Global sensitivity analysis of the kinematics obtained with a multi-body optimisation using a parallel mechanism of the shoulder

In this study, a global sensitivity analysis is performed on a multi-body optimisation using a parallel mechanism of the shoulder. This parallelmechanism consists of a closed chain of scapula, thorax and humerus. The clavicle is introduced as a constant length between the thorax and scapula. The gleno-humeral joint is assumed to be a sphere-on-sphere contact and the scapulo-thoracic contact, a point-onellipsoid contact. The geometry of the parallel mechanism (centres of sterno-clavicular and acromio-clavicular joints, glenoid and humeral head, and centre and axes of thorax ellipsoid) is based on theVisibleHuman Project (VHP). It is scaled to the anthropometry of any subject in order to compute the shoulder kinematics using a multi-body optimisation (Duprey et al. 2010). The scaling procedure corresponds to an Affine mapping between the anatomical landmarks of VHP and those of the subject. This scaling procedure induces geometrical errors that impact the kinematics and a sensitivity analysis is performed to measure its influence. This analysis consists of generating a random sample (in this case, it represents the geometrical errors due to the scaling procedure) and propagating these errors through the multi-body optimisation. Given the random sample as inputs and the corresponding joint angles as outputs, the influence of the geometrical errors on the kinematics can be quantified.