Some newborn babies require particular cares and are therefore placed in neonatal incubators. Intracranial ultrasound examinations are regularly performed in order to monitor the development of their brain. Due to the repetitivity and uncomfortability associated with this clinical task, the design of a robotic system capable of performing this task is proposed. The manipulation of an ultrasound probe inside a neonatal incubator is studied using a motion capture system. The kinematic specifications associated with this clinical task are established. A mechanical architecture based on two combined pantographic linkages is proposed. One pantographic mechanism performs the linear positioning of the end effector around a center of rotation. The orientation of the ultrasound probe around another center of rotation is mainly provided by a second pantographic linkage. The forward and inverse kinematic models are calculated to study the linear and angular positioning of the mechanism. The trajectories measured during the motion capture experiments are then tested on the mechanism to validate its suitability with the intracranial echography on newborns inside incubators.