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Abstract: The paper discusses the concepts of isotropy and decoupling in n-DoF (degrees of freedom) manipulators: isotropy means that its kinetostatic properties are identical in all directions, while decoupling means that each DoF of the end effector is controlled by a single actuator. The role of different Jacobian matrices in the isotropy, decoupling and in the general mobility analysis of the manipulators is revised. These concepts are applied to a Gough–Stewart platform showing that it may be isotropic, but not decoupled. A modification of its leg structure is suggested to develop some new 6-DoF PKMs (parallel kinematic machine) decoupled and isotropic in the considered configuration. An introduction to the mobility analysis of serial and parallel manipulators is also presented. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]