论文标题
表征移动旋转锥和CNC加工中应用的信封
Characterizing envelopes of moving rotational cones and applications in CNC machining
论文作者
论文摘要
由CNC加工中的应用激励，我们提供了表面的表征，这些表面由一个一致的一致旋转锥所包围。作为限制案例，我们还解决了可开发的表面和统治表面。表征分别是高阶非线性PDE，分别用高斯和Monge概括为开发表面和统治表面。该推导包括通过革命锥的局部近似值的结果，这些结果通过平面空间中的接触顺序表示。这些结果本身是对几何计算的兴趣，例如在切割器选择和侧面CNC加工的定位方面。
Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.
