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 models were established [
12]. Quaternions are another way of describing rotation in three dimensions. Battista 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]. Acero R. 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. Cheng 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. Santolaria et al. [
18] and Luo 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 °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. Yu et al. [
20] and Vrhovec 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]. Luo 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. Virtual articulated arm coordinate measuring machines were developed for the determination of measurement results along with its uncertainty [
24,
25]. The uncertainty of the measurement point for an AACMM was modeled by ellipsoids [
24]. Zheng et al. [
26] measured a workpiece using an AACMM and found that the length measurement accuracy of the workpiece was not the same in different positions within the measuring space. The optimal measurement area, that is, the area with the highest accuracy, is supposed to exist in the whole measuring space. The optimal measuring area is related to the error characteristics of the angle measuring system. An ant colony algorithm was used to determine the optimal measurement area for an AACMM [
27].
However, random errors introduced by users cannot be controlled to ensure an optimal trajectory, constant force measurement, and stable contact direction. González-Madruga et al. [
28] stated that AACMMs lacked traceability and reliability, which was largely based on human error, but the error was not considered in current measurement and evaluation methods. Cuesta et al. [
29,
30] pointed out that AACMM errors related to human factors were caused by non-uniform contact forces, lack of stability, different velocities, and accelerations, among unpredictable probing trajectories, resulting in unpredictable structural deformation during the AACMM measurement process. AACMMs utilize a manual drag-and-drop measurement mode. Although this method avoids complicated path planning and control problems, it also introduces uncontrollable measurement force, random measurement posture, uneven sampling points, poor repeatability and stability [
29], and inapplicability to production lines or the online automatic measurement.
Therefore, this paper proposes a self-driven joint module for constructing self-driven articulated arm coordinate measuring machines. Based on theoretical analysis, a virtual prototype of a self-driven AACMM is established by using the MSC Adams 2016 software for simulation analysis and component selection. A physical single-joint prototype was developed and feasibility experiments were carried out. The proposed self-driven AACMM makes it possible to perform measurements with optimal measurement attitudes, in which grating sensor measurement error and machine deformation error are less.