Quantitative improvement of tool impact paths defined by isolines of scalar functions on triangular mesh workpiece surfaces.

Saved in:

Bibliographic Details
Title:	Quantitative improvement of tool impact paths defined by isolines of scalar functions on triangular mesh workpiece surfaces.
Authors:	Kout, Alexander¹ kout@ls7.cs.tu-dortmund.de, Müller, Heinrich¹
Source:	International Journal of Advanced Manufacturing Technology. Jan2014, Vol. 70 Issue 1-4, p237-255. 19p.
Subjects:	Quantitative research, Machine tools, Computer-control machine tool operators, Topology, Algorithms, Machine tool path, Multidisciplinary design optimization
Abstract:	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. [ABSTRACT FROM AUTHOR]
	Copyright of International Journal of Advanced Manufacturing Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Engineering Source

Description
Abstract:	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. [ABSTRACT FROM AUTHOR]
ISSN:	02683768
DOI:	10.1007/s00170-013-5152-1