ORIGINAL ARTICLE Origin offset and axes misalignment compensation in complex form parameter estimation using CMM Juan Antonio Aguirre-Cruz & Shivakumar Raman Received: 17 August 2010 / Accepted: 12 February 2013 # Springer-Verlag London 2013 Abstract Coordinate measuring machines (CMMs) play an important role in industry to verify dimensions and toler- ances of manufactured parts. The accuracy of measurements using CMMs depends on the capability of the mathematical models to represent the geometry of the part and on the fitting algorithms to find the best solution that will correct the axes orientation and origin offsets between the measure- ments and of the nominal form. This study describes two approaches: a dynamic angle approach that was developed to improve the performance of the Limacon approximation; and a free-form orientation approach that models the assessed form and cancels out the axes misalignments by using the flatness model. The accuracy of these models was tested using data that was available from previous studies. Results from this analysis showed that the two developed approaches improve the calculation of the zone of error of circular, spherical, cylindrical, and toroidal features; and the estimation of the parameters, origin offsets, and axis mis- alignments. Therefore, it can be concluded that the devel- oped approaches performed quite efficiently for adoption in product metrology. Keywords Origin offsets compensation . Axes misalignment . Limacon approximation . Form feature determination . Toricity form . Minimum zone estimation 1 Introduction The advantages in technology had allowed the manufactur- ing companies to created industrial parts with an unlimited range of shapes. Although, the precision and accuracy of the machining processes are very high, the tolerances of the machined part are significantly affected by the manner in which the process removes the material. The process leaves a unique fingerprint over the surface of the part, causing roughness, waviness, and form imperfections [1]. Similarly, inspection with a coordinate measuring machine (CMM) induces noise into the measurements that causes the rejec- tion of a good part or acceptance of a bad part. Hence, several studies have been performed to develop mathemat- ical models to accurately estimate the parameters of the machined features as well as to counteract the effects of the noise caused by the inspection process. Although CMMs have capabilities to adjust its own co- ordinate system, it is impossible to place the coordinate system of the machine and that of the part at the same position and orientation. Thus, in several studies related to the form tolerance verification of circles, planes, spheres, cylinders, cones, and torus; the mathematical models were created to describe the form deviations of these shapes by estimating the geometry of the part and counteracting the effects of the origin offsets and the misalignments due to the axis of assessment. One excellent example of such modeling is the Limacon approximation. The properties of the Limacon makes easy the study of round features because it linearly estimates the ge- ometry of the part and counteracts the effects of the origin offsets [2]. The approximation is very efficient as long as the origin of the inspection equipment is relatively closed to the geometrical origin of the part. Due to its simplicity, the ap- proximation has been used in the study of circular [3–6], spherical [7–11], conical [12, 13], and toroidal forms [14, 15]. The purpose of this study is to improve the existing methodology by providing different ways to counteract the effect of the origin offsets and the misalignments due to the axis of assessment. This paper focuses on developing two J. A. Aguirre-Cruz : S. Raman (*) School of Industrial Engineering, University of Oklahoma, 202 W. Boyd, Ste. 124, CEC, Norman, OK 73019, USA e-mail: raman@ou.edu Int J Adv Manuf Technol DOI 10.1007/s00170-013-4838-8