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Angular damping coefficient of the in vivo human knee joint.

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multiply<strong>in</strong>g <strong>the</strong> <strong>damp<strong>in</strong>g</strong> <strong>coefficient</strong><br />

by <strong>the</strong> angular velocity <strong>of</strong> <strong>the</strong> leg<br />

(<strong>in</strong> rad/s). For example, if <strong>the</strong><br />

angular velocity is 10 rad/s <strong>the</strong><br />

passive viscous moment at 10º<br />

would be about 13 N.m. S<strong>in</strong>cel <strong>the</strong><br />

small oscillation method is a l<strong>in</strong>ear<br />

approximation, <strong>the</strong> values <strong>of</strong> <strong>the</strong><br />

<strong>damp<strong>in</strong>g</strong> <strong>coefficient</strong>s presented <strong>in</strong><br />

this study probably represent <strong>the</strong><br />

upper limits s<strong>in</strong>ce at higher<br />

velocities <strong>the</strong> viscosity <strong>of</strong> <strong>the</strong><br />

passive tissues decreases due to <strong>the</strong><br />

nonnewtonian (thixotropic)<br />

characteristics <strong>of</strong> biological tissues<br />

and fluids (Fung, 1981).<br />

In summary, <strong>the</strong> passive<br />

moments which arise due to <strong>the</strong><br />

viscosity <strong>of</strong> <strong>the</strong> <strong>knee</strong> jo<strong>in</strong>t may be<br />

significant <strong>in</strong> magnitude especially<br />

for movements <strong>in</strong> which <strong>the</strong> <strong>knee</strong><br />

jo<strong>in</strong>t approaches its limits and <strong>the</strong><br />

magnitude <strong>of</strong> <strong>the</strong> net jo<strong>in</strong>t moment<br />

is relatively small - such as dur<strong>in</strong>g<br />

<strong>the</strong> late sw<strong>in</strong>g phase <strong>of</strong> gait. If a<br />

portion <strong>of</strong> <strong>the</strong> observed net jo<strong>in</strong>t<br />

Figure 1. Mean angular <strong>damp<strong>in</strong>g</strong> <strong>coefficient</strong> <strong>of</strong><br />

<strong>the</strong> <strong>knee</strong> jo<strong>in</strong>t as a function <strong>of</strong> jo<strong>in</strong>t angle.<br />

Dotted l<strong>in</strong>es are ± 1 S.D.<br />

moment could be satisfied passively, this will have implications <strong>in</strong> <strong>the</strong> magnitudes <strong>of</strong> <strong>the</strong><br />

predicted muscle forces.<br />

REFERENCES<br />

Davy, D.T., and Audu, M.L. (1987). Journal <strong>of</strong> Biomechanics, 20(2), 187-202.<br />

Fung, Y.C. (1981). Biomechanics: Mechanical Properties <strong>of</strong> Liv<strong>in</strong>g Tissues. New York:<br />

Spr<strong>in</strong>ger-Verlag.<br />

Hatze, H. (1975). European Journal <strong>of</strong> Applied Physiology, 34, 217-226.<br />

Hatze, H. (1975a). Ph.d. Thesis. University <strong>of</strong> South Africa.<br />

Hatze, H. (1976). Ma<strong>the</strong>matical Biosciences, 28, 99-135.<br />

W<strong>in</strong>ter, D.A. (1990). Biomechanics and Motor Control <strong>of</strong> Human Movement (2 nd ed.).<br />

New York: John Wiley and Sons.<br />

ACKNOWLEDGEMENTS<br />

This study was partly funded by <strong>the</strong> Natural Sciences and Eng<strong>in</strong>eer<strong>in</strong>g Council and<br />

<strong>the</strong> Research Committee <strong>of</strong> <strong>the</strong> University <strong>of</strong> Ottawa.

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