## 1 Introduction  
Traditional articulated arm coordinate measuring machines (AACMMs) are widely used in industrial fields based on their portability, wide measuring space, and low cost. The key technologies of articulated coordinate measuring machines were instrument structure, error analysis, measurement model, eccentric error correction of circular grating installation, development of standard components for parameter calibration or performance evaluation of AACMM, optimization of parameter calibration algorithm, etc. [1]. Methods for improving the accuracy of AACMMs largely focus on kinematics modeling and the calibration of structural parameters [2; 3; 4; 5; 6; 7]. AACMMs have complex error performance. The structural parameter error of AACMMs cannot be avoided in the manufacturing process. It is necessary to identify the structural parameters through parameter calibration to enhance AACMMs measurement accuracy. A kinematic calibration procedure normally consists of four steps: determination of the kinematic model, data acquisition for calibration, parameter identification using calibration data, and experimental validation [8]. The Denavit-Hartenberg (DH) approach or the modified Denavit-Hartenberg (MDH) approach is widely employed to establish a kinematic model [9; 10; 11; 12]. The coupling relationship between kinematic parameters was considered and obtained via the singular value decomposition before the identification and compensation modelswere established [12]. Quaternions are another way of describing rotation in three dimensions. [PERSON] et al. [13] introduced a kinematic model established by quaternions. Data acquisition is carried usually out by using various artifacts, for example, a 3D artifact [14] was composed of 14 reference points with three different heights, another example was a kind of ball bar used for length reference that calibration tests were carried out in larger space by changing ball bar pose [7; 11]. [PERSON] et al. [15] used a laser tracker as a reference instrument for AACMM calibration and verification procedures. The technique increases the flexibility for defining test positions. In general, parameter calibration is performed using a mathematical method to process the sampled data. It is important to select optimization methods. [PERSON] et al. [8] compared the nonlinear least method, genetic algorithm method, and simulated annealing method. Experimental results show that nonlinear least square method is very suitable for parameter identification of AACMM and is widely used [10; 11; 12; 13; 16]. The sampled data was processed for the exclusion of rough error [11]. Interior point method was used to identify the structural parameters of AACMM and has no requirement on the iterative initial value, which can effectively improve the success rate of parameter calibration [17]. Moreover, researchers summarize error sources and try to compensate them to improve the performance of AACMM. [PERSON] et al. [18] and [PERSON] et al. [19] tried to compensate for temperature error. The temperature error correction models were established on the basis of the kinematic model established at 20 \({}^{\circ}\)C by using the experimental modeling method that found out the variation of the structural parameters at other temperature and added the variation to the corresponding parameters. [PERSON] et al. [20] and [PERSON] et al. [21] developed laser measurement systems to acquire the deformation of the serial mechanism link. Deformations due to external forces were measured and corrected. Probe errors of coordinate measuring arm were studied [22; 23]. [PERSON] et al. [22] studied the error source and influencing factors of the probe, and a mathematical model by the simulated annealing method of the relationship between the equivalent diameter and the measuring force of the AACMM was built to compensate for the equivalent diameter error of the probe caused by the measuring force.