title: Stability analysis of the elbow with a load.
abstract: We present a model of the human elbow and study the problem of existence and stability of equilibrium states. Our main goal is to demonstrate that stable equilibrium states exist just on grounds of the mechanical properties of the muscles and the skeleton. In particular, additional control mechanisms such as reflexes are not necessary to obtain stability. We assume that the activation of flexor and extensor muscles is constant and such that the right angle is an equilibrium state. We give a complete bifurcation diagram of all equilibrium states in terms of the elbow angle, the activation of the muscles and the mass of a load. Moreover, we define a dimensionless model parameter which allows to determine whether or not there are stable equilibria at an angle of ninety degrees. It turns out that the dependency of the muscle forces on the length of the muscles is the crucial factor for the stability of such an equilibrium.
authors.affiliation: Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching bei München, Germany. giesl@ma.tum.de
authors.forename: Peter
authors.initials: P
authors.lastname: Giesl
authors.forename: Dorothea
authors.initials: D
authors.lastname: Meisel
authors.forename: Jürgen
authors.initials: J
authors.lastname: Scheurle
authors.forename: Heiko
authors.initials: H
authors.lastname: Wagner
mesh_terms: D001696:Biomechanical Phenomena; D004551:Elbow Joint / Q000502:physiology*; D006706:Homeostasis / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D009038:Motion; D018482:Muscle, Skeletal / Q000502:physiology; D012026:Reflex, Stretch / Q000502:physiology