Biomechanical model of the shoulder

Biomechanical model of the shoulder: a highly overactuated manipulator

Yvan Michellod, Philippe Müllhaupt, Denis Gillet, Alexandre Terrier, Dominique Pioletti, Roland Longchamp, Martin Aeberhard


The shoulder is a very complex system of four articulations, actuated by more than twenty muscles. Hence the system is highly overactuated and the force-distribution on the different muscles must be determined by optimization. The muscle-forces have a direct impact on the resulting force inside the articulations. Arthrisis seems to be a consequence of an eccentric load on the glenohumeral joint. Also the design of shoulder implants is highly influenced by the prevailing reaction-forces.

In collaboration with the Joint Biomechanics group of the laboratory of Biomechanical Orthopedics LBO , a dynamic model of the shoulder is currently developed including the glenohumeral joint and eleven muscles.

Keywords : Biomechanics; Overactuation; Muscle Wrapping; Null Space; Pseudoinverse; Shoulder; Dynamic Model; Glenohumeral Joint;



The muscles are considered as cables connecting two bones. These cables are often not a straight line but they wrap over the bony structure of the articulation. This phenomenon must be considered in the model for it influences the moment-arm and hence the muscle-force acting on the articulation. It is important that the moment-arm can be calculated analytically as a function of the humeral position in order to obtain a mapping between the muscle forces and the resulting moment of force on the articulation.
This mapping permits to find a possible solution of the muscle-force distribution for a given articulation-moment of force. In a first step, the matrix of lever-arms is inverted (pseudo-inverse). In a second step, the obtained set of muscle-forces is adapted such as it verifies the constraints of minimal and maximal force of each muscle. This second optimization is done using the null space of the matrix of lever-arms.
Animated shoulder simulations


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