Research Article Articulated Arm Coordinate Measuring Machine Calibration by Laser Tracker Multilateration Jorge Santolaria, Ana C. Majarena, David Samper, Agustín Brau, and Jesús Velázquez Departamento de Ingenier´ ıa de Dise˜ no y Fabricaci´ on, Edifcio Torres Quevedo, EINA, Universidad de Zaragoza, 50018 Zaragoza, Spain Correspondence should be addressed to Jorge Santolaria; jsmazo@unizar.es Received 27 August 2013; Accepted 3 November 2013; Published 29 January 2014 Academic Editors: G. Huang and D. Veeger Copyright © 2014 Jorge Santolaria et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. Te spatial localization of a retrorefector target, placed in diferent 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 identifcation procedure of the AACMM is explained. An objective function based on Euclidean distances and standard deviations is developed. Tis 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 identifed model parameters that minimize this diference. Finally, results show that the procedure presented, using the measurements of the LTs as a gauge instrument, is very efective by improving the AACMM precision. 1. Introduction In recent years, there has been an increasing interest in AACMM’s because of their advantages in terms of accuracy, portability and suitability for inspection and quality control tasks in machining tool processes and in the automotive and aerospace industry [1]. Nevertheless, few researches have focused on the cali- bration of these mechanisms. Moreover, there is an absence of standards on verifcation and calibration procedures. For that reason, AACMM manufacturers have developed its own evaluation procedures. Tese evaluation methods are based on the three main standards for performance evaluation in current CMM’s, UNE-EN ISO 10360, ASME B89.4.1, and VDI/VDE 2617 and are still carried out today to compare and evaluate the accuracy of an arm from the point of view of the CMM’s. In [1], the author presented a procedure to check the performance of coordinate measuring arms by calculating the distances between the centers of diferent spheres. Te results obtained were compared with the application of the ANSI/ASME B89 volumetric performance test showing good agreement between the two approaches and a cost reduction. In [2], Shimojima et al. presented a new method to estimate the uncertainty of a measuring arm using a tridimensional gauge. Tis method consists of a fat plate with 9 spheres fxed at three diferent heights with respect to the metallic surface of the plate. Ten the spheres centers are measured with the measuring arm at diferent locations and orientations, and distances between spheres centers are compared to the nominal distances to evaluate the measuring performance of the arm. Other works have been found in the literature whose main goal is also to evaluate the performance of measuring arms [3–5]. However, the AACMM presents diferent characteristics, and diferent verifcation procedures are therefore required. A point clearly defnes a position of the three machine axes for a CMM. Nevertheless, the possible positions of the AACMM elements to achieve a fxed point defned in the measurement volume are practically infnite. Moreover, for CMMs, evaluation tests can be performed to extract the positioning errors, allowing correction models to be imple- mented [1]. Tus, a high level of maintenance of the physical- mathematical relations between the error model parameters and the error physically committed by the machine can be achieved. However, the application of these models does not make sense in AACMM’s, given the difculty of directly Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 681853, 11 pages http://dx.doi.org/10.1155/2014/681853