# Calibration of a Hybrid Machine Tool from the Point of View of Positioning Accuracy
###### Abstract
In order to make maximum use of the advantages of serial and parallel mechanisms and to reduce the impact of their shortcomings, hybrid, serial-parallel mechanisms have been used in the development of machine tools for many years. In this way, a good compromise solution that has proven to be applicable to the production of machine tools, manipulation systems, and industrial robots is provided. Examples of successful applications of hybrid mechanisms [12] include Tricept [13], Execon [13], Ecospeed [14], Geodetic Hexapod [15], and George V [16]. In machine tools with serial kinematics, the kinematic relationship between the executive part of the machine and the moving elements is linear. Therefore, we can call them machine tools with linear kinematics. In contrast, the kinematic relationships of machine tools with parallel or hybrid kinematics are significantly more complex and not linear, which is why they can be called machine tools with nonlinear kinematics [17]. In current research on the characteristics of machine tools with linear and non-linear (parallel and hybrid) kinematics, problems related to the accuracy of the machines [18], as well as the possibilities of their calibration [19], are often considered. Calibrating machine tools ensures maximum utilization of the machine's mechanical and control systems. The calibration of machine tools is a process that is carried out periodically in order to verify and improve the characteristics of machine tools [5]. This process is carried out to reduce or eliminate errors due to thermal, static, dynamic loads, and control system errors. Calibration of linear axes of machine tools includes the following:  
* Testing the positioning accuracy of the complete machine;* Identification of systematic and random errors;
* Their removal or numerical compensation in the control system of the machine tool. The fundamental problem of applying this procedure to machine tools with parallel or hybrid kinematics is the need to recalculate the errors on the internal coordinates of the machine defined by the nonlinear kinematics of the mechanism, even when defining the calibration parameters, and the test parameters (movement method, movement speed, stopping time) that are not explicitly defined by the standard adapt to the appropriate mechanism and its characteristics. This paper presents part of the research conducted to determine the influence of machine tool calibration with an O-X glide kinematic structure on the positioning accuracy of the moving platform. The research was conducted to enable the compensation of errors through the calibration process by applying standardized techniques for identifying errors in the mechanical structure. In the paper, research was carried out according to the ISO 230-4 [20] standard, in static conditions, on a machine tool prototype that was made for research. In contrast, the standard parameters for which no selection recommendation was varied in a range corresponding to the exploitation values for a specific kinematic machine configuration. The results were processed according to the kinematic differences between the mechanical structure of machines with linear and non-linear kinematics. The calibration was carried out using the mono- and bi-directional compensation of systematic errors obtained by measuring accuracy.