The design of a spherical wrist with parallel architecture is the object of this article. This study is part of a larger project, which aims to design and to build an eel robot for inspection of immersed piping. The kinematic analysis of the mechanism is presented first to characterize the singular configurations as well as the isotropic configurations. We add the design constraints related to the application, such as (i) the compactness of the mechanism, (ii) the symmetry of the elements in order to ensure static and dynamic balance and (iii) the possibility of the mechanism to fill the elliptic form of the ell sections.