◽  
Vol 148 (1) ◽  
pp. 129-146 ◽  
Author(s):  
R. J. Full ◽  
M. S. Tu
Keyword(s):  
Mechanical Energy ◽  
Center Of Mass ◽  
Force Production ◽  
Stride Frequency ◽  
Gravitational Potential Energy ◽  
Vertical Force ◽  
Body Form ◽  
Blaberus Discoidalis ◽  
Ghost Crabs ◽  
Reaction Forces

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.

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.

Mass Transfer of God Particle or Higgs Boson

2012 ◽  
Vol 326-328 ◽  
pp. 164-169
Author(s):  
R. Leticia Corral Bustamante ◽  
Aarón Raúl Rodríguez-Corral ◽  
G. Irigoyen-Chávez ◽  
A. Heiras-Torres
Keyword(s):  
Mass Transfer ◽  
Gravitational Field ◽  
Higgs Boson ◽  
Potential Energy ◽  
Mechanical Energy ◽  
Planck Scale ◽  
Gravitational Potential Energy ◽  
Field Source ◽  
Conservation Of Energy ◽  
Show Evidence

This paper presents a mathematical model to predict the behaviour of the God particle, the Higgs boson, which adds mass to elementary particles appearing and disappearing in the time of Planck. The phenomenon of turbulence in the Planck scale in the modelling of space-time is the base on which is sustained this work. We measured the flow of fluid through the boundary that contains the studied mass (composed of virtual particles with characteristics similar to the Higgs boson) in full bubbling in a gravitational field with enormous surface gravity by calculating the divergence, the rotational and circulation of the fluid. The results show evidence of mass transfer of the particles consistent with the Theory of Special Relativity. The gravitational field (with mass like field source) acts as a conservative field, since its circulation along any closed curve is zero. By Stokes theorem, the flow is irrotational and therefore without vortices. In two arbitrary points of the gravitational field is found that the mechanical energy (sum of kinetic and potential energy) of the particles is constant, satisfying the theorem of conservation of energy in this inertial system isolated from conservative forces. Green's theorem defines sources and sinks of particles around a singularity in the mass center. For heat flow, the sources represent the heat production and the sinks represent its consumption. The irrotational gravitational field where is hosted the God particle has electrostatic and gravitational potential energy.

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