用快速傅里叶变换进行球面四杆机构连杆轨迹综合

根据给出的球面四杆机构连杆轨迹的数学模型,借助傅里叶级数这一数学工具,对连杆轨迹的谐波成分进行理论分析,发现连杆轨迹的谐波成分与其相应转角函数谐波特征参数和机构尺寸参数的内在联系。确定球面四杆机构的基本尺寸型,在此基础上建立包含600余万组机构基本尺寸型的球面四杆机构连杆轨迹的谐波特征参数数值图谱库。利用傅里叶级数理论建立球面四杆机构处于空间任意位置时连杆曲线的数学方程,推导出计算机构的实际安装尺寸、连杆上点的位置和机构安装尺寸参数的理论计算公式。利用建立的谐波特征参数数值图谱和推导的理论公式解决了球面四杆机构的轨迹综合问题,最后给出算例证明本方法的可行性。     

基于傅里叶级数理论的连杆机构轨迹综合方法

探讨傅里叶级数在平面和空间连杆机构中的几何意义,给出平面和空间连杆机构连杆曲线的统一数学表达式。借助傅里叶级数理论,对该表达式的谐波成分进行理论分析,发现连杆曲线谐波成分与其相应连杆转角函数谐波特征参数和机构尺寸参数的内在联系。通过连杆机构基本尺寸型与连杆转角函数的关系,提出建立连杆曲线数值图谱,以及推导连杆机构实际尺寸、连杆上点的位置和安装尺寸参数理论公式的一般方法。建立由平面机构到空间机构在形式上和内容上统一的连杆机构轨迹综合理论。从而为连杆机构轨迹综合提供了一种有效的通用方法。最后通过空间连杆机构轨迹综合算例,说明了本方法的有效性。     

Fourier变换在空间连杆机构轨迹综合中的应用

从空间连杆机构连杆曲线的Fourier级数表达式入手,解决了空间连杆机构连杆曲线的数学描述问题.通过分析找到了连杆曲线谐波特征参数与连杆转角算子谐波特征参数之间的内在联系,在此基础上给出了轨迹综合的步骤,为解决空间连杆机构的轨迹综合问题提供了一个新的思路.最后通过解决球面四杆机构轨迹综合问题,证明了本方法的有效性.     

带有预定时标平面四杆机构连杆轨迹的尺度综合

应用复矢量方法和Ｆｏｕｒｉｅｒ级数理论建立了在一般位置时平面四杆机构连杆轨迹生成的数学公式,对其轨迹的谐波成分进行了理论分析;讨论了连杆轨迹与连杆转角算子之间的内在联系;推导出了在基本尺寸型通过模糊识别方法确定后机构实际尺寸、连杆上点的位置和机构安装尺寸参数的理论计算公式;结合这一思想建立了带有预定时标连杆轨迹尺度综合的步骤和方法;文中最后给出了综合算例。     

基于BP神经网络的平面机构连杆运动综合

针对要求实现连杆运动位置数目大于机构的精确点数目的平面连杆机构的综合问题,提出了利用BP神经 网络的综合方法。首先,将连杆的运动映射为映射空间的一条曲线,利用二维实数的傅里叶变换提取曲线的傅里 叶描述,然后,在大量的机构运动仿真的基础上,将连杆运动的映像曲线的傅里叶描述作为BP神经网络的输入, 相应的机构的几何参数作为网络的输出,训练BP网络。研究结果表明,训练后的神经网络不仅对连杆机构运动 综合问题能够做出正确的反应,而且具有其他方法所不具有的优点。     

采用傅里叶描述子提取连杆曲线特征参数的方法研究

分析总结了现有的提取平面连杆曲线特征参数方法的优缺点。基于傅里叶描述子的高频分量能够很好地解释细节,而低频分量则决定物体边界整体形状的性质,提出了采用傅里叶描述子提取平面连杆曲线特征参数的方法,同时建立了平面连杆曲线特征参数数值图谱库。计算结果表明,傅里叶描述子的低频项经过傅里叶逆变换能够很好地复现原封闭曲线,并且经过归一化后的傅里叶描述子具有很好的鲁棒性,相应的数值图谱具有精度高、计算简单、冗余度小的优点。     

平面滑块RRPRR型五杆机构的轨迹综合

滑块五杆机构可以看作是在曲柄摇杆机构的基础之上,将C点位置的铰链副转换成转动副和移动副的复合副,其运动特性相当于不同连杆长度的四杆机构运动叠加,通过对标准和一般位置连杆曲线进行快速傅里叶变换后提取谐波特征参数,利用两种位置傅里叶级数展开式之间的关系,推导出机构的实际尺寸和安装参数,并基于遗传算法对滑块五杆机构的连杆曲线进行了轨迹综合与优化,能够快速准确地求得滑块五杆机构的杆长及安装参数。该方法与代数求解和电子图谱法相比,减少了优化参数,提高了运算效率,是一种较为理想的设计方法。     

连杆曲线轨迹综合的特征图谱

提出了连杆曲线轨迹综合的特征图谱。该方法通过对连杆平面上所有连杆曲线的类别和尺度特征分析，建立了连杆曲线特征图谱。其方法是，用尖点曲线、自切点曲线及凹凸分界线把连杆平面划分出若干个区域，不同区域内的连杆曲线具有各自的类别特征。而尺寸特征则使用如L、W、J、J1、J2等外形参数来描述，并用绘制等值线的方法建立连杆曲线特征图谱。特征图谱不仅有利于轨迹综合，利用它也可预知任意位置的连杆点的运动轨迹。     

平面四杆机构轨迹综合的模糊数学方法

本文将连杆曲线用一组特性参数描述并建立“电子图谱”,用模糊数学方法对特性参数进行处理,可以较快地从数千条连杆曲线中找出与预期轨迹相似的曲线以及产生该曲线的机构的几何尺寸。该方法较好地解决了连杆曲线图谱使用不便的问题。文中有应用实例。     

小波分析在平面四杆机构轨迹综合中的应用研究

将小波多分辨分析理论应用于提取连杆轨迹特征参数并以此构造连杆曲线图谱库,建立了相应的轨迹评价和轨迹复演模型。所提取的特征参数保留了相对斜率角曲线的仅与所取基点有关,与轨迹曲线方位及缩放比例无关的特性。本法减少了图谱数据库的数据冗余、提高了机构综合检索速度。通过与最小二乘距离对比表明本法仍然具有很好的检索排序效果,说明了小波分析可以有效地应用于连杆轨迹的综合课题。     

Vereinfachte bestimmungsgleichungen für bewegungs-weiterleitungen von koppelkurven mit spitzenSimplified equations for motion transmissions using coupler curves with two cusps

Each four-bar linkage running as a crank and rocker mechanism has one unique coupler point producing a coupler curve with two cusps using this special coupler point, complex mechanisms can be designed having exact dwells. In this paper a four-bar linkage is used having the most favorable transmission behavior. Using simple equations, the mechanism and the coupler point location can be calculated. Using a rotating inverted slider output link, the designer can produce two rather long dwells through a full motion period.     

用快速傅立叶变换进行再现平面四杆机构连杆曲线的综合

利用信号分析中的快速傅立叶变换（简称FFT）,把连杆机构中,连杆上的曲线用它所含的谐波分量来表示。这样就可以根据连杆曲线所含的谐波分量对连杆曲线进行识别和选取。根据这些谐波分量,我们还可以得到有关连杆曲线的速度和加速度信息。这对于连杆机构连杆曲线的分析与综合有比较重要的意义。把不同的连杆曲线所对应的结构尺寸及所含的谐波分量一起存到一个数据库中,于是就得到一个有关连杆曲线的数值图谱。以四杆机构为例,得到了含16728条曲线的图谱,利用该图谱进行连杆曲线的分析与综合,要比传统图谱方便且精确。     

用谐波理论和快速傅立叶变换进行五杆机构的轨迹综合

从谐波理论的角度出发,采用平面曲线的快速傅立叶变换,可得到由谐波成分表示的任意五杆机构连杆轨迹的数学描述;应用归一化处理,可将形状、大小、方位、偏移各异的连杆曲线统一到相同的机构特征参数下,从而揭示出各类曲线与机构尺寸型及两输入构件初始角度之间的内在联系。本文首次提出了求解实际机构各参数的数学公式,使利用各种驱动类型和不同定传动比的五杆机构特征参数数值图谱进行五杆机构轨迹综合更为有效。     

Triangular nomograms for symmetrical coupler curvesHoмoгpaммa тpeyгoльнoй фopмы длы cиммeтpичныч мaтyнныч кpaивычNomogrammes triangulaires pour les courbes symmetriques

Triangular nomograms have been constructed as a simple means of finding symmetrical coupler curves of the crank-rocker linkage. A nomogram of this kind has been presented by the author of this article during a Conference of the Institution of Mechanical Engineers at London in 1972. Twenty-seven versions have now been developed and fully worked out.They are dimensionless and have then three angles as parameters to determine the type of curve with all its properties.The curve types are concerned with those characteristics which the crank-rocker linkage yields for symmetrical coupler curves such as: curves with one or two points of reversal; with internal contact; 8-shaped curves; curves with 2 equal radii of curvature; curves with one or two undulation points on the axis of symmetry; curves with two undulation points oriented symmetrically in relation to each other and a top angle; curves with Burmester points, where the second derivative of the radius of curvature is zero; and curves with one or two tangents which touch the curve at three different points each.The 27 triangular nomograms refer to the symmetrical coupler curves of the 4-bar linkage and are used for selection of the type of curve and corresponding data for the linkage.This article will deal with three of them which relate to coupler curves with the property that a tangent touches the curve at three separate points, while two more examples of the various verions of the nomogram will be presented.A example of the application of the nomogram is given by the design of a transfer mechanism, where use has been made of a curve with two cusps and further modification to a 6-bar linkage.     

曲柄摇杆机构对称连杆曲线的研究

分析了曲柄摇杆机构产生对称连杆曲线的条件、曲线的类型及相应机构的尺度关系，并制成了相应的图谱。研究了对称曲线ＦＦＴ分析结果的特点。产生了对称连杆曲线的特征参数数据库，为相应机构尺度综合打下了基础。     

基于Matlab/Simulink的四杆机构连杆点轨迹仿真

应用Matlab/Simulink对机构领域中应用广泛的基本机构--双曲柄机构、曲柄摇杆机构、曲柄滑块机构等的连杆点轨迹作仿真,该方法编程工作量小、轨迹图形显示便捷,所建模型只需作少量更改即可适应四杆机构的不同特征值,并可推广至多杆机构情况.     

Verbesserung der genauigkeit und laufgüte sechsglierdriger koppel-schwingrastgetriebeImprovement of accuracy and quality of transmission in six-bar mechanisms for oscillating-dwell motions

In order to produce dwell-rise-dwell motions cam mechanisms can be designed much simpler than linkages. Because of the many advantages of linkages, more attention should be spent to their design and at first to the six-linked structures which fulfill the given problem by smallest expense. The six-bar coupler linkage is discussed here. It realizes the dwells by approximation of the coupler-curve to a circle which is represented by the length of an additional coupler link. Many investigations have been made to meet this problem best. So the circle point curve (Burmester-curve) represents a four-fold coincidence of coupler-curve and circle. If a dwell at the end of an oscillating motion is ordered, the curvature of coupler-curve must show an extremum value. If, in addition, two end-dwells are asked for the classic Burmester Theory never can solve this problem. Now the computer-aided design is able to give new ideas as follows: The major size of coupler-curves is well-known by tables like Hrones and Nelson's atlas and also the ranges usable for dwell-motions. Such four-bars are computer-programmed to find maximum values of curvature automatically. Deviations of the transmitting link from radius of maximum curvature enlarge the duration of dwell but increase the errors during the dwell period. In each case a four-fold coincidence is realized. The computer automatically finds all extremum curvature point and there are no difficulties in finding a second end-dwell. Using special four-bars with equal lengths of coupler, output link and coupler point distance, symmetrical coupler curves are produced in which extremum curvatures correspond to crank displacements of 180°. If non-symmetrical motions are wanted, four-bars with general dimensions have to be computer-investigated. It should be stated that by the method explained eight precision points of coupler curve have been found when the maximum of them is nine. For each problem a certain number of usable four-bars can be found. The computer cam then be ordered to find that one having smallest maximum acceleration. Further investigations in this direction should be started in order to find the limits of six-linked mechanisms and to learn exactly for which requirements linkages of higher order have to be used, i.e. how to produce longer dwells and those ones with higher accuracy, also how to produce two dwells having a larger difference in back and forth motion between dwells and finally how to design linkages for more than two dwells.     

Some properties of the coupler curve of the spatia RRRSR mechanismHeкoтopыe Xapaктepиcтики шaтyннoй кpивoй пpocтpaнcтвeннoгo пятиэвeннoгo мeчaниэмa типoв вввcв мин-чжэ-чэнв

In this paper the author has developed a parameteric equation for the coupler curve of the spatial RRRSR mechanism. Then it is proved by the projective method that the coupler curve and the ruled surface generated by the coupler are of the 32nd order. Finally the imaginary circular point on the coupler curve are discussed.