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.     

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.     

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.     

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.     

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。     

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.     

一种含挠性传动的平面四杆机构传动特性的研究

本文提出了一种具有挠性传动的连杆作为平面四杆机构输入件的挠性件——四杆组合机构;研究了该种组合机构零价至二阶的传动函数,分析了该种组合机构的６种传动特性,并提出了输入轴与输出轴具有任意轴距和恒速比传动的几何条件。设计实例表明了该种组合机构设计简单,制造方便,工作平稳。     

Complete force and moment balancing of inline four-bar linkages

Design equations and techniques are presented which allow an inline four-bar linkage to be completely force and moment balanced, regardless of any variation of input angular velocity. The balance includes all mass effects due to both linear and rotary inertia, but excludes external loads. The key components utilized are the “inertia counterweight” and the “physical pendulum” link. The effect of such complete force and moment balancing on the input torque and the moment of ground bearing forces is examined. An example is included which translates the theory into meaningful practice.     

平面四杆机构刚体导引综合的小波特征参数法

针对傅里叶级数理论不能进行非整周期刚体导引综合的问题,提出了基于Haar小波级数的解决方法,将早期提出的解决平面四杆机构轨迹综合问题的方法扩展到平面四杆机构的刚体导引综合中。通过对刚体转角和其对应基本尺寸型的连杆转角小波系数进行分析,发现了二者的内在联系。在此基础上建立了101 408组基本尺寸型的平面四杆机构刚体导引输出特征参数数据库。将位置输出问题转化为平面四杆机构轨迹综合问题,并给出了计算平面四杆机构实际尺寸和机构安装位置参数的理论公式。利用建立的数据库和理论公式,实现了平面四杆机构非整周期刚体导引综合。以生产线上的输送工件的铰链四杆机构为例,证明了本文方法的有效性和可行性。     

瞬心无穷远时近似直线轨迹的四杆机构综合

连杆拐点圆上点附近曲线段与直线之间的近似度很高,工程上常利用其机构作为直线导引机构。针对铰链四杆机构连杆瞬心无穷远时拐点圆不存在,现有的方法不能综合出近似直线轨迹四杆机构的问题,提出瞬心无穷远时连杆曲率叠加原理,根据运动学原理进行分析,推导连杆上任意点曲率计算公式,证明曲率叠加原理的正确性,并得到求解铰链四杆机构连杆两铰链线上零曲率点的图解法。利用图解法能够解决瞬心无穷远时近似直线导引机构的综合问题,从理论上解决了瞬心无穷远时这一特定位置近似直线轨迹导引机构的综合问题。得到的方法简单、直观、适用,是拐点圆理论有力的补充和完善。     

基于Pro/ MECHANICA实现铰链四杆机构的优化设计

根据铰链四杆机构的特点以及传统设计方法存在的问题,提出了在Pro/MECHANICA环境下实现铰链四杆机构优化设计的方法。通过具体的设计实例,定义约束条件和目标函数,将设计过程可视化和参数化,复杂的计算过程由计算机完成,最终得到符合条件的设计结果,并可在Pro/E环境中升级模型,得到其优化的实体模型。     

Beitrag zur synthese ebener viergliedriger funktionsgetriebe in Steg-, Tot- und ParallellagenA contribution to synthesis of plane four-bar function generators in fixed link,dead center and parallel positions

The velocity ratio i = dψ/d? and its derivatives i′ = d²ψ/d?₂ and i″ = d³ψ/d?₃ of the four-bar linkage (Fig. 1) along with angular velocity ω_an of the input link lead to the angular velocity ω_ab of the output link, the angular accelleration ge_ab and its derivative $\text{?}\text{dot}{}_{\mathrm{ab}}$. Equations for computing i, i′ and i″ are known [2, 11, 4, 6, 7, 9, 10]. It is proper to have them in the form i = f(q) = f(i, λ) and i″ = f(i′, i, D) ; q, λ and D are parameters which can be taken from the drawing of a linkage in a fixed position. The equations are suitable for analysis. Synthesis of linkages is possible if q, λ and D are on the left side of the equations. In this way it is very easy to perform the synthesis for a four-bar function generator with four precision-points in an infinite neighborhood.In the equation i″ = f(i′, i, D) the drawing parameter D is the diameter of the so called Carter-Hall-circle [1,5,7]. With constant values of i, i″ it is the geometrical line of all velocity poles P of four-bar linkages (Fig. 1), whose transmission functions have four precision points in common with a desired function.The author has developed special equations for fixed link, dead center and parallel positions of plane four-bar linkages. In these special cases we often get indeterminate terms with the known equations and then have to seek for new drawing parameters instead of λ or D[8]. Similar derivations give the corresponding equations for slider-crank mechanisms too. All equations are compiled with the respective special positions of the four-bar linkages in a table.     

Multiobjective optimization for force and moment balance of a four-bar linkage using evolutionary algorithms

In this study, force and moment balance of a planar four-bar linkage is implemented using evolutionary algorithms. In the current problem, the concepts of inertia counterweights and physical pendulum are utilized to complete balance of all mass effects, independent of input angular velocity. A proposed multiobjective particle swarm optimization, and non-dominated sorting genetic algorithm II are applied to minimize two objective functions subject to some design constraints. The applied algorithms produced a set of feasible solutions called pareto optimal solutions for the design problem. Finally, a fuzzy decision maker is utilized to select the best solution among the obtained pareto solutions. The results show that optimal solutions minimize the weights of applied counterweights and eliminate both shaking forces and moments transmitted to the ground, simultaneously.     

采用Matlab和误差函数法对轨迹生成四杆机构的优化及仿真

提出了一个修正的距离误差函数,主要是针对轨迹产生四杆机构的优化,并对优化结果进行仿真。首先,给出了轨迹生成四杆机构的设计变量,给出了所常用的基于欧几里得距离误差的误差函数。同时,对修正的距离误差函数公式进行推导,并由此推出了目标函数的表达式。其次,采取优化的方法得出最佳机构的设计变量参数值。最后,将优化结果的参数值导入到Matlab软件中进行仿真,并且与传统的欧几里得距离误差仿真结果进行了对比。误差仿真曲线表明,采用修正的距离误差函数对轨迹生成的四杆机构所产生的横向及纵向误差较小,效果良好,从而为轨迹生成四杆机构提供了新的研究方法。     

A study of overconstrained linkage geometry by solution of closure equations — Part II. Four-bar linkages with lower pair joints other than screw joints

The methods of Part I are applied to four-bar linkages with revolute, prismatic, cylindric, planar and spherical joints. 21 forms of overconstrained linkage without passive degrees of freedom are derived.This paper is intended to be read in conjunction with Part I[24].     

连杆曲线上有两尖点位置的曲柄四杆机构的最优设计

本文以四杆机构的最小传动角的最大化为目标函数，用解析法确定出连杆曲线上有两尖点位置的曲柄四杆机构的最优解。     

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。     

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。     

Optimum synthesis of function generators involving derivative constraintsLa synthese optimale de generateurs de fonction impliquant des derivees comme contraintes

Presented in this article is the method of optimum synthesis of mechanisms satisfying derivatives of the generated displacements along with the displacements at a discrete set of design positions. Although the method is illustrated for the synthesis of four-bar function generators, where the first and second derivatives of the generated functions are also generated at all or some of the design positions in order to increase the efficiency of approximating the generated function, the method is readily applicable for the synthesis of mechanisms to generate paths and rigid-body positions satisfying path velocities, path accelerations, and rigid-body angular velocities. Mechanisms of precision control units, vibratory feeders and conveyors, transfer robots and mechanical arms, and linkages replacing noncircular gear drives require the application of such synthesis techniques involving derivatives of the generated displacements.     

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.