* Corresponding author. Tel.: #30-1-772-1457; fax: #30-1-772- 1197. E-mail address: vosniak@central.ntua.gr (G. Vosniakos). Robotics and Computer Integrated Manufacturing 16 (2000) 425}435 Multiple tool path planning for NC machining of convex pockets without islands G. Vosniakos*, P. Papapanagiotou Department of Mechanical Engineering, National Technical University of Athens, Manufacturing Division, 157 80 Zografou, Athens, Greece Abstract This work focuses on machining of pockets with convex angles and containing no islands. The approach is a hybrid contouring } staircasing one. Contouring aims at clearing enough space around the boundary to allow e$cient staircasing in the interior. Three tools are foreseen: two for contouring and one for staircasing. The algorithm for contouring is based on creating o!sets of the pocket boundary and checking them for self-crossing. Staircasing is based on parametrisation of the tool path with respect to its orientation to the pocket, so as to minimise the tool path length. Machining strategy is complemented by choosing the best combination of diameters of the three tools used. This is simply done by "rst enumerating all available combinations and then excluding the non-feasible ones, in order to compare the rest according to tool path length (or to machining time when individual feed values are known). The output of the program, which was implemented in Fortran, is the tool path, the CNC part program, which is created automatically, and a numerical comparison of all the tool-angle combinations tried out. A machining simulation based on the CNC program output is conducted on commercial CAM software to demonstrate validity of the result.  2000 Elsevier Science Ltd. All rights reserved. Keywords: CNC; Pocketing algorithm; Tool path; Staircasing; Contouring 1. Introduction Pocketing is a very common machining process refer- ring to the creation of an inner empty volume starting from a component face. In some cases, the empty volume contains protrusions known as `islandsa. Pocketing has similarities to face milling, but also di!ers from it in at least two important respects:  To begin machining the tool has to move and cut in a direction normal to the pocket entry. This cutting action is commonly called plunging and consequently such capability is required of the tool.  The pocket walls constrain the tool path all around causing an additional clearance problem at the corners, which always have a "nite radius. Generic pockets consisting of non-planar faces and continuous variation of their depth may be termed `3Da, while those with planar entry and bottom faces and walls being normal to those faces are termed `2-1/2-Da. Although the pocket walls can be planar, cylindrical or, in general, any part of a tabulated cylinder surface, for the sake of simplicity in this work they are assumed to be only planar connected by cylindrical radii. In addition, the radius connecting the bottom surface of the pocket to its walls is ignored. Such pockets may be thought of as the extrusion of a polygon (with radii connecting adjac- ent edges) along a straight line normal to it. The polygon in this work is considered to be convex and no islands are allowed. Under those circumstances, it is attempted to "nd the combination of tools that can clear the pocket volume as quickly as possible which is equivalent to tool paths with minimum length. The main strategies for pocket machining are [1]:  `staircasinga, where the volume is cleared with a series of parallel passes successively taken in opposite direc- tions;  `o!settinga, where the volume is cleared with a series of closed contour passes which are produced as inner o!sets of the original pocket wall contour. In this work, a combination of these strategies is employed. Other research work has also been based on those strategies as follows. 0736-5845/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 6 - 5 8 4 5 ( 0 0 ) 0 0 0 2 5 - 9