Parameterized inverse kinematics of parallel mechanism based on CGA

Abstract

A parameterized inverse kinematic model is the theoretical basis for performance analysis, design and control of parallel mechanism (PM). Current methods are either computationally expensive or difficult to get analytical form. To deal with this problem, this paper proposes a parameterized method by conformal geometric algebra (CGA). Based on the description and computation of screw motions in CGA, closure equations about successive screw displacements of any PM can be formulated. Joint displacements of each limb and screw parameters of end-effector are then solved in an analytical manner. The proposed method is exemplified by a 3 degree-of-freedom (DoF) PM, which shows high efficiency in deriving the analytical inverse kinematic model.