We introduce a new approach to the problem of collision detection in multi-axis NC-machining. Due to the directional nature (tool axis) of multi-axis NC-machining, space subdivision techniques are adopted from ray-tracing algorithms and are extended to suit the peculiarities of the problem in hand. We exploit the axial-symmetry inherent in the tool's rotational motion to derive a precise (to within machine precision) polygon-tool intersection algorithm which, combined with the proper data structure, also yields efficient computation times. Other advantages of the proposed method is the separation of the entire computation into a preprocessing stage that is executed only once, allowing more than one toolpath to be efficiently verified thereafter, and the introduced ability to test for collisions against arbitrary shaped tools such as flat-end or ball-end, or even test for interference with the tool holder or other parts of the NC-machine. Support for continuous analysis along the tools path is also possible. The image on the left presents a 5-axes tool path that was analyzed, intersections detected, and corrected by rotating the ball end tool's orientation.
This work considers computation of visibility for two-dimensional shapes whose boundaries are C^1 continuous curves. We assume we are given a one-parameter family of candidate viewpoints, which may be interior or exterior to the object, and at finite or infinite locations. We consider how to compute whether the whole boundary of the shape is visible from some finite set of viewpoints taken from this family, and if so, how to compute a minimal set of such viewpoints. The viewpoint families we can handle include (i) the set of viewing directions from infinity, (ii) viewpoints on a circle located outside the object (for inspection from a turntable), and (iii) viewpoints located on the walls of the shape itself. We compute a structure called a visibility chart, which simultaneously encodes the visible part of the shape's boundary from every view in the family. Using such a visibility chart, finding a minimal set of viewpoints reduces to the set-covering problem over the reals. Practical algorithms are obtained by a discrete sampling of the visibility chart. For exterior visibility problems, a reasonable approach is to compute an almost-optimal solution (in terms of number of viewpoints), which can be done in almost-linear time. For interior visibility problems, or when a more correct solution is required, we solve the general set-covering problem, guaranteeing an optimal solution but taking exponential time. In either case, conservative solutions are obtained, ensuring that no part of the curve remains invisible from some viewpoint. Examples are given to illustrate our algorithm. The presented image shows (from left to right) the visible portion (in yellow) of the curve from one view, the visibility chart in the middle, and the three views that covers the entire domain (right). These three views could be used to create a 2D mold of 3 pieces.
This work presents a precise approach to the generation of optimized collision-free and gouging-free tool paths for 5-axis CNC machining of freeform NURBS surfaces using flat-end and rounded-end (bull nose) tools having cylindrical shank. To achieve high approximation quality, we employ analysis of hyper-osculating circles (HOCs) (Wang et al., 1993a,b), that have third order contact with the target surface, and lead to a locally collision-free configuration between the tool and the target surface. At locations where an HOC is not possible, we aim at a double tangential contact among the tool and the target surface, and use it as a bridge between the feasible HOC tool paths. We formulate all such possible two-contact configurations as systems of algebraic constraints and solve them. For all feasible HOCs and two-contact configurations, we perform a global optimization to find the tool path that maximizes the approximation quality of the machining, while being gouge-free and possibly satisfying constraints on the tool tilt and the tool acceleration. We demonstrate the effectiveness of our approach via several experimental results.
This work presents an efficient algorithm for generating a continuous precise contact motion between planar geometric models bounded by piecewise polynomial C^1-continuous parametric B-spline curves. A system of algebraic constraint equations is formulated and then efficiently solved for the two/three-contact configuration between two planar B-spline curves. The result is essentially the same as the generation of configuration space obstacle for a moving curve (with translation and rotation) against a stationary curve. The two-contact motion can be characterized as the intersection curve in the boundary of the configuration space obstacle. The topology of the reconstructed solution is guaranteed to be correct up to a prescribed tolerance and we demonstrate the effectiveness of the proposed approach using several test examples of continuous contact motion among planar freeform smooth geometric models.