Methods for Surgical Serial Manipulators Isotropy Indexing

In this paper three methods to characterize isotropy in the workspace of serial manipulators are introduced. The first method is based on the Principle of Virtual Works, since the manipulator is assumed to be still under the control action, with prescribed values of the joint stiffness. The end effector displacements are compared to the externally applied load under the general hypothesis that some joints are dependent upon the others. Such hypothesis applies to the da Vinci surgical robot and allows to generalize the procedure to evaluate the condition number and, therefore, the isotropy index. The second method is based on the Lie product, while the third one relies on the definition of a deviant part of the compliance matrix. The three methods are compared and results show that isotropy evaluations are very similar along prescribed paths.