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 consisted of eleven muscles. The glenohumeral joint is modeled as a spherical joint, allowing for three rotations. Muscle wrapping around a spherical humeral head is calculated analytically. The problem of indeterminated muscle forces is solved in two steps. First, an intermediate solution is calculated using the pseudo-inverse of the moment arms matrix providing 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. This approach of modifying the muscle forces assures that the predicted movement is followed precisely. The joint reaction force calculated by the model for abduction is comparable to results found in the litterature.