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The influence of technical parameters for volumetric error compensation in large-volume machine tools (MTs) is presented in this paper. The techniques presented are based on characterization models using nonlinear optimization procedures. The parameters presented allow for the characterization of different errors in the MT studied and depend on the kinematics and geometry of the system, regardless of the optimization methodology. The kinematics is affected by the MT errors on the number and type of axes and movements. To relate the coordinates of the tool to the coordinates of a laser tracker, a kinematic model of the MT that includes the measurement system must be defined. Kinematic models can be realized by using homogeneous transformation matrices or independent rotation and translation arrays according to the type of machine. Chebyshev, simple or Legendre polynomial regression functions can be used to characterize the geometric errors of the MT and are presented and compared. The distribution of measurement points, mesh or cloud, and optimization constraints of polynomial regressions are factors that also affect volumetric error compensation. Therefore, these parameters were studied and presented as well. In addition to the parameters discussed above, another parameter that affects the accuracy of data capture is the measurement noise. To improve the measurement accuracy, multilateration techniques need to be applied. Each of the aforementioned parameters has been studied by using a synthetic test generated by a parametric synthetic data generator. The selected parameters constitute a package of optimization improvement regardless of the optimization methodology, which have improved the nonlinear optimization from 60–70% to 98%.

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This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters.

A new procedure for the calibration of an articulated arm coordinate measuring machine (AACMM) is presented in this paper. First, a self-calibration algorithm of four laser trackers (LTs) is developed. The spatial localization of a retroreflector target, placed in different positions within the workspace, is determined by means of a geometric multilateration system constructed from the four LTs. Next, a nonlinear optimization algorithm for the identification procedure of the AACMM is explained. An objective function based on Euclidean distances and standard deviations is developed. This function is obtained from the captured nominal data (given by the LTs used as a gauge instrument) and the data obtained by the AACMM and compares the measured and calculated coordinates of the target to obtain the identified model parameters that minimize this difference. Finally, results show that the procedure presented, using the measurements of the LTs as a gauge instrument, is very effective by improving the AACMM precision.