A Non-Overconstrained Variant of the Agile Eye with a Special Decoupled Kinematics

A non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to
the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected
to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns
from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute
joints are active joints, while all other joints are passive ones. Based on a special configuration, some
three projective angles of the end-effector coordinates are fully decoupled with respect to the input
actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the
corresponding projective angle changes with the same angular displacement. The fully decoupled
motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics
solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.