Modeling Errors in Coordinate Measuring Machines and Machine Tools Using Homogeneous Transformation Matrices (HTM)

Abstract

Coordinate Measuring Machines (CMM's) have attributes to provide results with accuracy and repeatability in measurements, so they are considered equipment with potential for application in industrial environments, specifically in inspection processes. However, as in a machine tools the knowledge of the errors in CMM is needed and allows applying techniques of error compensation. This study aimed to develop a mathematical model of the kinematic errors of a bridge type CMM in "X", "Y" and "Z" directions. Modeling of the errors was accomplished using coordinate transformations applied to the rigid body kinematics; the method of the homogeneous transformation was used for the development of the model. The position and angular errors for the three axes of CMM, in addition to errors related to the absence of orthogonality between them were equated. This study allowed to conclude that modeling of errors applied to CMM allied to calibration is able to evaluate the metrological performance of equipment with displacement on guides, thus is possible to use this technique as error budget analysis in machines.