螺旋面

Based on this property, by solving a series ODEs we construct a two-parametric family of helicoidal surfaces under cubic screw motion with prescribed mean curvature or Gauss curvature and solve an open problem left by Beneki.

基于这一点，当螺旋面的平均曲率或Gauss曲率为给定光滑函数时，本文选取伪正交标架，使得两类螺旋面的平均曲率和Gauss曲率的表达式相对简化，通过求解一系列的非线性常微分方程，即可确定一族生成曲线，从而最终确定平均血率或Gauss曲率为给定光滑函数的双参数族螺旋面，并在这一过程中解决了Beneki等人留下的一个公开问题。

Being formed by linear grain curved surface, helicoid can be expressed by a group of simple lines. Writing two equations of inside and outside of the helicoid, getting any one of simple line′s equation and from which getting the coordinations of two end points by projection transformation, the CAD system of helicoid is achieved. It...

由于螺旋面为直纹曲面，因此可用它的一组素线表示，用极坐标的形式写出内外两条螺旋线的方程，求出任一素线的方程，并通过投影变换求得素线上两端点的坐标矩阵，进而设计出螺旋面的CAD系统，并将其应用于实践，为设计优化决策提供有力的证据。

A helicoidal surface in Minkowski 3-space is defined as the orbit of a plane curve under a screw motion.

三维Minkowski空间中的螺旋面是一条平面曲线经由螺旋运动所生成的曲面。

It is analyzed by means of computer simulation that the contact-track shape and related factors, the influence of installing angle error and interpolation error to machining precision, and some important conclusion is drawn, all of which sets a foundation to improve the precision of helical surface machining.

论文以计算机仿真为手段，详细分析了截面包络法加工螺旋面时工件与刀具上的接触迹形状及影响因素；分析了安装误差及插补误差对工件加工精度的影响，并得出相关结论，为提高螺旋面的加工精度奠定了基础。

A crowned gear may be shaved by a modified plunge shaving cutter which is designed and manufactured based on the one to one mapping principle that means the axial modification of the cutter corresponds that of the crowned gear to be shaved. The calculation algorithm is given in dissertation.

考虑到目前国内的加工条件，本学位论文通过构造标准渐开螺旋面，令两齿面在中截面上节圆处重合，并采用计算机数值算法，求解了径向剃齿刀相对渐开螺旋面在齿形、齿向的修形量，从而使径向剃齿刀可以采用普通剃齿刀磨床加工。

A compensation method of ball radius in measuring an arbitrarysectional shape of spiral surface is introduced.

但由于螺旋面的扭曲及测头半径的影响，采用一股的平面曲线侧量方法对测头半径进行补偿和数据处理，求得的齿形其误差较大，很难满足要求；另外，对螺旋面任意截形的测量目前还没有一个通用的补偿计算公式。

Detect drive way too much space is a fixed power input shaft and output shaft rotation shaking, in the case of the transmission structure of conventional design and manufacture of machine tools, the transmission output shaft angle space at more than ten degrees to the dozens of degrees Transmission gap caused by too large spiral screw groove surface then there is obvious marks, thus affecting the machining accuracy of the screw.

检测驱动方式太多空间是一个固定的动力输入轴与输出轴旋转摇晃在常规情况下传动结构设计和制造的机床，传动输出轴角空间超过度到10度的数十个输电差距过大造成的螺旋槽螺旋面则有明显的标志，从而影响了螺丝加工精度。

Spiral stair cases ; three dimensional modeling ; spiral surface ; straight-grained surface ; AutoLISP program

螺旋楼梯；三维建模；螺旋面；直纹曲面； AutoLISP程序

The mathematical model of ruled helicoids on torus is constructed and two expression methods of ruled helicoids are discussed.

基于圆柱螺旋面和圆环螺旋线的形成原理，构建了圆环直纹螺旋面的数学模型，讨论了圆环直纹螺旋面的两种表示方法。

The important parameters of designed flutes, such as rake angle, clearance angle, are analyzed, and the calculating method of tangential vector, normal vector, and so on, is discussed.

基于刀刃曲线模型和刀槽螺旋面的生成原理，提出了可满足各种设计要求的刀槽螺旋面的几何建模方法，推导了铣刀和旋转锉的多种类型的刀槽螺旋面方程。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失