Dynamical biomechanical model of the shoulder: null space based optimization of the overactuated system

A new dynamical model of the shoulder has been developed. It consists of eleven muscles. The glenohumeral joint, modeled as a spherical joint, allows three rotations and blocks the translations. Muscle wrapping around a spherical humeral head is calculated analytically. The problem of indeterminated muscle forces has been solved in two steps: first an intermediate solution is calculated using the pseudo-inverse of the moment-arms matrix which provides the mapping between the muscle forces (actuators) and the generalized forces (system). In a second step the intermediate solution is modified using the column vectors of the moment-arms matrix's null space in order to verify the constraints on the muscle forces.