An optimization procedure based on kinematics analysis for the design parameters of a 4-UPU parallel manipulator

The paper presents the kinematics analysis of a 4-UPU fully parallel manipulator and a numerical procedure for its optimization. The 4-UPU kinematics is featured by four UPU legs, moreover the prismatic joint of each leg is supposed to be actuated. The end-effector has 4 degrees of freedom (Dofs), the three translations and the rotation along the direction perpendicular to the base platform. Singularity configurations have been analytically determined and the analysis of both actuation and constraint Jacobian by screw theory has been performed. Finally, a numerical procedure for the optimization of the design parameters of the manipulator is presented. The optimization procedure has been carried out using adimensional parameters in order to generalize the obtained results. The presented optimization procedure allows to define the ratios between the geometrical features of the manipulator which maximize a generic performance parameter in a designed workspace by avoiding all the possible singularity conditions. The obtained results are useful for the design of all the manipulators based on the 4-UPU kinematics. In particular, the case study of the design of a wearable fingertip haptic device is presented and discussed.