Mobility analysis of planar four-bar mechanisms through the parallel coordinate system

This paper presents a new method for the mobility analysis of planar mechanisms. The method utilizes a geometrical representation known as “parallel coordinates.” It is a transformation that maps the Euclidean space R^N to N parallel coordinates in the projective plane. Points in R² are transformed to line segments in the parallel coordinate plane, and circles in R² are transformed to hyperbolae. Also, in this investigation, special techniques required for mobility analysis are developed. First, the intersection of circles is performed graphically through the parallel coordinate system. The parallel coordinate plane is then appended to relate this intersection data to the angular coordinates of the various members of the linkage. The ranges of these angular coordinates are the results of the mobility analysis.     

平面四杆机构的可靠性分析

将诸原始误差均视为随机变量，对平面四杆机构具有杆长尺寸误差、铰链间隙误差及磨损量等各项随机变量分别进行了分析；应用微小位移的线性叠加原理综合出各项误差导致的机构运动输出总误差，建立了机构运动精度可靠性分析模型；利用计算机数字仿真技术，考察了机构中杆长尺寸误差和铰链间隙(或磨损)误差随机变量均值和方差的改变，对机构输出运动精度可靠度的影响，从中获得了一些有意义的结论。     

Graphical angular jerk analysis of four-bar linkages

Graphical methods of analyzing angular jerks in a four-bar linkage are described. No jerk polygon or complicated calculations are involved. Only a few lines are needed in these methods. The technique is extended to four-bar linkages connected in series as well as to a slider-crank mechanism. Extremes of angular accelerations may be found whenever the angular jerks vanish.     

A complete classification of planar four-bar linkages

A system of classification of planar four-bar mechanisms is presented in which the three major categories are Grashof, non-Grashof and change point. The Grashof and non-Grashof categories are each organized to include four classes while the change point has six classes. The classification system is closely related to a partitioning of the positive octant of a three-dimensional space in which the coordinate axes are nondimensional ratios of the bar lengths. The positive octant is first reduced in size by four zero mobility planes which eliminate from consideration regions where the bar lengths would not permit assembly. The remaining volume is designated as the solution space, and it is partitioned by three change point planes into eight volumes each of which represent a class of Grashof and non-Grashof mechanism. All of the change point classes reside in the change point planes. This paper describes the classification system and the geometry of the solution space, and lays the foundation for future work to study the properties of planar four-bar mechanisms. Because all of the mechanisms within a particular volume share in common characteristics of the bar lengths which are unique to their class, they also share particular properties with regard to the maximum and minimum values of position angles, the range and average value of the position angles, the maximum and minimum value of angular velocity and angular acceleration, as well as time ratio. Hence all of the significant properties can be represented as characteristic surfaces within the solution space. The trace of the characteristic surfaces in the base plane can be used to construct design charts which will permit choosing mechanisms with desirable properties. The method can also be used to synthesize mechanisms by locating intersections of characteristic surfaces. These topics will be presented in forthcoming publications.     

Atlas of spherical four-bar mechanisms

An atlas or catalogue of mechanisms provides a useful aid in the synthesis of mechanisms for new applications. The atlas stores mechanisms together with their coupler paths. Fourier techniques can be used as a convenient means for representing, in normalized form, curves for planar mechanisms. This paper looks at the extension to spherical four-bar mechanisms. In particular, a means for projecting a spherical curve onto a plane is discussed which depends only on the geometry of the curve and not on the choice of world coordinate system.     

平面四连杆机构运动综合线性优化算法

针对平面连杆运动位置数多于确定机构的精确点数的运动综合问题,提出了以最小误差为目标函数的线性优化算法.根据角度的范围有限性,降低了平面连杆机构运动的非线性方程维数,然后根据所得到的结果将平面四连杆机构的非线性方程转换为线性方程组.按照线性方程组的最小误差优化方法可解出最优参数值.例证说明该算法的正确性,线性优化与一般优化算法相比具有快速性和通用性.     

平面四连杆机构位置综合的最小误差算法

针对平面连杆运动位置数多于确定机构的精确点数的运动综合问题,提出运用最小误差为目标函数的参数辩识法算法。通过分析典型的平面四连杆机构的非线性解析方程,根据给定的位置,分解方程,构建线性方程组,引入最小误差目标函数和伪逆的处理方法,得出最优的参数值。通过例证说明该算法的正确性、通用性和有效性。     

车辆转向平面四杆机构的运动综合

基于实现转向条件，结合四杆机构的环路方程，建立起了车辆转向四杆机构近似运动综合的目标函数。根据极值条件，获得相应的方程组。基于消元法，推导出只含一个变量的多项式方程，以获得机构综合的所有解，从而可选择出最优解。     

Real inflections of hinged planar four-bar coupler curves

Plücker's and Klein's equations provide an upper bound on the number of real inflections on the coupler curve of a hinged planar four-bar mechanism. Generally, for any configuration of the four-bar, the coupler points whose trajectories exhibit inflections lie on a circle. The coupler plane is partitioned by the envelope of the inflection circles into connected regions within which every coupler point has the same number of inflections on its trajectory. This enables us to locate coupler curves exhibiting the maximum possible number of inflections.     

平面四杆机构刚体导引综合的符号解法

本文应用的数学机械化方法和计算机符号处理技术,对平面四杆机构刚体与引综合问题进行了符号求妥,该法通过对变量的排序,分组,约化,构成基列,求余等运算,将一个非线性多基式方程组化简为一个同价的三角方程组,得到了原方程组的封闭形式的解析解。     

Synthesis method based on solution regions for planar four-bar straight-line linkages

An analytical method for synthesizing and selecting desired four-bar straight-line mechanisms based on solution regions is presented. Given two fixed pivots, the point position and direction of the target straight-line, an infinite number of mechanism solutions can be produced by employing this method, both in the general case and all three special cases. Unifying the straight-line direction and the displacement from the given point to the instant center into the same form with different angles as parameters, infinite mechanism solutions can be expressed with different solution region charts. The mechanism property graphs have been computed to enable the designers to find out the involved mechanism information more intuitively and avoid aimlessness in selecting optimal mechanisms.     

一种新型平面连杆机构——四偏心机构

为扩大传统平面连杆机构的应用范围、丰富其结构形式,通过完全采用以偏心构件代替连杆,以转动副代替铰接,构成一种新型的四偏心式平面四连杆机构,即带有大转动副的微型平面四连杆机构.为促进此机构向实用阶段转化,给出了两种基本的结构形式,并对其进行了初步的结构分析、运动分析、CAE仿真以及实验验证.给出了各构件的基本尺寸关系和结构优化的方法,求出了从动构件的转角位移运动方程和曲线.通过仿真获得了与理论推导结果相同的从动构件的转角位移运动曲线;同时得出了此机构与传统平面田连杆机构的运动仿真轨迹曲线一致.指出了此机构相对于传统四连杆机构的特点和实施要点.上述分析证明此机构与传统平面田连杆机构的运动规律在本质上具有一致性.     

VB在平面四连杆机构运动分析中的应用

介绍了基于VB实现对平面四连杆机构进行全面运动分析的方法.通过一种简单有效的方法建立了数学模型,采用计算机模拟技术,能动态演示机构的运动和自动绘制连杆上任意点的轨迹曲线,并能输出各运动构件的位移图、速度图和加速度图.为平面四连杆的运动分析提供了一条简单易行的途径.     

用广义逆矩阵进行平面四杆机构的近似函数综合

提出了平面四杆机构近似函数综合的一种新方法,其基本思路是：首先利用广义逆矩阵将四杆机构的近似函数综合方程组转化为一个二元二次方程组,然后采用消元法得到一个一元三次方程,由此可得机构近似运动综合方程组的所有解。为平面四杆机构近似函数综合提供了高效的实用方法。     

广义逆矩阵在平面四杆机构综合中的应用

将平面R－R刚体导引的位移约束方程简化为四个变量的超静定拟线性方程组，应用广义逆矩阵以及适当的变量代换，将求解方程归结为一个四次代数方程的求根问题。进而不用初值就能求出最小二乘意义下机构参数全部最优解的近似值，通过适当参数替换，证明该方法能推广至四杆机构实现函数及点位－角移量综合问题中，由此解决了此类机构近似综合问题中的机构参数初值选取问题。     

极紫外望远镜角分辨率评价方法

极紫外望远镜工作波段与可见光波段相差近两个数量级,其工作波段的衍射极限很低,达到0.036″,使该波段望远镜角分辨率的检测很困难。本文介绍了一种极紫外望远镜角分辨率的评价方法。该方法利用通用可见光波段面形检测仪器,检测出极紫外望远镜光学元件面形误差和装调误差,将检测到的与波长无关的Zernike系数代入光学设计程序,计算出极紫外望远镜工作波段的点扩散函数和环绕能分布,进而计算出望远镜在极紫外波段的角分辨率。实验结果表明,极紫外望远镜的角分辨率可以达到0.18″。该方法是一种快捷、有效的极紫外波段成像仪器的评价方法。     

含移动副四杆机构运动仿真设计的数学模型

综述了计算机仿真连杆机构运动的技术特点,建立了曲柄滑块机构和导杆机构二种含移动副四杆机构运动仿真设计的数学模型。     

Synthesis of four-bar mechanisms by Freudenstein–Chebyshev

A new dimensional synthesis method is described in the paper. The position function of the four-bar mechanism is presented by the Freudenstein’s equation and it is minimized by the Chebyshev’s best approximation theory. The target function is used as an exactly satisfied equation and the Freudenstein’s equation is considered as a Chebyshev’s polynomial. In some cases the method provides possibilities to find simple solutions of the synthesis tasks. These solutions are known as the best Chebyshev’s approach of the weighted target function. This approach is near the best one for the original target function. A numerical example given here explains the essence of the method.     

按行程速比系数设计曲柄摇杆机构的一种新的解析算法

介绍了推导了按已知的行程速比系数k,摇杆的长度c和摆角ψ及其余三个构件中任意一个构件的长度,并由此确定其余各构件长度的解析公式。