A minimal principle in biomechanics

Nubar, Yves; Contini, Renato

doi:10.1007/bf02476493

Cited by 94 publications

(35 citation statements)

References 2 publications

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“…This function is related to the "effort" required in the maintenance of upright posture (Nubar and Contini, 1961). Figure 9A shows a U-shaped relation in this function in cats GR and MI, and an L-shaped relation in cats PR and LU.…”

Section: Resultsmentioning

confidence: 98%

“…The actual distance is likely a function of the length of the trunk axis. According to the "principle of minimum effort" proposed by Nubar and Contini (1961), the most probable motion or posture adopted by the individual is one in which the joint torques minimize the cost function, E, while simultaneously satisfying some imposed constraints which may take the form of anatomical or structural limitations. In order to minimize joint torque in the standing cat, the force vector at the ground must remain closely aligned with the limb axis as stance distance changes, otherwise the muscle activation level and net torque will increase in one or more joints due to the change in moment arm length.…”

Section: Discussionmentioning

confidence: 99%

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Determinants of postural orientation in quadrupedal stance

Fung¹,

Macpherson²

1995

J. Neurosci.

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The purpose of this study was to investigate the determinants of postural orientation by examining stance kinematics and kinetics at various interpaw distances. Four adult cats were trained to stand, unrestrained, on a force platform. Three-dimensional ground reaction forces and kinematics, as well as EMG activities, were recorded during stance at five different anteroposterior (AP) distances and two widths. Stance distance was varied by changing the distance between the four force plates mounted on the platform. All cats used a strategy of maintaining a constant horizontal orientation of the trunk and levering the limbs at the girdles while maintaining constant intralimb geometry to accommodate the changes in stance distance. The direction of the ground reaction forces covaried with the limb axes. As a result, the joint torques were conserved in the forelimb, and varied within small ranges in the hind. Increased tonic activity in the extensors of the back, the hip, and the ankle was observed at shorter distances while increased knee extensor activity was observed at longer distances. A cost function, defined as the sum of squared 3-D joint torques, was minimal for the hindlimb at a stance distance which corresponded to the preferred distance naturally assumed by each cat on the floor. Thus, in the maintenance of stance posture, trunk orientation and intralimb geometry is constrained, the goal of which is to minimize muscular effort or energy expenditure.

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Section: Resultsmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Determinants of postural orientation in quadrupedal stance

Fung¹,

Macpherson²

1995

J. Neurosci.

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“…The third and fourth terms restricted θ and θ̇ to remain within the physical limits determined by experimental data (Luttgens and Hamilton, 1997). To facilitate convergence in this first attempt to simulate gait and slip recovery, we adopted a common scheme (Nubar and Contini, 1961;Redfield and Hull, 1986) to minimize the integral of the square of the torque (term 5). The sixth and seventh terms constrained the horizontal velocity and acceleration of the right heel to remain below the corresponding peak values observed in gait experiments.…”

Section: At Eachmentioning

confidence: 99%

Predicted threshold against backward balance loss following a slip in gait

Yang

Anderson

Pai

2008

Journal of Biomechanics

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The purpose of this study was to use a 7-link, moment-actuated human model to predict, at liftoff of the trailing foot in gait, the threshold of the center of mass (COM) velocity relative to the base of support (BOS) required to prevent backward balance loss during single stance recovery from a slip. Five dynamic optimization problems were solved to find the minimum COM velocities that would allow the simulation to terminate with the COM above the BOS when the COM started 0.25, 0.5, 0.75, 1.0, and 1.25 foot lengths behind the heel of the stance foot (i.e., behind the BOS). The initial joint angles of the model were based on averaged data from experimental trials. Foot-ground contact was modeled using 16 visco-elastic springs distributed under the stance foot. Slipping was modeled by setting the sliding coefficient of friction of these springs to 0.02. The forward velocity of the COM necessary to avoid a backward balance loss is nearly two times larger under slip conditions than under non-slip conditions. The predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking. In all trials in which a subject's COM had a velocity below the predicted threshold, the subject's recovery foot landed posterior to the slipping foot as predicted. Finally, combining experimental data with optimization, we verified that the 7-link model could more accurately predict gait stability than a 2-link model.

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“…Earlier results were obtained by Atzler and Herbst. Theoretical attempts to formulate or demonstrate a "minimal" principle were made by Nubar and Contini [27] and Beckett and Chang [28]. [20] and his associates performed quantitative study of EMG activity of the muscles of the lower extremities in connection with the programmed electrostimulation problem.…”

Section: Energy Expenditure and "Optimality" In Locomotionmentioning

confidence: 99%