中文摘要：

基于齿轮啮合原理，建立了平面包络环面蜗杆副的数学模型。结合工程实际，深入分析了蜗杆、蜗轮的几何特征。以典型传动蜗轮齿面二次区为例，研究了信息点呈不等距分布的复杂曲面的构造方法。结果表明：主曲线采用平面曲线，交叉曲线采用非均匀有理B样条曲线（NURBS）构造的空间曲面精度高且易于编程实现。基于Unigraphics-Grip编程开发平台开发了平面包络环面蜗杆传动实体建模系统，并通过实例验证实体模型的精度：特征点的最大线偏差为4．7μm。

英文摘要：

Based on the gear engagement theory, the mathematical model of the planar enveloping hourglass worm gears was established. By combination with engineering practice, the geometrical features of worm and gear are analyzed. Taking the secondary contact zone of worm gears in typical design as an example, reconfiguration methods of curved surface composed of unequally distribute data points are researched. Result shows that the required precision of the space surface can be achieved and the surface can be built easily through programming, when principal curves are planer curve and the cross ones are Non-Uniform Rational B-Splines（NURBS） curve. On UG-GRIP platform, three-dimensional model building system of planar enveloping hourglass worm drives is developed. The accuracy of the solid model is validated by example, that the max error of the data points is 4.7 μm