Calculation of the swept volume of a cutter is the heart of any numerical controlled (NC) simulation system. In NC machining, a wide variety of cutter shapes are used such as¯at end mills, dome end mills, ball nose end mills, angle cutters, face mills and side-and-face cutters. There are also many types of cutter paths along which the cutter is guided by the NC controller: rapid motion, linear motion and circular motion are the most commonly used cutter paths among them. Furthermore, the kinematics of the NC machines also dier leading to 2.5-axis, 3-axis and a variety of 5-axis con®gurations. The swept volume algorithms have to take into account all these variations of cutter shapes, motion types and machine kinematics. In this paper, ®rst the parametric de®nition of a generic cutter is presented that can emulate all types of cutter shapes. Subsequently, the motions are classi®ed into six types considering the cutter path and kinematic variations for ease of swept volume calculations. Finally, the swept volume algorithms for each of these six motion types are presented. These algorithms are used in a volumetric NC simulation system for which applications are envisaged in (a) NC veri®cation and (b) optimization of the feed rate.

At the completion of building an object in laminated object manufacturing rapid prototyping (LOM-RP), a block with the required object inside is obtained. The remaining stock inside and surrounding the object is in the form of tiny tiles. The operator ‘decubes’ these tiles using sharp tools and extracts the object. After cutting the object contours in each laminate during the building process, the remaining sheet is cut into square grids that grow into these tiles. This grid cutting method, though very simple and innovative, is very inefficient due to poor cutting efficiency and a long decubing time. In this paper, a novel method is presented for extracting the object that is analogous with the extraction of a casting from its permanent mould. This method has a very high cutting efficiency and simplifies and speeds up decubing. The concepts of convex hull and visibility are utilized in the algorithm.