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Interdependence of torque, joint angle, angular velocity and muscle action during human multi-joint leg extension

Abstract

Purpose

Force and torque production of human muscles depends upon their lengths and contraction velocity. However, these factors are widely assumed to be independent of each other and the few studies that dealt with interactions of torque, angle and angular velocity are based on isolated single-joint movements. Thus, the purpose of this study was to determine force/torque–angle and force/torque–angular velocity properties for multi-joint leg extensions.

Methods

Human leg extension was investigated (n = 18) on a motor-driven leg press dynamometer while measuring external reaction forces at the feet. Extensor torque in the knee joint was calculated using inverse dynamics. Isometric contractions were performed at eight joint angle configurations of the lower limb corresponding to increments of 10° at the knee from 30 to 100° of knee flexion. Concentric and eccentric contractions were performed over the same range of motion at mean angular velocities of the knee from 30 to 240° s−1.

Results

For contractions of increasing velocity, optimum knee angle shifted from 52 ± 7 to 64 ± 4° knee flexion. Furthermore, the curvature of the concentric force/torque–angular velocity relations varied with joint angles and maximum angular velocities increased from 866 ± 79 to 1,238 ± 132° s−1 for 90–50° knee flexion. Normalised eccentric forces/torques ranged from 0.85 ± 0.12 to 1.32 ± 0.16 of their isometric reference, only showing significant increases above isometric and an effect of angular velocity for joint angles greater than optimum knee angle.

Conclusions

The findings reveal that force/torque production during multi-joint leg extension depends on the combined effects of angle and angular velocity. This finding should be accounted for in modelling and optimisation of human movement.

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Abbreviations

ANOVA:

Analysis of variance

θ 0 :

Optimum velocity-specific knee joint angle

F 0 :

Angle-specific isometric external force

F ext :

External reaction force

F/T-θ-r :

Force/torque–angle relation

F/T-θ-ω-r :

Force/torque–angle–velocity relation

F/T-ω-r :

Force/torque–velocity relation

l 0 :

Optimum muscle length

M 0 :

Angle-specific isometric knee joint torque

M K :

Knee joint torque

MTC:

Muscle tendon complex

ROM:

Range of motion

SD:

Standard deviation

v max :

Maximum velocity of unloaded shortening of an (isolated) muscle

ω max :

Maximum angular velocity during unrestricted leg extension

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Correspondence to Daniel Hahn.

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Communicated by Olivier Seynnes.

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Hahn, D., Herzog, W. & Schwirtz, A. Interdependence of torque, joint angle, angular velocity and muscle action during human multi-joint leg extension. Eur J Appl Physiol 114, 1691–1702 (2014). https://doi.org/10.1007/s00421-014-2899-5

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Keywords

  • Knee joint torques
  • Maximum unresisted velocity
  • Multi-joint leg extension
  • Torque–angle relationship
  • Torque–velocity relationship