Closed-form solutions for the inverse kinematics of the Agile Eye with constraint errors on the revolute joint axes

Manufacturing process yield errors that change the kinematics of parallel robots. In this paper we describe how the constraint errors due to the manufacturing of the revolute axes can influence the inverse kinematic model of the Agile Eye, a Spherical Parallel Robot largely studied in the literature. Starting from the nominal inverse kinematic model a complete model to take into account geometric errors on the axes of the revolute joints is obtained in closed form. Numerical simulations compare the results from the nominal and real design to show relevant changes and to confirm the statistical nonlinear nature of the problem. Finally, an application to the elastodynamics is provided to verify the influence of the constraint errors on the frequency range.