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Constant cusp height tool paths as geodesic parallels on an abstract Riemannian manifold
Authors:Taejung Kim
Affiliation:Dankook University, 147 Hannam St., Yongsan-gu, Seoul, Republic of Korea
Abstract:In free-form surface milling, cusps on a part surface need to be regulated. They should be small enough for precision purposes. On the other hand, we should maintain high enough cusps so as not to waste effort making unnecessary cuts. A widely accepted practice is to maintain a constant cusp height over the surface. This paper introduces a new approach to generating constant cusp height tool paths. First, we define a Riemannian manifold by assigning a new metric to a part surface without embedding. This new metric is constructed from the curvature tensors of a part and a tool surface, which we refer to as a cusp-metric. Then, we construct geodesic parallels on the new Riemannian manifold. We prove that a selection from such a family of geodesic parallels constitutes a “rational” approximation of accurate constant cusp height tool paths.
Keywords:Free-form surfaces  Geodesics  Geodesic parallels  Tool paths  Riemannian metric
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