# Positioning Errors Measurement of CNC Machine Tools Based on J-DBB Method
## 5 Discussions  
This paper study the positioning errors measurement of machine tool at the whole area used by the J-DBB method. The feasibility of the J-DBB method is theoretically verified. The J-DBB synthesized the structural characteristics of traditional DBB and two-bar linkage DBB. The spherical joint with three degrees of freedom in space is the key innovation for the J-DBB method. The free measurement of machine tool error in space is also called the full-scale measurement of machine tools [23]. By adding a spherical joint, the flexibility and measurement range of the DBB are greatly improved. The positioning errors of the machine tool can be calculated from data measured with the free radius. The discontinuous measurement with a constant radius is extended to the continuous measurement with an arbitrary radius. The radius is determined by the angle of the bars, as shown in Figures 4-8. The simulation research is based on a vertical machine tool; when it executes circular motion, it is affected by the error of the positioning mechanism to simulate and analyze. The simulation results based on the J-DBB method show that the equipment error increases with the increase of length \(L\) and remains unchangeable with the variation of angle. The J-DBB method also has another significant advantage: it allows to detect errors of machine tool drive unit. These errors are caused by defects in control commands or incorrect operating procedures. Its manifestation is like machine tool positioning error, so this method can be used to analyze it.  
It is noted that we studied only four kinds of positioning errors of the machine tool used by the J-DBB method. For other positioning errors in real operation, we can adopt a similar method to measure. Firstly, we analyze these errors and translate these errors into positioning errors or pendulum errors. The pendulum errors can also be transformed into positioning errors. Then, we add the positioning errors of each axis and obtain the error vectors. The positive and negative relationship of the error vectors should be seriously considered. Finally, we substitute the error vector and obtain the error equations of the CNC machine tool.  
The simulated trajectory by the J-DBB method is like that by the DBB method. It shows that J-DBB-based machine tool error measurement is feasible. Some preliminary exploration of the positioning error measurement of the machine tool has been carried out in this paper. In addition, the device used in this paper verifies the measurement principle of the J-DBB method. Unfortunately, the accuracy of the MDF decoupling spatial angle is  
Figure 8: Simulation results of the influence of the opposite clearance on the circular motion trajectory of machine tool. (**a**) The result under different bar lengths. (**b**) The result under different pose angles.  
limited, so that J-DBB cannot be directly used to measure machine tool errors. In future research, it is necessary to design a more accurate spatial angle measurement device to replace the MDF so that the J-DBB device can be effectively applied to real measurement.