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Musculoskeletal Stabilization of the Elbow - Complex or Real
journal contributionposted on 2023-06-07, 23:05 authored by Heiko Wagner, Peter GieslPeter Giesl, Reinhard Blickhan
Both sensory information and mechanical properties of the musculoskeletal system are necessary for fast and appropriate reactions of humans and animals to environmental perturbations. In this paper, we focus on the musculoskeletal system and study the stability of a human elbow in an equilibrium state. We derive a biomechanical model of the human elbow, including an antagonistic pair of muscles, and investigate the stability analytically based on the theory of Ljapunov. Depending on the elbow angle and the level of coactivation, we obtain the following three qualitatively different behaviors: unstable, stable with real eigenvalues, and stable with complex eigenvalues. If the eigenvalues are real, then the system is critically damped; for complex eigenvalues, solutions near the equilibrium are oscillating. Based on experimental data, we found that in principle real and complex behaviors may occur in human arm movements. The experiments support the analytical predictions. Furthermore, in agreement with the simulations, we found differences in the experimental results among the subjects. The results of this study support the assumption that arm movements around an equilibrium point may be self-stabilized without sensory feedback or motor control, based only on mechanical properties of musculoskeletal systems.
JournalJournal of Mechanics in Medicine and Biology
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- Mathematics Publications
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