We propose the measurement method for location errors in a horizontal 4-axis machine tool using a touch trigger probe and a sphere artifact. Location errors (type of geometric errors), are values that do not change with the position of each feed axis because these errors are usually fixed in an assembly procedure. There are seven location errors in a horizontal 4-axis machine tool; three squareness errors in three linear axes and two squareness and two offset errors in a rotary axis. The positions of center point of sphere artifact on a rotary axis are measured by a touch trigger probe mounted on a tool axis. Because measured center points are expressed by seven location errors via the homogeneous transformation matrix, location errors can be separated by analyzing measured data. To validate the proposed method, measurement experiments were performed on a horizontal 4-axis machine tool. Measurement results were verified by comparing before and after compensation.

Various types of 5-axis machine tools have been developed. In the case of a machine tool composed from linear motion, the kinematic equation can be obtained easily and intuitively. However, machine tools with more than four axes, including rotating axes, have generally performed kinematic and dynamic performance analyses using mathematical methods. In this paper, the kinematic equations of various types of machine tools are obtained, based on the Homogeneous Transformation Matrix method. The loop stiffness was then calculated as a mathematical model. A mathematical model of loop stiffness was verified by using a method to calculate the loop stiffness of a commercial program. The results of the mathematical model showed less than a 1% error with the commercial program, and this could show the validity of the mathematical model. Then, this model was applied to two types of machine tools. The minimum loop stiffness of both models is compared.