ISO 13041-3:2009 specifies, with reference to ISO 230-1 and ISO 230-7, the geometric tests on general‑purpose, numerically controlled (NC) turning machines and turning centres with inverted vertical workholding spindles, as well as the corresponding applicable tolerances.

It presents the different concepts or configurations and common features of NC turning machines and turning centres with inverted vertical spindles. It also provides a terminology and designation of controlled axes.

ISO 13041-3:2009 deals only with the verification of the accuracy of the machine. It does not apply to the operational testing of the machine (e.g. vibration, abnormal noise, stick-slip motion of components), nor to machine characteristics (e.g. speeds, feeds), as such checks are generally carried out before testing accuracy.