Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths

In earlier work, we introduced the concept of time-optimal toolpaths, modeled the behavior and constraints of machining, and formulated the optimization problem mathematically. The question was by what toolpath it would be possible to machine a surface in minimum time-while considering the kinematic performance of a machine, the speed limits of the motors and the surface finish requirements. The time-optimal problem is a difficult one, and does not generally yield a closed-form solution. Here we present a heuristics-based approach to the problem, which we refer to as the greedy approach. The performance envelope of the machine at a point on the surface is very anisotropic, and material can be removed much more rapidly in some directions than in other directions. The greedy approach seeks the directions of the best performance. We describe algorithms to first find such advantageous directions. We then show how they can be fitted by a continuous vector field. We also show how toolpaths with the proper side-steps can be generated from this field. We end with results showing the improvement of performance that can be derived from greedy toolpaths. (C) 2002 Elsevier Science Ltd. All rights reserved.