A model of the flexion-extension motion in the elbow joint some problems concerning muscle forces modelling and computation.

This paper represents an application of a general approach for modelling and mathematical investigation of the human upper limb considered in a previous paper (Raikova, 1992, J. Biomechanics 25, 857-867). Six ways of modelling the muscle force in a plane are suggested and compared to each other. A model of the flexion-extension motion in the elbow joint is proposed, which includes two extensor muscles and three flexor muscles. An optimization task is formulated and solved analytically using the Lagrange multipliers method with an objective function dependent on the n-th power of the muscle forces moduli: sigma c(i)F(i)/(n) (n > 1). The influence of a set of parameters (the power n in the objective function, the weight coefficients c i, the lever arms of the modelled muscle forces, an external force applied to the forearm) on the predicted muscle forces and on the joint reaction is investigated. The results demonstrate that strictly positive and continuous solutions for all muscle forces (for synergistic muscles, also for the antagonistic ones) may be simultaneously predicted if the coefficients C(i) are properly chosen.