This paper deals with processes of optimisation for the design of a four degree-of-freedom robot dedicated to remote ultrasound tele-echography. This robot is designed to track the medical gestures of a remote expert moving an ultrasound probe. The goal is to optimise the kinematic structure by fixing the geometric parameters; these have a significant role in robot configuration singularities, with respect to current medical gestures and mechanism compactness. After choosing a dedicated kinematic structure, several optimisations are presented. Then an optimal choice of geometrical parameters of a global function in relation with kinematic performance indices and compactness is proposed. This robot is soon to be used in the experimental medical phase of the Prosit project.