Inverse kinematics model and trajectory generation of a dual-stage micro milling machine

Multiaxis micromachining centers, designed for precision in miniature parts due to their high degrees of freedom, face significant challenges in motion planning to achieve high accuracy and speed. This paper presents a trajectory generation algorithm for a novel dual-stage 9-axis micro milling machine, comprising a Cartesian 3-axis stage and a high-bandwidth 6-degree-of-freedom magnetically levitated table. To address the inherent challenge of kinematic redundancy, the inverse kinematics model is developed to determine the position of each axis corresponding to the desired tool position and orientation. The feedrate is determined by considering the kinematics constraints of all nine axes. With the tool paths in the machine coordinate system fitted using B-spline curves, two linear optimization problems are formulated and solved to obtain the feedrate profile. Finally, interpolation points are calculated using a feedback method to obtain the position commands. The proposed method outperforms traditional methods using the Moore Penrose pseudoinverse of the Jacobian matrix, reducing cycle time by up to 44.55 % and contour error by up to 15.64 %, demonstrating significant efficiency and accuracy improvements.