Semi-isotropic design of a Stewart platform through constrained optimization

The isotropic property at home configuration for a semi-regular Stewart platform manipulator with equal leg lengths has been found to be nonachievable by kinematic design optimization study. In this context, a new approach of design optimization has been formulated here for achieving semi-isotropicity through variable transformation that has rendered the constrained optimization over a finite workspace to infinite workspace in the transformed domain. The proposed minimization methodology of a positive definite function for all the angular and translational motion has exhibited strong convergence to zero for values of the design parameters that can be worked out as a closed-form solution only for the cases of linear translation. Finally, the variations of the condition number over the permissible range of all single-degree-of-freedom motions have been carried out. The absence of any other minima in the entire workspace has clearly established the home position as globally optimized.