Continuous path verification in multi-axis NC-machining

We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter continuously moves near the workpiece. Having five degrees of motion freedom, this problem is hard to solve exactly and we approximate the motion of the tool by a sequence of sub-paths of pure translations interleaved with pure rotations. The collision-detection problem along each sub-path is then solved by using radial projection of the obstacles (the workpiece and the static parts of the NC-machine) around the tool axis to obtain a collection of critical surface patches in ℝ3, and by examining planar silhouettes of these surface patches. We thus reduce the problem to successive computations of the lower envelope of a set of planar curves, which we intersect with the profile of the tool. Our reduction is exact, and incurs no loss of accuracy. We have implemented our algorithm in the IRIT environment for solid modeling, using an extension package of the CGAL library for computing envelopes. The algorithm, combined with the proper data structures, solves the collision detection problem in a robust manner, yet it yields efficient computation times as our experiments show. Our approach produces exact results in case of purely translational motion, and provides guaranteed (and good) approximation bounds in case the motion includes rotation.

[1]  Martin Held,et al.  On the Computational Geometry of Pocket Machining , 1991, Lecture Notes in Computer Science.

[2]  Gershon Elber,et al.  Precise Global Collision Detection in Multi-Axis NC-Machining , 2004 .

[3]  Bert Lauwers,et al.  Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation , 2003, Comput. Aided Des..

[4]  Gershon Elber,et al.  Freeform surface region optimization for 3-axis and 5-axis milling , 1995, Comput. Aided Des..

[5]  Robert B. Jerard,et al.  Approximate methods for simulation and verification of numerically controlled machining programs , 1989, The Visual Computer.

[6]  Iddo Hanniel,et al.  The Design and Implementation of Planar Maps in CGAL , 1999, WAE.

[7]  Micha Sharir,et al.  Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes , 1986, FOCS.

[8]  Ron Wein,et al.  High-Level Filtering for Arrangements of Conic Arcs , 2002, ESA.

[9]  Dinesh Manocha,et al.  Fast swept volume approximation of complex polyhedral models , 2003, SM '03.

[10]  Yuan-Shin Lee,et al.  2-Phase approach to global tool interference avoidance in 5-axis machining , 1995, Comput. Aided Des..

[11]  M. Sharir,et al.  Pipes, Cigars, and Kreplach: the Union of Minkowski Sums in Three Dimensions , 2000 .

[12]  John F. Canny,et al.  Collision Detection for Moving Polyhedra , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Gershon Elber,et al.  Geometric modeling with splines - an introduction , 2001 .

[14]  Sanjay E. Sarma,et al.  Collision-free finishing toolpaths from visibility data , 2003, Comput. Aided Des..

[15]  Jarek Rossignac,et al.  Collision prediction for polyhedra under screw motions , 2003, SM '03.

[16]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[17]  John Hershberger,et al.  Finding the Upper Envelope of n Line Segments in O(n log n) Time , 1989, Inf. Process. Lett..

[18]  Erik L. J. Bohez,et al.  The stencil buffer sweep plane algorithm for 5-axis CNC tool path verification , 2003, Comput. Aided Des..

[19]  Dinesh Manocha,et al.  Collision and Proximity Queries , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[20]  Dinesh Manocha,et al.  Fast continuous collision detection for articulated models , 2004, SM '04.

[21]  Yoshitaka Adachi,et al.  Real-time interference analysis between a tool and an environment , 2001, Comput. Aided Des..

[22]  M. Atallah.  Some dynamic computational geometry problems , 1985 .

[23]  Gershon Elber,et al.  Continuous path verification in multi-axis NC-machining , 2004, SCG '04.

[24]  Micha Sharir,et al.  Davenport-Schinzel sequences and their geometric applications , 1995, Handbook of Computational Geometry.