Modelling tool path in wire electric discharge machining using Denavit–Hartenberg notation

Abstract

This paper presents a systematic methodology for producing the numerical control (NC) data required to fabricate complex three-dimensional (3D) ruled surfaces using five-axis computer numerical control (CNC) wire electrical discharge machining (WEDM). The proposed approach commences by using the Denavit–Hartenberg (D–H) notation to establish the ability matrix of the WEDM machine. The Plucker coordinate representation is then applied to design the desired ruled surface in terms of a set of control lines. In addition, an offset ruled surface is derived in accordance with the principles of differential geometry in order to account for the wire radius and spark gap. Finally, the required NC data equations are obtained by equating the corresponding elements of the ability matrix and the configuration matrices of the upper and lower wire guide heads respectively. The validity of the proposed methodology is confirmed by machining a workpiece with a cubic Bezier ruled surface on a commercial five-axis CNC WEDM machine.