The concept of isotropy for serial and parallel manipulators and its influence on force, velocity, stiffness, accuracy, and repeatability performances

The significance of the classical definition of manipulability ellipsoid highlighting its lack of significance in some circumstances was investigated. A new extended definition of isotropy which takes into account the different performances of each actuator was presented. This definition was found to be useful for manipulators with actuators of different types for which the classical definition is meaningless. The relation existing between the isotropy and the position of the Tool Center Point (TCP) was investigated. The new concept of Point of Isotropy was introduced and it was shown that any serial or parallel manipulator, for each joint configuration, can have at most one possible choice for TCP that makes it isotropic. The geometrical conditions for the presence of an isotropy point were also derived in analytical form.