动旋转锥包络面的刻画及其在CNC加工中的应用
Characterizing envelopes of moving rotational cones and applications in CNC machining
AI总结：
受CNC加工启发，本文刻画了由全等旋转锥单参数族包络的曲面，推导出推广Gauss和Monge结果的高阶非线性PDE，并给出了曲面被旋转锥局部逼近的接触阶结果，应用于侧刃CNC加工的刀具选择与定位。
摘要：
受CNC加工应用的启发，我们刻画了由全等旋转锥的单参数族所包络的曲面。作为极限情形，我们也探讨了可展曲面与直纹曲面。这些刻画是高阶非线性PDE，分别推广了Gauss和Monge针对可展曲面与直纹曲面的结果。推导过程包含了曲面被旋转锥局部逼近的结果，这些结果通过平面空间中的接触阶来表示。这些结果在几何计算中本身也具有意义，例如在侧刃CNC加工的刀具选择与定位中。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
