Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure

1977 ◽  
Vol 233 (5) ◽  
pp. R243-R261 ◽  
Author(s):  
G. A. Cavagna ◽  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Center Of Mass ◽  
Forward Direction ◽  
Gravitational Energy ◽  
The Body ◽  
Unit Weight ◽  
Gravitational Potential Energy ◽  
Terrestrial Locomotion ◽  
Energy Conserving ◽  
Walking Speeds ◽  
Work Done

The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic “bounce” of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.

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.

A Nonlinear Oscillator Model to Generate Lateral Walking Force on a Rigid Flat Surface

2018 ◽  
Vol 18 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Prakash Kumar ◽  
Anil Kumar ◽  
Silvano Erlicher
Keyword(s):  
Nonlinear Oscillator ◽  
Perturbation Technique ◽  
Center Of Mass ◽  
Reaction Force ◽  
Lateral Force ◽  
The Body ◽  
Model Parameters ◽  
Lateral Direction ◽  
Van Der Pol Oscillators ◽  
Walking Speeds

This study proposes a single degree of freedom nonlinear oscillator to model the lateral movement of the body center of mass of a pedestrian walking on a flat rigid surface. Experimentally recorded ground reaction force of a dozen of pedestrians in the lateral direction is used to develop the model. In detail, the hardening and softening effects are observed in the stiffness curve as well as higher odd harmonics are present in the frequency spectrum of the lateral force signals. The proposed oscillator is a modification of the Rayleigh and the Van der Pol oscillators with additional nonlinear softening and hardening terms. To obtain an approximation of the limit cycle of the oscillator and its stability, two methods are studied: the energy balance method and the Lindstedt–Poincare perturbation technique. The experimental force signals of pedestrians at four different walking speeds are used for the identification of the values of the model parameters. The results obtained from the proposed model show a good agreement with the experimental ones.

scholarly journals Kinematic patterns while walking on a slope at different speeds

2018 ◽  
Vol 125 (2) ◽  
pp. 642-653 ◽  
Author(s):  
A. H. Dewolf ◽  
Y. Ivanenko ◽  
K. E. Zelik ◽  
F. Lacquaniti ◽  
P. A. Willems
Keyword(s):  
Principal Components ◽  
Center Of Mass ◽  
Principal Component ◽  
Vertical Displacement ◽  
The Body ◽  
Limb Length ◽  
Intersegmental Coordination ◽  
Body Center ◽  
Coordination Change ◽  
Walking Speeds

During walking, the elevation angles of the thigh, shank, and foot (i.e., the angle between the segment and the vertical) covary along a characteristic loop constrained on a plane. Here, we investigate how the shape of the loop and the orientation of the plane, which reflect the intersegmental coordination, change with the slope of the terrain and the speed of progression. Ten subjects walked on an inclined treadmill at different slopes (between −9° and +9°) and speeds (from 0.56 to 2.22 m/s). A principal component analysis was performed on the covariance matrix of the thigh, shank, and foot elevation angles. At each slope and speed, the variance accounted for by the two principal components was >99%, indicating that the planar covariation is maintained. The two principal components can be associated to the limb orientation (PC1*) and the limb length (PC2*). At low walking speeds, changes in the intersegmental coordination across slopes are characterized mainly by a change in the orientation of the covariation plane and in PC2* and to a lesser extent, by a change in PC1*. As speed increases, changes in the intersegmental coordination across slopes are more related to a change in PC1 *, with limited changes in the orientation of the plane and in PC 2*. Our results show that the kinematic patterns highly depend on both slope and speed. NEW & NOTEWORTHY In this paper, changes in the lower-limb intersegmental coordination during walking with slope and speed are linked to changes in the trajectory of the body center of mass. Modifications in the kinematic pattern with slope depend on speed: at slow speeds, the net vertical displacement of the body during each step is related to changes in limb length and orientation. When speed increases, the vertical displacement is mostly related to a change in limb orientation.

Introduction of New Concepts and Problem Solving in Engineering Dynamics

2007 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Problem Solving ◽  
Concept Maps ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
New Concepts ◽  
Body Dynamics ◽  
Basic Equations ◽  
And Mathematics ◽  
Work Done

A survey of a large number of well-known textbooks for an undergraduate dynamics class showed that often new concepts are introduced without a clear connection to previously discussed material. For example, the concepts of work done by a force, linear momentum, angular momentum, and power are often introduced without a clear direct connection to Newton’s law. Similarly, in rigid body dynamics, important concepts such as the center of mass and the moments of inertia of the body are often introduced with little or no background. This article shows how all the important concepts in dynamics flow directly and logically from Newton’s laws. This is done through simple direct derivations. Connections are made clear by concept maps that help students understand how these different concepts are related. In addition to introducing new concepts and deriving some of the basic equations, a dynamics class should also introduce students to problem solving help them develop a systematic approach. This article describes a five step approach that is recommended for both high context and low context problems. In that context we stress that problem solving is a process that involves the application of known concepts and mathematics.

Increased musculoskeletal stiffness during load carriage at increasing walking speeds maintains constant vertical excursion of the body center of mass

2003 ◽  
Vol 36 (4) ◽  
pp. 465-471 ◽  
Author(s):  
Kenneth G Holt ◽  
Robert C Wagenaar ◽  
Michael E LaFiandra ◽  
Masayoshi Kubo ◽  
John P Obusek
Keyword(s):  
Center Of Mass ◽  
The Body ◽  
Load Carriage ◽  
Body Center ◽  
Walking Speeds

scholarly journals Body and Tail Coordination in the Bluespot Salamander (Ambystoma laterale) During Limb Regeneration

2021 ◽  
Vol 8 ◽  
Author(s):  
Cassandra M. Donatelli ◽  
Keegan Lutek ◽  
Keshav Gupta ◽  
Emily M. Standen
Keyword(s):  
Body Wave ◽  
Limb Regeneration ◽  
The Body ◽  
Pectoral Girdle ◽  
Terrestrial Locomotion ◽  
Bending Waves ◽  
Ambystoma Laterale ◽  
Polypterus Senegalus ◽  
Walking Speeds ◽  
Over Time

Animals are incredibly good at adapting to changes in their environment, a trait envied by most roboticists. Many animals use different gaits to seamlessly transition between land and water and move through non-uniform terrains. In addition to adjusting to changes in their environment, animals can adjust their locomotion to deal with missing or regenerating limbs. Salamanders are an amphibious group of animals that can regenerate limbs, tails, and even parts of the spinal cord in some species. After the loss of a limb, the salamander successfully adjusts to constantly changing morphology as it regenerates the missing part. This quality is of particular interest to roboticists looking to design devices that can adapt to missing or malfunctioning components. While walking, an intact salamander uses its limbs, body, and tail to propel itself along the ground. Its body and tail are coordinated in a distinctive wave-like pattern. Understanding how their bending kinematics change as they regrow lost limbs would provide important information to roboticists designing amphibious machines meant to navigate through unpredictable and diverse terrain. We amputated both hindlimbs of blue-spotted salamanders (Ambystoma laterale) and measured their body and tail kinematics as the limbs regenerated. We quantified the change in the body wave over time and compared them to an amphibious fish species, Polypterus senegalus. We found that salamanders in the early stages of regeneration shift their kinematics, mostly around their pectoral girdle, where there is a local increase in undulation frequency. Amputated salamanders also show a reduced range of preferred walking speeds and an increase in the number of bending waves along the body. This work could assist roboticists working on terrestrial locomotion and water to land transitions.

Neuromuscular changes for hopping on a range of damped surfaces

2004 ◽  
Vol 96 (5) ◽  
pp. 1996-2004 ◽  
Author(s):  
Chet T. Moritz ◽  
Spencer M. Greene ◽  
Claire T. Farley
Keyword(s):  
Center Of Mass ◽  
Reaction Force ◽  
Surface Emg ◽  
Knee Extensors ◽  
Energy Conserving ◽  
Work Done ◽  
Male Subjects ◽  
Positive Work ◽  
Elastic Surfaces ◽  
Ankle Mechanics

Humans hopping and running on elastic and damped surfaces maintain similar center-of-mass dynamics by adjusting stance leg mechanics. We tested the hypothesis that the leg transitions from acting like an energy-conserving spring on elastic surfaces to a power-producing actuator on damped surfaces during hopping due to changes in ankle mechanics. To test this hypothesis, we collected surface electromyography, video kinematics, and ground reaction force while eight male subjects (body mass: 76.2 ± 1.7 kg) hopped in place on a range of damped surfaces. On the most damped surface, most of the mechanical work done by the leg appeared at the ankle (52%), whereas 23 and 25% appeared at the knee and hip, respectively. Hoppers extended all three joints during takeoff further than they flexed during landing and thereby did more net positive work on more heavily damped surfaces. Also, all three joints reached peak flexion sooner after touchdown on more heavily damped surfaces. Consequently, peak moment occurred during joint extension rather than at peak flexion as on elastic surfaces. These strategies caused the positive work during extension to exceed the negative work during flexion to a greater extent on more heavily damped surfaces. At the muscle level, surface EMG increased by 50-440% in ankle and knee extensors as surface damping increased to compensate for greater surface energy dissipation. Our findings, and those of previous studies of hopping on elastic surfaces, show that the ankle joint is the key determinant of both springlike and actuator-like leg mechanics during hopping in place.

scholarly journals Maintaining balance against force perturbations: impaired mechanisms unresponsive to levodopa in Parkinson's disease

2016 ◽  
Vol 116 (2) ◽  
pp. 493-502 ◽  
Author(s):  
Irene Di Giulio ◽  
Rebecca J. St George ◽  
Eirini Kalliolia ◽  
Amy L. Peters ◽  
Patricia Limousin ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Force Feedback ◽  
Center Of Mass ◽  
Reaction Force ◽  
Knee Extensor ◽  
Forward Direction ◽  
Postural Instability ◽  
The Body ◽  
External Forces

There is evidence that postural instability associated with Parkinson's disease (PD) is not adequately improved by levodopa, implying involvement of nondopaminergic pathways. However, the mechanisms contributing to postural instability have yet to be fully identified and tested for their levodopa responsiveness. In this report we investigate balance processes that resist external forces to the body when standing. These include in-place responses and the transition to protective stepping. Forward and backward shoulder pulls were delivered using two force-feedback-controlled motors and were randomized for direction, magnitude, and onset. Sixteen patients with PD were tested OFF and ON levodopa, and 16 healthy controls were tested twice. Response behavior was quantified from 3-dimensional ground reaction forces and kinematic measurements of body segments and total body center-of-mass (CoM) motion. In-place responses resisting the pull were significantly smaller in PD as reflected in reduced horizontal anteroposterior ground reaction force and increased CoM displacement. Ankle, knee, and hip moments contributing to this resistance were smaller in PD, with the knee extensor moment to backward pulls being the most affected. The threshold force needed to evoke a step was also smaller for PD in the forward direction. Protective steps evoked by suprathreshold pulls showed deficits in PD in the backward direction, with steps being shorter and more steps being required to arrest the body. Levodopa administration had no significant effect on either in-place or protective stepping deficits. We conclude that processes employed to maintain balance in the face of external forces show impairment in PD consistent with disruption to nondopaminergic systems.

THE WIND TUNNEL DEVELOPMENT OF A PROPOSED EXTERNAL FORM FOR STEAM LOCOMOTIVES

1933 ◽  
Vol 8 (1) ◽  
pp. 37-61
Author(s):  
J. J. Green
Keyword(s):  
Wind Tunnel ◽  
Maximum Degree ◽  
Air Flow ◽  
Forward Direction ◽  
The Body ◽  
Air Resistance ◽  
Clean Air ◽  
Work Done ◽  
External Form ◽  
External Shape

The existing shape and arrangement of steam locomotives are such that smoke from the stack tends to sweep back along the boiler top and descend in front of the cab windows, seriously impairing forward vision. For the maximum degree of safety it is essential that the view from the cab, especially in a forward direction, should be unobstructed at all times. It is therefore desirable that some means be found for improving the manner in which the smoke is carried away from the stack. In addition to preventing the descent of smoke at the cab it is desirable that the external shape of the locomotive should be so modified as to result in a decreased air resistance, in view of the growing demand for economical running at increasingly higher speeds.The paper describes work done in the wind tunnel of the National Research Laboratories and discusses the steps whereby an improved external shape has been evolved for locomotives such that the smoke is lifted over the cab thus making possible an unimpaired vision ahead.The new design is the result of the application of elementary aerodynamics to the problem and aims at providing smoother air flow about the locomotive. Further, a layer of clean air is introduced between the smoke and the body of the locomotive and is responsible for maintaining the smoke above the cab. By removing the violent eddying flow about the locomotive the air resistance of the engine and tender has been reduced to the extent of some 35%.

Performance Analysis and Feedback Control of ATRIAS, A Three-Dimensional Bipedal Robot

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Alireza Ramezani ◽  
Jonathan W. Hurst ◽  
Kaveh Akbari Hamed ◽  
J. W. Grizzle
Keyword(s):  
Energy Efficiency ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Energetic Efficiency ◽  
Natural Terrain ◽  
Walking Speeds

This paper develops feedback controllers for walking in 3D, on level ground, with energy efficiency as the performance objective. Assume The Robot Is A Sphere (ATRIAS) 2.1 is a new robot that has been designed for the study of 3D bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having 6 actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits of a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (CMT), a dimensionless measure of energetic efficiency, for walking speeds ranging from 0.5 (m/s) to 1.4 (m/s). A feedback controller is designed that stabilizes the 3D walking gaits, despite the high degree of underactuation of the robot. The 3D results are illustrated in simulation. In experiments on a planarized (2D) version of the robot, the controller yielded stable walking.

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