Evaluation of the stiffness isotropy for spatially isotropic Stewart platforms

Abstract

It is known that a six-degree-of-freedom (DOF) Stewart platform that has been designed to be spatially isotropic in the central configuration cannot be spatially isotropic in any other configuration. Hence, in order to evaluate the practical usefulness of the mechanism, it is necessary to evaluate the stiffness isotropy around the spatially isotropic configuration in the workspace. One of the most popular methods for assessing the stiffness isotropy is based on the condition number, because parallel robots are spatially isotropic when the condition number of the Cartesian stiffness matrix of the robot is equal to one. However, the methods based on the condition number have several drawbacks, such as the fact that the effect of the middle eigenvalues or middle singular values is not considered. This paper first introduces the calculation steps of the Cartesian stiffness matrix for each configuration of the workspace. Thereafter, three novel methods for evaluating the stiffness isotropy of the Cartesian stiffness matrix in non-spatially isotropic configurations are introduced. Finally, two spatially isotropic variants are selected to verify these three methods.