During Otologic surgery, and more broadly during microsurgery, the surgeon encounters several difficulties due to the confined spaces and micro-manipulations. The purpose of the paper is to design a robot with a prescribed regular workspace shape to handle an endoscope to assist the Otologic surgery. A spherical parallel mechanism with two degrees of freedom is analysed in its design parameter space. This mechanism is composed of three legs (2USP-U) to connect the base to a moving platform connected to a double parallelogram to create a remote center of motion (RCM). Its kinematic properties, i.e. the singularity locus and the number of direct kinematic solutions, are investigated. For some design parameters, non-singular assembly modes changing trajectories may exist and have to be investigated inside the prescribed regular workspace shape. Two sets of design parameters are presented with their advantages and disadvantages.