## 1 Introduction  
Rotary axes are widely applied in computer numerical control machining, robotics, aerospace, and other fields. Rotary axes with inadequate motion accuracy directly reduce the working accuracy of the related precision machines. The first and most important step to increase the accuracy of the axes and decrease the influence of the errors is to quickly and accurately measure the motion errors of the rotary axes.  
A complete description of the motion errors of a rotary axis requires six physical quantities [1]: the angular positioning error (\(E_{\text{CC}}\)), the tilt motion error around the \(y\) axis (\(E_{\text{BC}}\)), the tilt motion error around the \(x\) axis (\(E_{\text{AC}}\)), the radial motion error along the \(x\) axis (\(E_{\text{XC}}\)), the radial motion error along the \(y\) axis (\(E_{\text{YC}}\)), and the axial motion error (\(E_{\text{ZC}}\)). In order to make the symbols convenient for the subsequent calculation of the coordinate transformation, we use the simpler symbols \(\varepsilon_{x}\), \(\varepsilon_{y}\), \(\varepsilon_{x}\), \(\delta_{x}\), \(\delta_{y}\), and \(\delta_{z}\) instead of \(E_{\text{CC}}\), \(E_{\text{BC}}\), \(E_{\text{AC}}\), \(E_{\text{XC}}\), \(E_{\text{YC}}\), and \(E_{\text{ZC}}\) in the calculation. The real motion trajectory of the axis can be reconstructed using these six motion errors, and the application precision of the related mechanical equipment can be improved by compensating for the errors. Therefore, the key problem to be solved is how to obtain the six degrees-of-freedom (DOF) motion errors of the axis with high precision and high efficiency. At present, the simultaneous measurement methods of multi-DOFmotion errors are mainly based on laser properties [2; 3; 4], material profile [5], trajectory analysis [6], and other factors [7].  
[PERSON]'s apparatus, using three lasers, is a rare method that can measure the six DOF motion errors of a rotary axis simultaneously and directly [8]. While its structure is complicated, [PERSON] used the laser tracker [9] to study the measurement of the six DOF errors. [PERSON] used the R-test [10; 11] method to identify the six errors. However, most of these indirect measurement methods need to determine each error using complex function-fitting algorithms. Unlike these existing methods, our method can measure the six DOF errors directly at the same time. It also has the advantages of easy installation and high measurement efficiency. Two important methods--a servo-tracking strategy and error model analysis--are used to realize and improve the functions of the measuring device.  
In this paper, a device for the simultaneous measurement of the six DOF errors of a rotary axis is introduced, and a method to improve the measurement accuracy is proposed based on our previous research for five DOF errors [2; 12]. The automatic measurement is achieved by using the servo-tracking strategy. It is also used to overcome the difficulty of the beam needing to be uninterrupted during the interferometric process. A complete model for measuring all six DOF motion errors is proposed. The factors influencing the measurement result are analyzed, and a compensation method is proposed. In Section 2, the measurement principle of our device is briefly introduced. The servo-tracking strategy of the reference rotary axis is described in detail. An error model is established using the homogeneous transformation matrix (HTM) [13; 14]. In Section 3, we describe a series of experiments, which were carried out to simultaneously measure the six DOF errors of a rotary axis. The repeatability and comparison results were obtained after compensation and demonstrate the effectiveness of our method and the error compensation model.