The robust design of parallel spherical robots

In this paper a robust methodology, reported in a previous work, is applied to the design of the unactuated joints of a spherical three-degree-of-freedom parallel robot, the Agile Wrist (AW). Robustness is needed because of the extremely difficult task of manufacturing a spherical mechanism with all its joint axes concurrent at a single point. In order to account for the unavoidable manufacturing errors, it is proposed here to replace the unactuated revolute (R) joints of an existing design by cylindrical (C) joints. The latter function even in the presence of nonconcurrent axes. A procedure, based on dual numbers, is used to solve the inverse kinematics of the entire mechanism in order to determine the rotations and translations of each C joint. Based on statistical results of the kinematic analysis, the C joints are suitably dimensioned.