Leg Joint Mechanics When Hopping at Different Frequencies

2021 ◽  
pp. 1-9
Author(s):  
Mu Qiao
Keyword(s):  
Energy Storage ◽  
Mechanical Load ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Low Frequency ◽  
Frequency Hopping ◽  
Constant Load ◽  
Joint Mechanics ◽  
Mass Model ◽  
Total Mechanical Energy

Although the dynamics of center of mass can be accounted for by a spring-mass model during hopping, less is known about how each leg joint (ie, hip, knee, and ankle) contributes to center of mass dynamics. This work investigated the function of individual leg joints when hopping unilaterally and vertically at 4 frequencies (ie, 1.6, 2.0, 2.4, and 2.8 Hz). The hypotheses are (1) all leg joints maintain the function as torsional springs and increase their stiffness when hopping faster and (2) leg joints are controlled to maintain the mechanical load in the joints or vertical peak accelerations at different body locations when hopping at different frequencies. Results showed that all leg joints behaved as torsional springs during low-frequency hopping (ie, 1.6 Hz). As hopping frequency increased, leg joints changed their functions differently; that is, the hip and knee shifted to strut, and the ankle remained as spring. When hopping fast, the body’s total mechanical energy decreased, and the ankle increased the amount of energy storage and return from 50% to 62%. Leg joints did not maintain a constant load at the joints or vertical peak accelerations at different body locations when hopping at different frequencies.

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.

Three-dimensional kinematics and limb kinetic energy of running cockroaches.

1997 ◽  
Vol 200 (13) ◽  
pp. 1919-1929 ◽  
Author(s):  
R Kram ◽  
B Wong ◽  
R J Full
Keyword(s):  
Kinetic Energy ◽  
High Speed ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Morphological Data ◽  
Fast Running ◽  
Total Mechanical Energy ◽  
Reaction Forces

We tested the hypothesis that fast-running hexapeds must generate high levels of kinetic energy to cycle their limbs rapidly compared with bipeds and quadrupeds. We used high-speed video analysis to determine the three-dimensional movements of the limbs and bodies of cockroaches (Blaberus discoidalis) running on a motorized treadmill at 21 cm s-1 using an alternating tripod gait. We combined these kinematic data with morphological data to calculate the mechanical energy produced to move the limbs relative to the overall center of mass and the mechanical energy generated to rotate the body (head + thorax + abdomen) about the overall center of mass. The kinetic energy involved in moving the limbs was 8 microJ stride-1 (a power output of 21 mW kg-1, which was only approximately 13% of the external mechanical energy generated to lift and accelerate the overall center of mass at this speed. Pitch, yaw and roll rotational movements of the body were modest (less than +/- 7 degrees), and the mechanical energy required for these rotations was surprisingly small (1.7 microJ stride-1 for pitch, 0.5 microJ stride-1 for yaw and 0.4 microJ stride-1 for roll) as was the power (4.2, 1.2 and 1.1 mW kg-1, respectively). Compared at the same absolute forward speed, the mass-specific kinetic energy generated by the trotting hexaped to swing its limbs was approximately half of that predicted from data on much larger two- and four-legged animals. Compared at an equivalent speed (mid-trotting speed), limb kinetic energy was a smaller fraction of total mechanical energy for cockroaches than for large bipedal runners and hoppers and for quadrupedal trotters. Cockroaches operate at relatively high stride frequencies, but distribute ground reaction forces over a greater number of relatively small legs. The relatively small leg mass and inertia of hexapeds may allow relatively high leg cycling frequencies without exceptionally high internal mechanical energy generation.

A Generalized Treatment of the Energetics of Translating Continua

1995 ◽  
Author(s):  
Seung-Yop Lee ◽  
C. D. Mote
Keyword(s):  
Energy Flux ◽  
Amplitude Ratio ◽  
Mechanical Energy ◽  
Low Frequency ◽  
Mechanical Impedance ◽  
Viscous Damping ◽  
One Dimensional ◽  
Propagating Waves ◽  
Total Mechanical Energy ◽  
Energy Ratios

Abstract The energetics of translating, one-dimensional continua, like uniform strings or tensioned beams, that travel between two supports is analyzed in this paper. The non-conservative interaction between the supports and the translating continua causes energy flux at the boundaries. The total mechanical energy is not conserved, and a periodic transfer of energy into and out of the system occurs. From the power flows in traveling waves, the energy flux for a string translating through fixed, free, elastic and viscous damping boundary conditions is obtained explicitly in terms of the transport speed and the ratio of the reflected to incident amplitudes. The time-dependent character of the total energy of a translating tensioned beam is complex because the beam is dispersive. The energy variation in the beam is represented in terms of the mechanical impedance and the amplitude ratio between the reflected and incident propagating waves. At low frequency, frequency-dependent energy ratios are identical to those of translating strings. The amount of energy flux at boundaries decreases with frequency, and increases with transport speed. Numerical simulations verify the analytically predicted energy variations for the different supports.

Minor preload dependence of O2 consumption of unloaded contraction in dog heart

1989 ◽  
Vol 256 (5) ◽  
pp. H1289-H1294 ◽  
Author(s):  
Y. Yasumura ◽  
T. Nozawa ◽  
S. Futaki ◽  
N. Tanaka ◽  
H. Suga
Keyword(s):  
Mechanical Load ◽  
Mechanical Energy ◽  
Systolic Pressure ◽  
Ventricular Volume ◽  
Dog Heart ◽  
End Diastolic Volume ◽  
Pressure Development ◽  
Total Mechanical Energy ◽  
Whole Heart ◽  
Length Dependent Activation

We studied whether end-diastolic volume (EDV) would affect myocardial oxygen consumption (VO2) of mechanically unloaded contraction in the cross-circulated dog heart, as expected from the concept of the myocardial length-dependent activation. We made preloaded but maximally unloaded contractions from different EDVs by quickly releasing ventricular volume to eliminate systolic pressure development and hence to minimize the VO2 for mechanical load during the contraction. We then studied the relation between VO2 and EDV. The VO2 of the almost unloaded contraction from a relatively large EDV slightly exceeded the VO2 of the isovolumic contraction at V0, where V0 is the volume at which peak isovolumic pressure was zero. However, the excess VO2 could be ascribed to the residual systolic pressure-volume area (PVA) adversely produced from the large EDV, where PVA is a measure of the total mechanical energy generated during contraction. Therefore, we considered that VO2 was practically little dependent on EDV. We interpreted this finding as an indication that an increase, if any, in VO2 due to the length-dependent activation of the excitation-contraction coupling was practically negligible in the whole heart preparation.

scholarly journals ԼՐԻՎ ՄԵԽԱՆԻԿԱԿԱՆ ԷՆԵՐԳԻԱՅԻ ՓՈՓՈԽՈՒԹՅԱՆ ԹԵՈՐԵՄԻ ԵՎ ՄՈՄԵՆՏՆԵՐԻ ԿԱՆՈՆԻ ՄԵԿ ՀԱՄԱՏԵՂ ԿԻՐԱՌՈՒԹՅԱՆ ՄԱՍԻՆ / ON THE JOINT APPLICATION OF A FULL MECHANICAL ENERGY CHANGE THEOREM AND THE RULES OF MOMENTS

2021 ◽  
pp. 245-250
Author(s):  
V. Manukyan ◽  
G. Nikoghosyan ◽  
H. Yengoyan
Keyword(s):  
Specific Problem ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Energy Change ◽  
Central Angle ◽  
Circular Arc ◽  
Joint Application ◽  
Total Mechanical Energy ◽  
Physics Course

Աշխատանքը նվիրված է ֆիզիկայի դպրոցական դասընթացում լրիվ մեխանիկական էներգիայի փոփոխության թեորեմի և մոմենտների կանոնի հնարավոր համատեղ կիրառությունների վերհանմանըֈ Դիտարկված է կոնկրետ խնդիր, որի շրջանակում վերոգրյալ երկու կանոների կիրառման արդյունքում հնարավոր է դառնում որոշել համասեռ շրջանագծային աղեղի զանգվածի կենտրոնըֈ Խնդրի շրջանակում ստացված արդյունքն ընդհանրացվել է կամայական կենտրոնային անկյունով համասեռ շրջանաձև աղեղի համարֈ: / The work is devoted to identifying possible joint applications of the rule of moments and the theorem for changing the total mechanical energy in a school physics course. A specific problem is considered, within the framework of which, as a result of the application of the above two rules, it becomes possible to determine the center of mass of a uniform circular arc. The result obtained in the framework of the problem is generalized to a homogeneous circular arc with an arbitrary central angle.

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 Elastic energy savings and active energy cost in a simple model of running

2021 ◽  
Author(s):  
Ryan T. Schroeder ◽  
Arthur D. Kuo
Keyword(s):  
Elastic Energy ◽  
Energy Cost ◽  
Energy Savings ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Mass Model

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic Spring-mass computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. Conversely, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running. Here we add explicit actuation and dissipation to the Spring-mass model, resulting in substantial active (and thus costly) work for running on level ground and up or down slopes. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m/s) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

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