In this paper, we present a measuring approach to assessing the volumetric accuracy of machine tools or kinematics with more than 3 interpolating feed axes. It is based on an inexpensive Double Ballbar and suitable for fast performance-tests in an operational state of the machine. The novelty is the recording of large amounts of data in a very short period while continuously moving along measuring paths with up to 6DoF. In order to facilitate this measuring approach, we developed a Double Ballbar with extended measuring range based on an optical sensor and a series of systematic methods, like kinematic error modeling, optimal design of 6D measuring paths as well as post-processing and evaluation of the captured data. We demonstrate that our approach is universally applicable to different types of kinematic structures such as 5-axis machine tools, industrial robots or even parallel kinematics. By experiments, we will also show that the measured data are essentially more informative than those of standardized circular DBB tests are. Moreover, the measuring procedure is automatable and to be carried out under production conditions in the workshop, what makes it practically applicable in various evaluation and decision scenarios.