ANGLE CORRECTION FOR FIVE-AXIS MILLING NEAR SINGULARITIES

The inverse kinematics of five-axis milling machines produce large errors near stationary points of the required surface. When the tool travels cross or around the point the rotation angles may jump considerably leading to unexpected deviations from the prescribed trajectories. We propose three new algorithms to repair the trajectories by adjusting the rotation angles in such a way that the kinematics error is minimized. Given the tool orientations and the inverse kinematics of the machine, we first eliminate the jumping angles exceeding ${\pi}$ by using the angle adjustment algorithm, leaving the jumps less than ${\pi}$ to be further optimized. Next, we propose to apply an angle switching algorithm to compute the rotations and identify an optimized sequence of rotations by the shortest path scheme. Further error reduction is accomplished by the angle insertion algorithm based an o special interpolation to obtain the required rotations near the singularity. We have verified the algorithms by five-axis milling machines, namely, MAHO600E at the CIM Lab of Asian Institute of Technology and HERMLE UWF902H at the CIM Lab of Kasetsart University.