Iterative Method for the Inverse Kinematics of a 3-Limb Parallel Mechanism with 3-DOF Using a 6-Limb Mechanism with 6-DOF

In general, constraint equations are needed for the inverse kinematics (IK) of the parallel mechanism (PM) with less than 6 degrees of freedom (DOF) and dependent parameters describing the pose of the moving platform. However, the applicability of such an approach is restricted to the mechanism configuration from which the constraint equations are derived. In order to solve this problem, this paper presents an iterative method for solving the IK of a 3-limb parallel mechanism with 3 DOF. Therefore, a kinematically equivalent mechanism, which is a virtual model composed of a 6-limb parallel mechanism with 6 DOF under the active joint motion constraint, is introduced. In this method, an iterative procedure for the IK of a 3-PRS parallel mechanism using the IK of the kinematically equivalent mechanism is proposed. Numerical examples demonstrate the convergence process during iteration, the ability to obtain all solutions, and the applicability to various structural parameters of the proposed method.