Analytical Formulation of Coupling Effects Matrix Between Degrees of Freedom Motion of Parallel Robots

This paper presents a coupling matrix formulation which can be useful for evaluating the coupling effects between degrees of freedom motions of parallel robots. The method is based on the formulation of coupling matrix using a transformation matrix and an orthogonal unitary matrix. Each row of the matrix describes the degree and nature of coupling effects between DOF motions with respect to physical task space frame. A mathematical description of the method is presented, with the analysis supported by results from simulation. The simulation results show good agreement with theoretical result therefore, reflecting the quite good potential of the proposed method to provide guidance to mechanism design to assess the value of the coupling effects at the initial design stage for a specific Gough Stewart platform.