Energetics of Actively Powered Locomotion Using the Simplest Walking Model

2001 ◽  
Vol 124 (1) ◽  
pp. 113-120 ◽  
Author(s):  
Arthur D. Kuo
Keyword(s):  
Simple Model ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Power Laws ◽  
Step Length ◽  
Heel Strike ◽  
Inertial Parameters ◽  
Complex Models ◽  
Effective Spring Constant ◽  
Nonlinear Equations Of Motion

We modified an irreducibly simple model of passive dynamic walking to walk on level ground, and used it to study the energetics of walking and the preferred relationship between speed and step length in humans. Powered walking was explored using an impulse applied at toe-off immediately before heel strike, and a torque applied on the stance leg. Although both methods can supply energy through mechanical work on the center of mass, the toe-off impulse is four times less costly because it decreases the collision loss at heel strike. We also studied the use of a hip torque on the swing leg that tunes its frequency but adds no propulsive energy to gait. This spring-like actuation can further reduce the collision loss at heel strike, improving walking energetics. An idealized model yields a set of simple power laws relating the toe-off impulses and effective spring constant to the speed and step length of the corresponding gait. Simulations incorporating nonlinear equations of motion and more realistic inertial parameters show that these power laws apply to more complex models as well.

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

scholarly journals A biomechanical study of load carriage by two paired subjects in response to increased load mass

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guillaume Fumery ◽  
Nicolas A. Turpin ◽  
Laetitia Claverie ◽  
Vincent Fourcassié ◽  
Pierre Moretto
Keyword(s):  
Recovery Rate ◽  
Energy Recovery ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Step Length ◽  
Biomechanical Study ◽  
Load Carriage ◽  
Joint Torque ◽  
Total Mechanical Energy ◽  
Load Mass

AbstractThe biomechanics of load carriage has been studied extensively with regards to single individuals, yet not so much with regards to collective transport. We investigated the biomechanics of walking in 10 paired individuals carrying a load that represented 20%, 30%, or 40% of the aggregated body-masses. We computed the energy recovery rate at the center of mass of the system consisting of the two individuals plus the carried load in order to test to what extent the pendulum-like behavior and the economy of the gait were affected. Joint torque was also computed to investigate the intra- and inter-subject strategies occurring in response to this. The ability of the subjects to move the whole system like a pendulum appeared rendered obvious through shortened step length and lowered vertical displacements at the center of mass of the system, while energy recovery rate and total mechanical energy remained constant. In parallel, an asymmetry of joint moment vertical amplitude and coupling among individuals in all pairs suggested the emergence of a leader/follower schema. Beyond the 30% threshold of increased load mass, the constraints at the joint level were balanced among individuals leading to a degraded pendulum-like behavior.

Frontal Rearfoot Kinematics in Running Prior to Volitional Exhaustion

1997 ◽  
Vol 13 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Bart Van Gheluwe ◽  
Claire Madsen
Keyword(s):  
Statistical Analysis ◽  
Frontal Plane ◽  
Step Length ◽  
Heel Strike ◽  
Volitional Exhaustion ◽  
Rearfoot Motion

Excessive rearfoot motion, especially in the frontal plane, is believed to be a major cause of overload injuries in running. The aim of this study was to determine the influence of fatigue on frontal rearfoot motion just before volitional abandonment during an exhaustive run on a treadmill. Rearfoot kinematics were recorded three-dimensionally and reconstructed in a frontal plane associated with the heel. Statistical analysis of the results suggested that exhaustion did not influence tibial varum substantially, except at first heel strike. However, maximal calcaneal eversion and subtalar pronation did increase significantly, while maximal pronation velocity accelerated to 100°/s more than at the start of the exhaustive run. Also, the results of this study suggest that the increase in rearfoot motion is directly affected by fatigue and not by a fatigue-induced increase in step length.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Measurement Method Research on Inertial Parameters of Motor Assembly

2013 ◽  
Vol 437 ◽  
pp. 663-668
Author(s):  
Ling Sun ◽  
Peng Yu ◽  
Tong Zhang
Keyword(s):  
Measurement Method ◽  
Center Of Mass ◽  
Moment Of Inertia ◽  
Balance Method ◽  
Test Error ◽  
Inertial Parameters ◽  
Drive Motor ◽  
Weight Method ◽  
Mass Position

Inertial parameters of the motor assembly include its mass, CM (center of mass) position, moment of inertia and product of inertia. Taking one vehicle drive motor as the research object, its mass and CM position are measured by using weight method and moment balance method respectively. Its moment of inertia and product of inertia are measured by using three-wire pendulum. On the basis of analyzing the test error, this paper proposed specific measures to reduce the test error.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

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