The objective of this article is to present the dimensional synthesis of serial andparallel spherical wrists, an important step in the design process of medical robots. Thisstep is carried out to obtain optimal dimensions of tool-guidance medical robots. Withthis goal, we have first studied the specifications of two robots with different medicalapplications: one for tele-echography examination and one for minimally invasive surgery.Then, we have established that the medical needs expressed by the doctors were verydifferent but the specifications in robotic terms have a lot of common points (kinematics,workspace, bulkiness). For both applications studied, robots need a mobility of threerotations around a fixed point (probe contact point on the patient’s skin or trocarincision). So, a spherical wrist architecture is adapted to their needs. An importantconstraint related to medical applications is that the robot must be compact in order tonot obstruct or collide with its environment (medical personnel or patient). We performdimensional synthesis allowing determination of dimensions of the mechanism for serial andparallel spherical wrists, for a tele-echography robot, and a serial wrist for a minimallyinvasive surgery robot. We use multi-criteria optimization methods minimizing a costfunction to obtain both good kinematic performance and compactness for the architecture.The difficulty/challenge of this design process, depending of the studied applications, isthe choice of efficient criteria describing the performances and the constraints of therobot. The design variables must faithfully represent the specifications of the robot sothat its performance can respond to the medical requirements. We show, here, the differentmethods used for optimizing the chosen kinematic architecture for the particular medicalapplication. These studies lead to prototypes which are validated after medicalexperiments. This process of dimensional synthesis will be applied to other medicalapplications with different sets of specified constraints.