基于微段插补模型的数控刀具运动优化控制

针对直线段与圆弧连接处的过渡,采用微小线段插补进行处理;通过前瞻分析的方法,控制直线段与圆弧段过渡处的进给速度提前减速,有效地减少了直线与圆弧过渡处的加工误差,建立混合S型双向加减速曲线模型,实现了圆弧段拐角处速度的控制.为了更好地优化数控刀具的加工时间,改进S型加速曲线原来加速缓慢耗时的前半部分,建立非零启动S型曲线加减速模型,从而减少启动时间,这种改进极大地优化刀具在走圆弧时的时间及平稳性.     

变分法在求解最速渡江路线问题的应用

本文在渡江者游速大小一定、水流速度大小一定或随水域均匀变化的情况下,建立变分法模型求解最速渡江问题,求得了最速渡江线路的解析解,并在此基础上,对＂2003年高教杯全国大学生数学建模竞赛＂＂抢渡长江＂题求得最优数值解     

摆线趣谈

一、问题的提出很早以前 ,人们就对沿直线前进的马车车轮上的点的轨迹产生了浓厚的研究兴趣 .有人误认为这个轨迹是一段段周而复始的圆弧 ,也有人误认为这个轨迹是一段段的抛物线 .实际上 ,当一个圆沿一条定直线作无滑动的滚动时 ,动圆圆周上一个定点的轨迹是一条摆线 ,也叫旋轮线 .二、摆线的方程和图像设圆的半径为ａ ,取圆滚动所沿的定直线为ｘ轴 ,圆周上定点Ｐ落在直线上的一个位置为原点 ,建立直角坐标系 (如图 1) .图 1设点Ｐ(ｘ ,ｙ)为轨迹上任意一点 ,圆心滚动到Ｂ点时 ,圆与直线相切于Ａ点 .取∠ＡＢＰ=θ为参数 ,作ＰＤ⊥Ｏｘ ,Ｐ…     

曲线的圆弧逼近与双圆弧逼近

众所周知,圆弧具有一系列简单而又重要的性质(如直观、实现方便、具有几何不变性、便于计算机存贮和传递图形等).目前国内外绝大多数插补器都采用直线-圆弧插补,因而研究曲线的圆弧逼近与拟合对于计算机辅助设计和制造有重要的现实意义.以前的计算方法很少研究象圆弧一类的几何曲线,近十几年由于计算机和数控技术的发展和应     

最速下降法的一次迭代收敛性的一点注记

推广了最速下降法经过一次迭代到达严格凸二次规划问题的最优解的充分必要条件：初始点可以表示为最优解和Hesse矩阵的一个特征向量之和.证明此条件也是最速下降法经过有限次迭代后到达最优解的充要条件.丰富了最速下降法的理论,有助于更好地认识和理解最速下降法,对相关算法的教学有一定的启发意义.     

动点运动路线长求解

动点运动路线长求解,一般应先模拟运动方式判断动点运动的路线形状,然后根据相应图形形状进行求解计算.下面举例加以说明.一、圆弧型例1如图1,将边长为a的正方形ABCD沿直线L按顺时针方向翻滚,当正方形翻滚一周时,正方形的中心O所经过的路径长为多少?     

弧长仪及其几何原理

弧长仪是一种圆弧长度测量仪。 长期以来,人们通常采用弧长公式:弧长=计算圆弧长度，弧长仪的出现改变了这种传统的方法，可以象直尺度量直线那样直接度量，因而，探讨弧长仪的几何原理成为许多人共同关心的问题。     

数学教学与现代信息技术的整合课例--动点间距离最小值的探索

课堂实录 :画面 :海洋、小岛、海岸线 .画外音 :这是一座美丽的小岛 ,岛上各种资源非常丰富 ,为了开发利用 ,在海岸线上需要建造码头 ,如果不考虑其它因素 ,为确保小岛与码头的距离最短 ,那么码头应选在何处 ?(画面 :从小岛指向码头缓慢划出一道航线 ) .(分组讨论 )生 1 :我们认为 ,这是平面上一点到给定曲线上一动点的距离的最小值问题 ,它一定存在 ,但还看不出点P的特征 (图 1 )生 2 :老师 ,我们能否先考虑海岸线是直线 ,若是直线 ,则当AP垂直直线a时 ,AP最短 (图 2 ) ;再考虑海岸线是圆弧 ,则当AP延长线过圆心O图 3时 ,AP最短 (图 3)…     

含曲线裂纹圆柱扭转问题的新边界元法

研究含曲线裂纹圆柱的Saint-Venant扭转,将问题化归为裂纹上边界积分方程的求解．利用裂纹尖端的奇异元和线性元插值模型,给出了扭转刚度和应力强度因子的边界元计算公式．对圆弧裂纹、曲折裂纹以及直线裂纹的典型问题进行了数值计算,并与用Gauss-Chebyshev求积法计算的直裂纹情形结果进行了比较,证明了方法的有效性和正确性．     

2006年全国高中数学联赛加试题及参考答案

性试题一、(本题满分50分)以B。和B，为焦点的椭圆与△AB。B:的边AB‘交于C(;一。，1).在AB。的延长线上任取点尸。，以B。为圆心，长线上，有B。P。一B，尸。‘.从而可知点只〕‘与点尸。重合.由于圆弧Q:尸。的圆心C。，圆弧尸。Q0的圆心B。以及尸。在同一直线上，所以圆弧Ql尸。和尸。Q0相内切于点尸(. B。尸。为半径作圆弧尸。Q0交C，B。的延长线于Q0;以CI为圆心，C，Q0为半径作圆弧Q。尸，交B、A的延长线于尸1;以Bl为圆心，B:尸l为半径作圆弧尸，Q，交B，C(〕的延长线于Q，;以C。为圆心，C。Q;为半径作圆弧Q:尸。‘，…     

交通网络连通性表达法的研究

通过对增设虚拟边网络连通性表达法和对偶图网络连通性表达法的描述和它们所面临问题的分析研究,说明这两种方法在交通网络连通性表达上,尤其是在引进交通转弯限制时所显示出来的需要大量处理工作的问题,提出了一种新的网络连通性表达法,作者称为“边标号法”,此法避免了对交通网络增设虚拟边或进行点边转化所带来的大量工作量问题,在对交通网络图不作任何修改的情况下,清楚而有效地表达出网络的连通特性。并用一个具体实例通过程序实现该方法,体现出了边标号法的优越性     

A fast line-sweep algorithm for hidden line elimination

Fast hidden line elimination algorithms can be obtained by minor modifications to algorithms developed for reporting intersections of polygons. We show how the same modifications which have been applied to segment trees can be applied to the data structure of Swart and Ladner as well, leading to anO((n+k)logn) time hidden line elimination algorithm (n is the number of boundary edges of the input polygons andk is the number of intersections of the edges on the projection plane). The algorithm improves the fastest previous line-sweep algorithm for the problem by a factorO(logn).This work was supported by the grant Ot 64/4-2 from the Deutsche Forschungsgemeinschaft.On leave from the Department of Computer Science, University of Helsinki, Finland.     

Bar Graphs and Histograms

<正>When am I ever going to use this?ANIMALS The cheetah is the fastest known and animal.The table shows its fastest speed and the top speeds of four other land animals.1.What are the fastest and slowest speeds recorded in the table?2.How can you create a visual representation to summarize the data?3.Do any of these representations show both the animal name and its speed?Abar graphis one method of comparing data by using solid bars to represent quantities.     

How good are extrapolated bi-projection methods for linear feasibility problems?

We consider extrapolated projection methods for solving linear feasibility problems. Both successive and sequential methods of a two-set projection scheme are examined. The best algorithm in the class of algorithms that we considered was an extrapolated sequential method. When this was compared to an interior point method using the CUTEr/Netlib linear programming test problems it was found that the bi-projection method was fastest (or equal fastest) for 31% of the cases, while the interior point code was fastest in 71% of the cases. The interior-point method succeeded on all examples, but the best bi-projection method considered here failed to solve 37% of the problems within reasonable CPU time or iteration thresholds.     

Double $S$-Breaking Cubic Turning Points and Their Computation

1.Introducti0nManynaturalphen0menapossessm0reorlessexactsymmetries,whicharelikelytobereflectedinanysensiblemathematicalm0del.Idealizationssuchasperiodicboundaryconditi0nscanproduceadditionaJsymmetries.Phen0menawhosemodelsexhibitbothsymmetryandnonlinearityleadtopr0blemswhicharechallengingandrichinc0mplexity.Problemswithsymmetriescanshowarichbifurcationbehavi0ur.Theoccurrenceofmultiplesteadystatebifurcationismostlyduetounderlyingsymmetries.Thisgivesrisetothedifficultiestonumericalcomputation-H…     

CNC车床的故障概率模型

本文从ＣＮＣ车床的故障数据的采集入手,建立了ＣＮＣ车床的故障数据库。应用模糊综合评价的方法对ＣＮＣ车床的故障模型进行了分析     

The Cichoń diagram for degrees of relative constructibility

Following a line of research initiated in [4], we describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cichoń diagram for cardinal characteristics of the continuum. We show that working from relatively modest assumptions about a notion of reduction, one can construct a robust version of such a diagram. As an application, we define and investigate the Cichoń diagram for degrees of constructibility relative to a fixed inner model W. Many analogies hold with the classical theory as well as some surprising differences. Along the way, we introduce a new axiom stating, roughly, that the constructibility diagram is as complex as possible.     

The linear search problem rides again

The Linear Search Problem concerns a search for a point in the real line by continuous motion starting at 0. The optimal turning points for such a search under the hypothesis that the location of the target is distributed normally about 0 have been approximated by mechanical calculation, but no proof has been given that there is only a single minimizing strategy or that the numbers calculated do indeed approximate that strategy. Plausible arguments have been made before, both by these authors and others. In this paper, the plausible arguments are supplanted by mathematical proofs. The research of the senior author has been supported by the Wisconsin Alumni Research Foundation. The research of the junior author has been supported by Hewlett Packard, Inc. under a Faculty Development Fellowship at Cornell University.     

一个非线性方程转向点问题

本文讨论了一个非线性方程的转向点问题 .研究了转向点的所处位置 ,以及问题解的渐近性态 .