Abstract
When we are trying to shape a surface X by 3-axis milling, we encounter a list of problems: First we have to decide if locally the milling tool Σ is able to move along the surface such that its envelope during the motion is the given surface. This is a question involving the curvatures of X and Σ. Second, we want to avoid that while milling in one part of X, Σ intersects another, already finished, part of the surface. This is a problem which involves global shape properties of the surface and can be successfully attacked by considering the general offset surface of X with respect to Σ. Third, in practice a cutting-tool is not able to perform a 2-dimensional motion along a surface. It has to trace out a finite number of piecewise smooth paths such that the resulting surface does not differ from X too much. This question again involves, in the limit case of very small error tolerance, only the curvatures of X and Σ. If we allow larger scallop heights, the path finding also requires the study of local and global properties.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35392-0_40
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© 1999 IFIP International Federation for Information Processing
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Wallner, J., Glaeser, G., Pottmann, H. (1999). Geometric Contributions to 3-Axis Milling of Sculptured Surfaces. In: Olling, G.J., Choi, B.K., Jerard, R.B. (eds) Machining Impossible Shapes. IFIP — The International Federation for Information Processing, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35392-0_4
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