Working and assembly modes of the agile eye

This paper deals with the in-depth kinematic analysis of a special parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical parallel robot with revolute joints, in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its workspace is unlimited and flawed only by six singularity curves (instead of surfaces). These curves correspond to self-motions of the mobile platform and of the legs, or to a lockup configuration. This paper also demonstrates that the four solutions to the direct kinematics of the Agile Eye (assembly modes) have a simple direct relationship with the eight solutions to the inverse kinematics (working modes).