The geometric error of machine axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position. Thus, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. Firstly, the workpiece coordinate system is selected to observe the error of tools cutter location and orientation. Then, the kinematics chain of the machine will be consolidated into one, and the closed chain can be changed to open series type. The transform matrix is adopted to convert the differential operator between the different basis, because of the geometric errors have a different basis between measurement and modeling. Eventually, the general geometric error model for multi-axis machines is established after a XYFZ type three-axis machine is studied in detail.
