In this paper, the design of a spherical three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Three different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) workspace maximization, and (c) isotropy. The associated problems are formulated and their solutions, one of them requiring to resort to a numerical method, are provided. Optimum designs are thereby obtained. A discussion on singularities is also included.