Screw Theory Based Metrology for Design and Error Compensation of Machine Tools

Abstract The paper presents a generalized mathematical framework for computation and compensation of tool tip errors in multi-axis machine tools using screw theory. In contrast to conventional Denavit–Hartenberg notation, Screw theory offers several advantages including: (i) modeling of complex machine tool configurations with rotational axes, (ii) tractability of error propagation which simplifies solution of inverse kinematics and subsequent error-compensation procedures, and (iii) functional representation of error screws in a global reference frame rather than cumbersome coordinate transformations of local reference frames. Kinestatic filtering technique [11,12] is adopted for evaluating the compensatability of errors and the Jacobian is used for error compensation. The methodology is illustrated using a five-axis machine tool with two rotational axes.