This paper deals with the optimization of the design of a 4 degree-of-freedom robot dedicated to tele-echography. It has been designed to reproduce in real time on a patient, the medical gestures performed by a remote expert moving a fictive probe. Our goal is to optimize the kinematic structure to determine geometrical parameters, as they have a significant role in the singularities localization. In this paper, we propose optimum solutions obtained from a combination of kinematic performances and compactness indices.