等距圆

With the theory, any straight lines and quadratic curve′s equidistance curve can be indirectly interpolated with the help of outline and wire circle′s information, it is unnecessary to calculate equidistance curve .

该理论直接利用轮廓曲线和丝圆的信息，不需计算等距曲线，间接实现任意直线和二次曲线的等距曲线的插补，有效地避免了传统计算等距曲线产生的计算误差，简化了数控机床控制程序设计，提高了机床的控制精度。

According to the concept of envelope evaluates equation of contour,the conclusion can be reached that the contour of torus is colse elliptc equidistant curve but is not ellipse.

根据包络的概念解出轮廓线的方程式，从而得出结论：圆环面的轮廓线是封闭的椭圆等距曲线，而不是椭圆。

The paper induces and analyzes research method of the tooth, including Method line of the tooth theory,Envlopment theory, Camus theory, Circling cluster theory and so on.Based on the past theories,the new measure to deduce the chain wheel tooth equation of roller chain at high speed,Circling cluster and envlopment theory,is proposed by analyzing basic concept of equidistant curve and Willis theory.Following the presentation of drawing lessons from traditional roller chainof the change of stanza line distance. A new type of roller chain at high speed is given in the paper.The paper studies deeply structural characteristics, the change of stanza line distance,separation between plank and bore and so on.According to design requst of roller chain at high speed and the study ofH_y--V_0 tooth chain,the impossibility that Quasi-conjugage engagement theory isrealized by the engagement of roller chain at high speed from the aspect of theory is decribed.

作者综述了高速滚子链国内外研究现状，并进行了以下研究工作：归纳分析了齿形法线法理论、包络法理论、卡姆士定理、圆族法理论等齿形研究方法，在此基础上，结合齿形啮合基本定律，分析了等距曲线的基本概念，提出了一种推导高速滚子链链轮齿廓方程的新方法—圆族包络法；在借鉴普通变节距滚子链的基础上，本文提出了一种新型的高速滚子链链条，深入研究了高速滚子链链条结构特性及其变节距、板孔中心分离等特性。

We prove in this paper that topological entropy is zero, in systems of equivariant mapping, that systems of compression mapping, and systems of the homeomorphism of unit circle onto itself, while the toppological entropy is positive, that extensible mapping in the compact toppological metric space.

证明了在一般的紧致度量空间上，等距映射的系统，压缩映射的系统，单位圆上的自同胚映射的系统等的拓扑熵都为零，而可扩映射的系统有正的拓扑熵。

In the paper, on the basis of aggregation of previous studies, the development of optical technology and development trends at home and abroad are introduced, the principle of Fresnel lens is summarized. In accordance with its principle, circle equidistant steps Fresnel lens design is described. And on this basis, based on Fresnel design, also based on a continuous upward spiral of the plane curve concept, incidence surface and the backlight is set up to greet Archimedes - Fresnel lens design formula and the Second parabolic type Fresnel lens design formula, and on this basis, the advantages and disadvantages of the three designs is discussed.

本文在充分了解非球面光学技术在国内外的发展状况和趋势的基础上，同时从菲涅尔透镜的光学原理出发，并根据它的工作原理推导了圆环等距菲涅尔透镜的设计步骤，并在此基础上依据菲涅尔的设计思想，同时依据平面曲线的连续又呈螺旋的构思，推导出了迎光面和背光面阿基米德型菲涅尔透镜的设计公式和二次抛物面型菲涅尔透镜的设计公式，并在此基础上讨论了这三种设计各自的优缺点。

Take the opportunity of this project, theoretical and experimental researches on the high-efficiency evaporator used in a large quick-freeze equipment have been done. The main work of experimental research is as follows:(1) Compare and analyze the influences of structural parameters on the heat transfer coefficient of an evaporator. The calculation results show that, under non-freezing conditions, the structure possessing the highest heat transfer coefficient is the one with circular fins, equilateral-triangle arranged small tubes and varying fin-spacing.

主要做了以下几方面的试验研究工作：(1)对不同翅片形状、管径大小、翅片管排列方式，以及是否带波纹等结构参数对蒸发器传热系数的影响进行了比较分析，得出在不结霜工况下，具有最高传热系数的蒸发器结构是圆翅片小管径正三角形排列等节距结构的结论。

The results are much better than the other approaches'. Then we give another method for approximating offset curves. The circle is first approximated by regular polygon within some tolerance. The exact offset curve is then approximated by the convolution of the regular polygon with a B-spline curve or a NURBS curve having the same degree.

与此同时作者从基圆的正多边形逼近出发，通过求解包络的技巧给出了等距曲线逼近的另一个算法，可整体估计误差，所得的等距逼近曲线为与基曲线同次数的B样条或NURBS曲线，克服了国际上现有同类算法中逼近曲线次数几倍于基曲线次数的缺陷。

In this paper, a region approximation idea that means using a "fat curve" with a width to approximate the offset curve is proposed, and a complete set of algorithms to approximate offset curve using disk Bézier curve are given and implemented. In the algorithms, the optimal and uniform approximate curve of the offset curve as the central curve of the Disk Bézier curve is found by using Remez method, and then the upper optimal and uniform approximation principle is proposed to compute the error radius function of the Disk Bézier curve. Thus, the whole Disk Bézier curve can be obtained. In the end of this paper, the approximate effect of the Disk Bézier curve is not only analyzed and assessed, but also some specific examples are provided.

提出用一条带宽度的"胖曲线"来逼近上述等距曲线的区域逼近思想，并建立与实现了圆域Bézier曲线等距逼近的整套算法，包括应用Remez方法求出等距曲线的最佳一致逼近曲线作为圆域Bézier曲线的中心曲线，提出上控最佳一致逼近的原理求出圆域Bézier曲线的误差半径函数，以及确定整条圆域Bézier曲线，最后还对该圆域Bézier逼近的效果做了分析和考核，并给出了一些具体实例。

Then calculates clearances in radius direction for all kinds of nonparallel degree between input shaft and output shaft, and presents conditions of adjustability. Applies the experimental device, which is developed for this paper research, as example, introduce calculation formulation of overlapping coefficient and pressure angle while the distance between two centers is uncertain, in this way, we get the range of the center distance.

以本论文的实验研究装置为例，引入了中心距不确定状况下的重迭系数、压力角等计算公式，以两齿轮啮合时的分度圆不能相割为最小中心距，以两齿轮啮合的重迭系数不小于1为最大中心距，从而得到相应的中心距范围。

In this paper,the fundamental conception of every kind of cycloids is introduced,the forming progress of the inner and outer rotor tooth profile is stated,and the reason why the inner rotor tooth profile should adopt the short amplitude outer cycloid inner equidistant line,while the common outer cycloid and the long amplitude outer cycloid are not suggested to use.

本文就各种摆线的基本概念作了介绍，并阐述了内、外转子齿廓的形成过程，分析了内转子齿廓为短幅外摆线圆内等距线，而不宜采用普通外摆线及长幅外摆线的原因。

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