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 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.     

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.     

Complete shaking force and shaking moment balancing of four types of six-bar linkages

The article presents design equations and techniques for the complete shaking force and shaking moment balancing of four types of six-bar linkages due to both linear and rotary inertia, but excludes external loads. The key components utilized are the geared inertia counterweight and planetary-gear-train-inertia counterweight. They are very useful for balancing of multi-bar linkages.     

General method for active balancing of combined shaking moment and torque fluctuations in planar linkages

The paper describes a novel method of active balancing designed to eliminate completely the shaking moment, the driving torque or both simultaneously. Active balancing is achieved by a single additional member: a balancerdisc revolving in a prescribed way related to the geometry and the mass characteristics of the original linkage. Noncircularr gear drive or other means may provide the necessary rotation. The synthesis of the balancing device is based on simple general principles equally applicable for any planar mechanism.     

The quantitative influence of complete force balancing on the forces and moments of certain families of four-bar linkages

The effects of full force balancing on all the bearing forces, the input moments and the shaking moments of 39 families of crank and rocker four-bar linkages of standard configuration are investigated. Dimensionless results are presented in tabular form, and their use is demonstrated. To enable mechanism designers to make similar comparisons for their own specific applications, all necessary expressions are compiled.     

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.     

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。     

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.     

On the coupler-great-circle envelopes of spherical four-bar linkages

With use of the techniques developed for coupler-point curves, the tangential equation is derived for the envelope of a great circle attached to the coupler of a general spherical four-bar linkage in the motion of this mechanism. The class of this envelope is determined to be 8. The dual relationships between the coupler-point curve and the coupler-great-circle envelope are discussed. With this concept, the techniques for designing a spherical four-bar coupler-great-circle envelope generator are introduced.     

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.     

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。     

General method for full force balancing of spatial and planar linkages by internal mass redistribution

In the present paper, a general method for full force balancing is developed. The method may be applied for any linkage both spatial or planar, single or multi-loop consisting of any kind of lower pairs. By the procedure, three sets of general force balancing conditions for the main directions X, Y and Z are derived. The conditions of identity or difference of these three sets are found the existence of particular balancing equations for some privileged directions are established. These equations do not follow from the Berkof and Lowen method. They could be usefully applied if the “Contour” theorem of Tepper and Lowen is violated or if the partial balancing along the existed privileged axes is preferred.     

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.     

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。     

平面四杆机构死点问题探讨及应用

主要以曲柄摇杆机构为例,分析了平面四杆机构死点实质、极限位置、形成死点条件等,为平面四杆机构解决死点问题、利用死点特性提供了理论依据。研究发现机构死点问题可以设法消除,而且存在着一定的应用和发展空间。     

Reducible compositions of spherical four-bar linkages with a spherical coupler component

We use the output angle of a spherical four-bar linkage C as the input angle of a second four-bar linkage D where the two frame links are assumed in aligned position as well as the follower of C and the input link of D. We determine all cases where the relation between the input angle of the input link of C and the output angle of the follower of D is reducible and where additionally at least one of these components produces a transmission which equals that of a single spherical coupler. The problem under consideration is of importance for the classification of flexible 3 × 3 complexes and for the determination of all flexible octahedra in the projective extension of the Euclidean 3-space.     

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.     

Design equations for the complete shaking force balancing of 6R 6-bar and 6-bar slider-crank mechanisms

The article presents the design equations for complete shaking force balancing of commonly used planar Stephenson's and Watt's type 6R 6-bar and 6-bar slider-crank regular force transmission mechanisms using the method of linearly independent mass vectors. Regular force transmission mechanisms are those in which the shaking force can be completely balanced by distributing the masses of the existing links. Design equations are developed by considering the existing links. Design equations are developed by considering mass distributions of the coupler links and sliders specified whenever possible, so that the counter-balancing masses are mounted on the shafts supported by the fixed frame of the mechanism. Industrial design applications of the design equations given are illustrated in two numerical examples where the shaking force in a Stephenson's Type-1 6R mechanism and a 6-bar double-slider-crank mechanism used in V-engines is balanced.