Optimal Design of 6 DOF Parallel Manipulators Using Three Point Coordinates

Abstract

Development of optimal design methods for general 6 degree-of-freedom parallel manipulators is important in obtaining an optimal architecture or pose for the best kinematic performance. Use of performance index such as the condition number of the Jacobian matrix that is composed of nonhomogeneous physical units may lack in physical significance. In order to avoid unit mismatch in the Jacobian matrix, this paper presents a new Jacobian formulation by use of three point generalized coordinates, which results in a (9×9) dimensionally homogeneous Jacobian matrix. The condition number of the new Jacobian matrix is used to design an optimal architecture or pose of parallel manipulators for best dexterity. A design example with Gough-Stewart platform parallel manipulator by using the proposed formulation is shown to generate the same optimal configuration as from using the other Jacobian formulation methods.