Kinematic isotropy and the optimum design of parallel manipulators

The differential kinematic equations (DKE) of parallel manipulators usually involve two Jacobian matrices that, depending on the role they play in the kinetostatic transformation between the joint and Cartesian variables, are commonly referred to as the forward and the inverse Jacobians. In this article, we make use of the special structure of these Jacobians to define a set of conditions under which a parallel manipulator con be rendered isotropic. These conditions are general, and provide a systematic method for the optimum kinematic design of parallel manipulators, with or without introducing structural constraints. The application of the proposed conditions is illustrated in detail through a few examples, one of which pertains to the design of a 6-DOF isotropic parallel manipulator.