关键词: 五轴加工, 奇异区域, 雅可比矩阵, 运动控制, 条件数, 奇异点

Abstract: To solve problems of excessively large non-linear error and damages to the workpiece and the machine tool near singular points in five-axis machining, took AC dual-table five-axis machine tool as study object，an algorithm based on Jacobian matrix to detect and treat singular area was advanced. The general parameter formula of Jacobian matrix of five-axis machine tools was set up. And then, changes of axis between two consecutive points were substituted into the Jacobian matrix. By checking the condition number of the Jacobian matrix, whether the tool was in singular area or not was concluded. For serious path section of Jacobian matrix ill-condition, a recursive interpolation, which was based on both the initial cutting location data and the value of axis was proceeded. A simulation test was performed to verify the effectiveness of this algorithm.

Key words: five-axis machining, singular area, Jacobian matrix, motion control, condition number, singular point