Characteristic surfaces for extreme values of angular velocity ratio in planar four-bar mechanisms

The extreme values of the angular velocity ratio of a planar four-bar mechanism are considered. A sixth order polynomial is used to find the exact roots for the double change point mechanisms. The range of the extreme values is defined for all of the Grashof cases. Characteristic surfaces are developed which prove to be useful for synthesizing linkages with prescribed extreme values of angular velocity ratio.     

On the classification of spherical four-bar linkagesÜber die klassifizierung von sphärischen viergelenkgetrieben

Spherical four-bar linkages can be classified according to the rotatability, i.e. the capability of performing complete revolutions, of one link relative to the other three links. For a spherical four-bar linkage, two link lengths may be replaced at a time by their respective supplementary arc lengths. This reduction process is carried out until the sum of all four link lengths is a minimum. Grashof's rule may then be applied to test the rotatability of the linkage. The shortest link of a Grashof linkage is capable of making complete revolutions. A Grashof linkage may be a crank-rocker, a drag-link or a double-rocker. A non-Grashof linkage is always a double-rocker. Examples are given.     

The balancing of bar mechanisms with unsymmetrical links

The present work considers a new method of static and statico-dynamic balancing of bar mechanisms with unsymmetrical links. The solution of the problem is illustrated by an example of a planar four-bar linkage.     

球面四杆机构的空间模型及尺寸型

基于特征球面四杆机构的概念，将球面四杆机构分为三类，并建立机构的尺寸型空间模型。每个空间模型可划分为若干个子区间，每个子区间都对应着一族球面四杆机构。按本文提出的尺寸型表示方法，可在全封闭图面内表示球面四杆机构的尺寸型，并在其上绘制出有工程应用价值的机构性能图谱。     

Transformations for the dimensions of non-Grashof 4-bar linkagesTranspormationen zu den dimensionen von Nicht-Grashofschen gelenkvierecken

A new family of four transformations is presented. Each of the transformations maps the dimensions of the movable quadrilaterals of planar 4-bar linkages onto a finite region of 3-space and, in particular, the dimensions of certain non-Grashof quadrilaterals symmetrically onto a unit cube within this region. This is the converse of the role played by a transformation previously reported which is particularly suited to crank-rocker quadrilaterals and which is also one of a family of four, each of which maps the dimensions of a category of Grashof quadrilaterals symmetrically onto a unit cube. The circumstances in which either or both might be used are briefly discussed.     

平面铰链四杆机构连杆平面上的运动瞬心线

推导了平面铰链四杆机构连杆平面上的动瞬心线方程和同一条连杆曲线产生两个、三个尖点时．机构参数所应满足的解析关系式，指出满足Ｇｒａｓｈｏｆ条件的机构的同一条连杆山线上，最多只能产生两个尖点。     

Stephenson型平面六杆机构的运动领域识别法

Stephenson型平面六杆机构，可分解为平面四杆机构和一个Ⅱ级杆组，其运动领域可分离为连杆轨迹曲线上的两个边界点或边界转向点。将这些分支的运动领域映射在数轴上，用雅可比矩阵的系数行列式的符号和相应构件角位移的正弦符号来识别。     

4R1P型平面五杆并联机构的可动性与特征图表示

针对4R1P型平面五杆并联机构,引入虚杆概念。基于Grashof定理,将滑块可达空间分割为若干可动性不同的子域。根据三根RR型构件的杆长关系,将运动链与机构划分为三类和若干子类,给出其可动性的特征图表示。在此基础上,根据移动副参数、滑块位置、构件结构约束以及移动副的主动与否,具体得出运动链与机构的可动性。特征图分析方法适合于4R1P型所有平面机构和3R型平面开链机构。     

Partial shaking moment balancing of fully force balanced linkages

This paper deals with a solution of the shaking force and shaking moment balancing of planar and spatial linkages. The conditions for balancing are formulated by the minimization of the root-mean-square value of the shaking moment. There are two cases considered: mechanism with the input link by constant angular velocity and mechanism with the input link by variable angular velocity. The method is realized by displacement of the axis of rotation of the input link connected with the counterweight. The efficiency of the suggested method is illustrated by two numerical examples: planar four-bar linkage and RSS'R spatial linkage.     

A note on the synthesis and dissimilar function-cognates of the RSSR and RCR0CR mechanisms

Function-cognates are those mechanisms that provide exactly the same input-output displacement relationships as the original mechanism. Dissimilar cognates are cognates having a different structure from that of the original mechanism. It is shown that there are no RSSR mechanisms function-cognate to a given planar four-bar or spherical four-bar. On the other hand, formulae for the infinity of RCR₀CR cognates of the planar four-bar are given. It is further shown that for a given RCR₀CR mechanism (or for a given general trigonometric implicit relationship linear in cosines and sines of input and output rotations individually), there is always one and only one RSSR mechanism giving the same relationship. The latter is therefore also the case for an eight-precision point synthesis of the RSSR mechanism.     

基于边界的最大间隔模糊分类器

对利用超平面、超(椭)球等几何形状实现数据分类的基于边界的主流分类方法进行了研究,在此基础上,提出了一种将空间点作为分类依据的最大间隔模糊分类器(MFC)。该方法首先在模式空间中找到一个模糊分类点c,c点距离两类样本要尽可能近且类间夹角间隔尽可能大。然后,测试样本通过c与训练样本间的最大化夹角间隔实现分类。最后,利用MFC的核化对偶式与最小包含球(MEB)的等价性,将MFC的应用范围从二类推广到单类。与主流分类方法的比较实验表明,MFC具有优良的分类性能和抗噪能力,其分类最高精度可达98.8%。     

制造误差对四杆机构轨迹综合精度的影响分析

通过建立杆长制造误差对平面四杆机构轨迹综合精度影响的数学模型,确定了杆长制造误差的敏感系数,分析了杆长制造误差对轨迹综合精度的影响规律。设计实例说明,合理设计四杆机构杆长制造公差,可使机构既满足精度要求又降低制造成本。     

Angular velocity RCCC-linkage of a spherical four-bar linkageWinkelgeschwindigkeits-RCCC-getriebe eines sphärischen Viergelenkgetriebes

The angular velocity diagram of a spherical four-bar linkage is a tetrahedron in space. Based on this angular velocity tetrahedron an RCCC-linkage may be devised. The driving link of this RCCC-linkage rotates with the same angular velocity as that of the driving link of the original spherical four-bar. The linear displacement and the sliding velocity of the output link of the RCCC-linkage represent respectively the angular velocity and angular acceleration of the output link of the original spherical four-bar. The shape of the equivalent dual spherical four-bar linkage of the RCCC-linkage is identical with that of the original spherical four-bar linkage.     

Optimum synthesis of the four-bar function generator in its symmetric embodiment: the Ackermann steering linkage

The problem of optimum synthesis of the planar four-bar function generator is investigated and the practical case of the Ackermann steering linkage considered as an example. The reduced number of design parameters of this symmetric four-bar linkage allowed inspecting the design space of various types of objective functions through 3D representations, and their properties suggestively highlighted. For practical purposes, the numerical results were summarized in a set of parametric design-charts useful to the automotive engineer in conceiving the steering linkage of a new vehicle.     

二次曲面钻头几何角度的统一模型

以麻花钻前后刀面的数学模型为基础，建立了二次曲面后刀面麻花钻各几何要素的平面像图；应用平面表像法，将麻花钻上复杂的空间角度计算问题转化为平面上的非欧距离和非欧夹角的计算问题，从而大大简化了计算分析的难度；建立了麻花钻切削角度与结构和刃磨参数关系的统一计算模型，为麻花钻的结构和刃磨参数的分析和优化设计提供了一种新的建模方法。     

Determination of the complete set of shaking force and shaking moment balanced planar four-bar linkages

A mechanism is said to be force balanced if, for any arbitrary motion, it does not apply reaction forces on the base. Moreover, if it does not apply torques on the base, the mechanism is said to be moment balanced or dynamically balanced. In this paper, a new method to determine the complete set of force and moment balanced planar four-bar linkages is presented. Using complex variables to model the kinematics of the linkage, the force and moment balancing constraints are written as algebraic equations over complex variables and joint angular velocities. Using polynomial division, necessary and sufficient conditions for the balancing of planar four-bar linkages are derived.     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

混合驱动平面两自由度五杆机构的完全分类

不使用传递角而利用四杆开链机构工作空间的位置关系及可装配条件 ,分析满足混合输入要求的所有五杆机构类型和它们的不等式。它比利用传递角得出的不等式更能确定尺寸关系。根据在混合五杆机构的四个杆中 ,可能为曲柄的杆的个数 ,将它分为三种类型 :无条件三曲柄两种、无条件两曲柄十种和无条件单曲柄十六种。根据五杆机构不出现奇异性的条件 ,进一步得到满足混合输入要求且不出现奇异位置的五杆机构的三种类型。这三种类型为混合五杆机构尺度综合提供重要的尺寸约束条件 ,同时也为混合五杆机构的分析和设计提供重要的理论基础。     

Konjugierte Stellungen bei sphäerischen Viergelenkgetrieben und die zugehoerigen speziellen KoppelkurvenConjugate positions of spherical four-bar mechanisms and corresponding special forms of the coupler curves

Conjugate positions of spherical four-bar mechanisms are corresponding to planar mechanisms those having the same output-angle ‘β’ and consequently two conjugate positions for every possible value of ‘β’. The geometric relations for conjugate positions of spherical four-bar mechanisms are derived in this paper. Furthermore, it is demonstrated how to gain spherical coupler curves having two or three cusps by kinematic inversion of special conjugate positions.     

The force transmissivity index of planar linkage mechanisms

In this paper, a new force transmissivity index (FTI) of planar linkage mechanisms is proposed. The index is used to quantitatively measure the force transmission quality from the input link to an output link. Traditionally, the transmission angle is used to measure the ability to transmit motion for planar four-bar linkages. However, the transmission angle is usually limited to be used at four-bar linkages due to the structural simplicity. For complex multi-loop mechanisms, it is often difficult to define the force transmissivity. Here we have established a procedure of force transmissivity analysis for planar linkage mechanisms. The method is based on the static force analysis and the concept of power flow path. It is found that the force transmissivity of a mechanism depends not only on the configurations of the mechanism, but also on the selection of the output link and the forms of the loading. We have compared the results based on the FTI with the results from the Jacobian matrix method and the joint force index (JFI) method for four-bar mechanisms. It shows that the proposed FTI can describe the force transmission performance more accurately than other methods do. It is concluded that the index can be used as a better measure of force transmissivity analysis for planar linkage mechanisms.