This work deals with modeling for the design of a four degree-of-freedom robot dedicated to tele-echography. It is designed to follow the medical gestures of a remote expert moving an ultrasound probe. The goal is to define the kinematic structure with optimal geometric parameters. These parameters have an important role in the robot singularities positions corresponding to the most current medical gestures. In this paper, we propose a value of these parameters validated by the kinematic indices point of view and an optimization.