# Calibration of a Hybrid Machine Tool from the Point of View of Positioning Accuracy
###### Abstract  
The development of machine tools in the last twenty years includes, among other things, the application of mechanisms with a non-linear kinematic structure as the mechanical basis of machines. This results in significant improvements in kinematic characteristics and problems related to non-linear dependencies of the accuracy of the drive elements and the realization of movement in the machine's external coordinates. The paper presents an approach to machine tool calibration based on the original O-X glide mechanism based on the ISO 230-4 standard with the mono- and bi-directional compensation of systematic errors and adaptation to the specifics of the mechanism's kinematics. A machine tool prototype was designed and built for the research presented in the paper. The obtained results indicate the possibility of applying the existing recommendations and standards for testing the accuracy of machine tools with the need to correct the methodology by using linear and non-linear kinematic structures in machine tools. machine tools; calibration; hybrid kinematic; O-X glide +
Footnote †: journal: Medical  
presented an overview of the measurement of quasi-static kinematic errors [3]; a very similar, modernized view has been given elsewhere [4]. [PERSON] et al. presented an overview of the most modern measurement methods, mathematical models, and compensation strategies for calibrating machine tools [5]. The basics of error compensation and available methods for measuring machine tool geometric errors are summarized and updated in [3]. In Refs. [1,6], the techniques were proposed and are based on artifacts. This research enables the control of machine tool error mapping and calibration by compensating them. A methodology for quantitatively evaluating the success of machine tool calibration methods was proposed by [PERSON] et al. [7]. Improvement of the mechanical concept of machine tools in the previous period included applying non-linear kinematic structures (parallel and hybrid mechanisms) to improve the machines' exploitation characteristics. Therefore, research was initiated into the accuracy and calibration of such machine tools. The first paper on the accuracy of these machines analyzes the accuracy of mechanisms based on the Stewart platform or other types of parallel mechanisms, in which external sensors were used to measure the position and orientation of the final end-effectors. A kinematic model was used to evaluate the influence of parallel manipulator mechanism errors relative to the final end-effector's positioning accuracy. The paper [8] proposed a new method of identifying mechanism errors for a 3-PUU parallel mechanism. It is based on the inverse kinematics model and volumetric error measurement techniques using a 3D laser ball bar device. The experimental results combined with the optimization technique can determine the errors of the mechanism of the tested machine, i.e., the structural symmetry errors of the rods and joints. This method can help machine tool manufacturers to determine the basic length parameters (rod lengths) and fine-tune the kinematics (by determining the position of joints or rods) in the assembly phase. Based on the results obtained from research on the impact of parallel kinematic structure on mechanical properties, the first commercial solutions of machine tools with parallel kinematics appeared at the end of the twentieth century. That solution enabled significant improvements in stiffness, accuracy, and movement dynamics. With the implementation of the new kinematic concept, it was observed that the application of parallel mechanisms in the development of machine tools, in addition to several advantages [9], also has certain disadvantages [10,11] that determine the area of their application (dimensions and shape of the workspace and specific control structure).