Publication Date:
2013-09-06
Description:
A common approach to the construction of surface-covering impact paths for computer-controlled manufacturing systems is to take a finite family of quasi-parallel offset curves of a seed curve on the workpiece surface. A possibility to get such curves is to consider the distance function of the seed curve in order to take the isolines of a finite sequence of increasing values. Besides several advantages, distance functions suffer from two problems which have an influence on the usefulness of the resulting curves: locations with discontinuous derivatives and local extrema. Optimization-based approaches for contour-parallel and direction-parallel offset curves, respectively, are presented to reduce these difficulties. For the contour-parallel case, the curvature, the mutual distance, and the topology of the isolines are optimized over a finite-dimensional family of scalar functions derived from the distance function of the contour. In the direction-parallel case, objectives including the number, the normal, and the geodesic curvature of isolines are optimized over the distance functions of a finite-dimensional family of seed curves. Algorithms to solve these optimization problems on triangular meshes are proposed and employed to demonstrate the usefulness of the methods.
Print ISSN:
0268-3768
Electronic ISSN:
1433-3015
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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