Formulation and evaluation of coupling effects between DOF motions of hydraulically driven 6 DOF parallel manipulator

This paper formulates a method that provides an index for evaluating the coupling effects between the degree-of-freedom motions of six-degrees-of-freedom parallel manipulators. The aim is to provide guidance for the initial design of mechanisms in which the decoupling of the displacement with respect to degrees of freedom motion is required. It is based on singular-value decomposition to the properties of the joint space inverse mass matrix. The method uses a transformation matrix, the product of transposed Jacobian matrix and an orthogonal unitary matrix.  Each element of the matrix quantifies the degree of coupling effects between degree-of-freedom motions with respect to the physical task space frame. A mathematical description of the method is presented, with the analysis supported by results from simulations and experiments. The results of the simulations show good agreement with the experimental results, indicating the good potential of the proposed method to provide guidance to mechanism designers in assessing the magnitude of the coupling effects at the initial design stage.