This paper presents a simple methodology for the quantitative and qualitative analysis of the performance of spherical parallel platforms. The quaternion formulation is used to represent the possible rotations, showing the workspace as a three-dimensional (3-D) solid object. The singularities of the platform intersect graphically with its workspace, allowing a graphical study of the mechanism kinematics. The performance criterion considered here has been the local dexterity of the manipulator. This methodology has been used to study and analyze three known orientation parallel platforms: 3-RRR, 3-UPU-wrist, and 2-UPS-1-RU. The objective of this study is to analyze the ability of these platforms to be utilized as mechanisms for the neck and shoulders of humanoid robots. Finally, the forces on actuators in some typical motions for neck and shoulder are plotted.