The “point of isotropy” and other properties of serial and parallel manipulators

As well known, the kinetostatic performances (repeatability, stiffness, maximum force or velocity) of serial and parallel manipulators depend strongly on the kinematic structure and on the manipulator configuration inside its working space. The manipulator performances are often analyzed using the manipulability ellipsoids which depend on the manipulator Jacobian. This paper investigates the significance of the classical definition of manipulability ellipsoid highlighting its lack of significance in some circumstances and proposes a new extended definition which takes into account the different performances of each actuator. This definition is particularly useful for manipulators with different kinematic chains and various types of actuated joints (e.g. revolute and prismatic). Then the paper reviews the concept of isotropy and its properties: a manipulator exhibits an isotropic behaviour when it has the same performances along all the directions of the working-space. Then, the authors introduce the new concept of Point of Isotropy both for serial and parallel manipulators, showing how in some circumstances a non-isotropic manipulator may be transformed into an isotropic one simply changing the location of its TCP (Tool Center Point). This concept may be used to design new manipulators or to make isotropic already existing manipulators just modifying the shape or dimension of the last link. The theoretical investigation of this new concept is supported by its application to the design of an isotropic Stewart–Gough platform.