doi:10.1016/j.rineng.2026.109762engAguado, SergioPueo, MarcosAcero, RaquelBrosed, Francisco JavierSantolaria, JorgeAguilar, Juan JoséKinematic modelling and volumetric error compensation of a 3-axis machine tool using a telescopic simultaneous ballbarART-2026-148396Volumetric verification (VV) is an effective method for improving the machining accuracy of three and five-axis machine tools (MTs). This paper presents the volumetric verification and error compensation procedure of a medium-sized 3-axis machine tool using a telescopic simultaneous ballbar (TSB). The paper presents the MT kinematic model, the error compensation process with the TSB and the validation in the MT selected. A two-phase optimisation was chosen, in which the squareness and linear errors were calculated together, while in a second phase the rotational errors were identified. A relevant aspect of the work is to evaluate the impact of influencing factors on the verification, such as the location and measurement uncertainty of the measuring system (TSB), the distribution of the points to be verified and the data filtering process. The average volumetric error is reduced by 79.8% in the line verification for a given work area and by 41.7% in a grid considering a global distribution of the MT working volume. The results obtained by the laser interferometer after compensation of the x-axis position error confirm that this technique effectively improves the MT accuracy, with maximum errors of 5 μm and 7 μm for the verification line and grid, respectively. The implemented algorithms are efficient and robust, and the results obtained using the TSB show a global correction of the MT over the entire working area.2026http://zaguan.unizar.es/record/16950210.1016/j.rineng.2026.109762http://zaguan.unizar.es/record/169502oai:zaguan.unizar.es:169502info:eu-repo/grantAgreement/ES/AEI/PID2022-139280OB-I00info:eu-repo/grantAgreement/ES/DGA/T56-23Rinfo:eu-repo/grantAgreement/ES/MINECO/DPI2017-90106-RResults in Engineering 29 (2026), 109762 [13 pp.]by-nchttps://creativecommons.org/licenses/by-nc/4.0/deed.esinfo:eu-repo/semantics/openAccess