The craniotomy is a surgical task that is required to allow access to the patient's brain. It consists of using neurosurgical drills to open a path through the skull. The high risk resulting from human dexterous limit justifies the use of an accurate robotic system to perform craniotomy. The present work introduces the kinematic design of a mechanism for a robotic manipulator dedicated to craniotomy. Motion capture experiments have been carried out to measure the motion of a surgical drill during the execution of craniotomy on human cadavers. The results of the experiments are discussed. As this medical application requires a remote center of motion (RCM), a new type of 3-RRR spherical parallel mechanism (SPM) is proposed to manipulate the surgical drill. The novelty of this mechanism is the integration of a reconfigurable base that re-orients the first revolute joint of the RRR legs. A mechanical architecture concept is introduced to implement this reconfiguration. It is made of three pantographic linkages that manipulate the base of the SPM. The kinematics of the new mechanism is analyzed. The influence of this reconfigurable parameter is studied on two different aspects: the mechanism workspace and kinematic performances. Based on these kinematic data, the optimization of a mechanism is performed. The drill motion trajectories are used to evaluate the behavior of the optimized mechanism. It is finally compared to the classical SPM with a trihedral base, showing the contribution of the new reconfiguration variable on the mechanism dexterity.