Since John Bosch edited and published the first version of this book in 1995, the world of manufacturing and coordinate measuring machines (CMMs) and coordinate measuring systems (CMSs) has changed considerably. However, the basic physics of the machines has not changed in essence but have become more deeply understood. Completely revised and updat

ABSTRACT: A calibration method using a 2-D artifact was developed for an optical coordinate measuring machine. The grid plate artifact was measured in four specified positions and a mathematical model was developed relating the grid plate data in these four positions with the machine parameters. The machine parameters were developed as geometric error terms expressed in terms of polynomial coefficients. The four positions of the grid plate were chosen in such a way to cover the 2-D measuring volume of the machine. To obtain best-fit values for the error polynomial coefficients, chi-squared was minimized and a set of simultaneous equations were formed. By using an elimination technique, the coefficients of error polynomials were determined. The geometric errors affecting the accuracy of 2-D measurement were measured using a laser interferometer and the first order polynomial coefficients for each type of error were determined by least squares method. The results from the grid plate method were comparable to that obtained from the laser interferometer.

Articulated arm coordinate measuring machine (AACMM) is a kind of portable coordinate measuring equipment, which employs a series of rotating joints. In order to improve the measuring accuracy and repeatability of AACMM, it is essential to calibrate the kinematic parameters of AACMM. The calibration process is a kind of nonlinear optimization problem and can be solved by employing various optimization algorithms most including Levenberg-Marquardt algorithm (LMA) and trust region algorithm. Recently, evolutionary computation (EC) has been extensively studied and applied to many engineering problems, since they have some positive features such as easy implementation, broad applicability and robust mechanism of escaping from the local optimum. Chaos optimization algorithm (COA) is one of the evolutionary computation, which utilizes chaotic numerical sequences. In this article, a new kinematic calibration approach for AACMM is proposed by using niching chaos optimization algorithm (NCOA). A hybrid objective function for kinematic calibration is proposed that reflects the various performance tests including single-point articulation performance test, effective diameter performance test and volumetric performance test. Levenberg-Marquardt algorithm and niching chaos optimization algorithm are applied for calibrating the kinematic parameters. Niching chaos optimization algorithm shows competitive calibration performance to Levenberg-Marquardt algorithm. The experimental results demonstrate that the measurement accuracy calibrated using NCOA has been better than that of using LMA in terms of the root-mean-square deviation. The experimental results demonstrate that the measurement accuracy calibrated using NCOA has been better than that of using LMA in terms of the root-mean-square deviation.

This book is a printed edition of the Special Issue "Design and Applications of Coordinate Measuring Machines" that was published in Applied Sciences

This book focuses on effective methods for assessing the accuracy of both coordinate measuring systems and coordinate measurements. It mainly reports on original research work conducted by Sladek’s team at Cracow University of Technology’s Laboratory of Coordinate Metrology. The book describes the implementation of different methods, including artificial neural networks, the Matrix Method, the Monte Carlo method and the virtual CMM (Coordinate Measuring Machine), and demonstrates how these methods can be effectively used in practice to gauge the accuracy of coordinate measurements. Moreover, the book includes an introduction to the theory of measurement uncertainty and to key techniques for assessing measurement accuracy. All methods and tools are presented in detail, using suitable mathematical formulations and illustrated with numerous examples. The book fills an important gap in the literature, providing readers with an advanced text on a topic that has been rapidly developing in recent years. The book is intended for master and PhD students, as well as for metrology engineers working at industrial and research laboratories. It not only provides them with a solid background for using existing coordinate metrology methods; it is also meant to inspire them to develop the state-of-the-art technologies that will play an important role in supporting quality growth and innovation in advanced manufacturing.