In this paper, fundamental functional requirements for the design of bevel-gear-type, spherical wrist mechanisms have been established. Using these functional requirements, all the admissible kinematic structures of spherical wrist mechanisms with eight or less links have been identified and categorized, and a representative wrist mechanism corresponding to each kinematic structure has been sketched for the purpose of demonstration. Sorne of these mechanisms have already been used in industrial robots, while others appear to be new and deserve further study.