A novel method to minimize the five-axis CNC machining error around singular points based on closed-loop inverse kinematics

Singularities in five-axis machining are a series of positions where the exact motion of the rotary axis becomes unpredictable or incalculable. In the neighborhood of a singular point, machining may cause unstable movements of drive axes and deteriorative dynamic performance of machine tools. In this paper, we proposed a closed-loop inverse kinematics method to solve accurately the five-axis joints' parameters around singular points. To achieve this purpose, the damped Jacobian pseudoinverse algorithm is introduced and the machine joints' velocities are calculated directly by the velocities of the five-axis cut points. The joints are then obtained by integrating the corresponding velocities. Furthermore, a feedback control method is applied to reduce the integrating error. In the end, simulations and experiments' results demonstrated the effectiveness of the closed-loop inverse kinematics method.