Kinematic analysis of planar higher pair mechanisms

In this paper, theory of kinematics analysis of planar higher pair mechanisms is presented. It has been found that the analysis procedure will be analytical or numerical depending on whether the geometry of the contacting surface(s) is given in an analytical form or in terms of coordinates of discrete points on the surface(s). For either of these options, solution procedures have been described. For the case when profile data is given in numerical form, a numerical scheme of kinematic analysis using cubic spline curve fitting technique has been developed. Two examples are presented: one to illustrate the analytical procedure and the other to illustrate the numerical technique.     

Kinematic analysis of combined roller-chain and planar mechanisms

This paper presents a suggested mechanical system comprising of two sprocket roller-chains (flexible system) in combination with rigid planar links either crank-coupler or drag-link linkage. The paper discusses and analyzes two alternatives in which the roller-chain is driving the rigid links and “inverse” possibility when the crank of the rigid planar links is the input element and the output motion is taken from the roller-chain. Moreover, replacing the crank of the rigid links by a variable length is discussed, and obtained by considering the coupler as being joined with a point on a drag-link mechanism. The merits of each version are presented and discussed. Of interest, is the unique advantage of obtaining particular output/input velocity ratios which no available mechanism can achieve. Moreover, the obtained results indicate quite a useful applicability of the analyzed system in the industrial packing process, motion transmission and, in particular, in conveying machinery. The kinematic analysis procedure is presented in simple formulation using trigonometric relations.     

平面机构误差分析的同伦法

提出考虑机构原始误差及由弹性变形等造成的平面机构位置误差分析的一种新的方法 ,其基本思路是 :建立平面理想机构与实际机构的位置方程组的同伦方程组 ,用同伦法求出实际机构的位置 ,从而得出平面机构的位置误差。最终得到平面机构误差的变化曲线图     

基于C语言的平面连杆机构的运动分析

提出一种基于C语言的平面连杆机构运动分析方法，为平面连杆机构运动分析提供一条简单易行的解析途径。     

平面机构运动分析的有限元件法

要使用一种特殊有限元的方法进行平面机构的运动分析,需首先对组成平面机构的常用单元进行分析,并给出了描述单元的变形模态参数与单元节点坐标之间的函数关系,进而用传递函数的概念对机构的位置,速度和加速度进行分析,在此基础上,编制了计算机程序,对ＺＬ５０装载机的工作装置的运动进行了计算给出了数值模拟结果。     

KIDYAN: Computer-aided kinematic and dynamic analysis of planar mechanisms

The paper deals with a method of kinematic and dynamic analyses of planar linkages and describes a general program based on it. Both make use of a theorem saying that every planar mechanism consists of several Assur groups and of one or more driving links. Likewise, the corresponding program is composed of subprograms for the analysis of these groups.Two examples are presented.     

Structural analysis of planar jointed mechanisms: Current state and problems

On the basis of study of the history of development of structural synthesis of planar jointed mechanisms, as well as Assur structural groups, Baranov statically determinate trusses, and Grubler closed kinematic chains, a picture of the current state of research in this field is provided.     

Kinematic configuration analysis of planar mechanisms based on basic kinematic chains

According to the single-link transformation principle, and based on the topological characteristic investigations to planar closed kinematic chains (PCKCs), a general study of the kinematic configuration analysis of planar mechanisms with R-pairs is conducted in this paper. Firstly, two new concepts, contract link distance sequence and basic link group code sequence, are defined, and a novel approach for identification of multi-bar basic kinematic chains (BKCs) within the kinematic chain left from the single-link transformation is proposed. Then, another two concepts, weight code and similarity code, are defined for aid to link similarity judgment and two judgment theorems are proposed as well. As a further step, weight code or similarity code of the transformed single-link will be employed for kinematic configuration analysis situation judgment. Finally, corresponding unified constraint equations are set up and solved with coefficient homotopy method, on the basis of aforementioned analysis results. The study shows that the method is reliable and effective, and it is especially applicable for the kinematic configuration analysis problem of PCKCs with multi-bars and multi-freedoms.     

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.     

A study on completely computer-assisted kinematic analysis of planar link mechanisms

For the purpose of complete computerization of the kinematic analysis of planar mechanisms, an iterative process of analysis has been determined by means of incidence matrices of prime structures. The prime structures have been defined as the structures composed of pin-jointed links that cannot be derived from other structures, and some of them have been introduced together with positional relations of their joints. Moreover, it is shown that kinematic analyses can also be carried out by means of the prime structures.     

平面闭链机构中过约束分析的研究与应用

由于不可避免的制造误差，平面闭链机构中广泛存在的过约束，导致对机械性能的一系列有害影响。因而越来越受到机械结构设计者的重视，提出了多种机构过约束的分析方法。但是，这些方法还存在一些不足，还需进一步发展完善。因此在深入、系统研究这些方法的基础上，重点介绍了其中两种较好的方法，提出了一些新的见解，并总结出了一些完善过约束分析方法及其在消除或减小过约束影响设计、应用方面的结论和原则。     

A general method for analysis of planar mechanisms using a modular approach

A method that covers both kinematic, inverse dynamic, dynamic, and static analysis of any type of planar mechanism is presented. The method is based on a subdivision of the mechanism to be analyzed into kinematic chains that are categorized as either neutral or expansion modules. The neutral modules are the well known Assur Groups, characterized by the fact that they have no effect on the degree of freedom of the mechanism. On the contrary each expansion module increases the degree of freedom by one. The coordinates that correspond to the indeterminancy of the expansion modules may be identified as a set of independent coordinates for the subdivided mechanism and used in any type of analysis. The method as it is described in the present paper has been implemented in a menu-controlled PC computer program CADME. A number of practical observations concerning the implementation of a modular approach is made and discussed.     

平面高级杆组装配构形的计算机代数解

建立了平面高级杆组装配构形的位置方程，应用计算机代数法，经过逐次消元，导出了对应装配构形位置方程的一系列导出方程组，由此得到了用结构参数表示的该类杆组装配构形全部位置的符号解。并根据Bezout结式及其相应各阶顺序主子式，分析了杆组结构参数对装配构形数1／1的影响。从理论与实践上解决了该类杆组装配构形分析使用常规迭代法的所带来的各种弊端。     

Synthesis of adjustable planar 4-bar mechanisms

The ability of planar 4-bar mechanism, to generate various kinds of motion, can be greatly enhanced if it is made adjustable. With a simple adjustment of the position of the driven crank fixed pivot(s), a variety of outputs can be obtained with the same set of hardware.

This paper outlines synthesis techniques for 4-bar linkages, having adjustable driven crank pivots, for different motion generation problems. For a 4-bar mechanism, no more than five design positions can be specified. All the possible maximal motion specifications for the two “phases”, consisting of different combination of the five positions, are enumerated. This leads to four classes of motion generation problems. Synthesis procedure for each class is presented. An example of the P₁-P₂-P₃:P₁-P₄-P₅ case is solved. The method of solution is analytical in nature, and, therefore well suited for use on a digital computer.     

3-RRR平面并联机构刚度分析

刚度是并联机构重要性能指标,为了评价并联机构刚度,提出了一种刚度评价方法.基于3-RRR机构的逆运动学模型,推导出其雅可比矩阵.在力雅可比矩阵的基础上,给出了刚度评价指标,该指标不仅适用于3-RRR并联机构,而且可以应用于其它并联机构.将提出的刚度指标应用于3-RRR并联机构,数值仿真结果表明3-RRR机构在工作空间中具有对称的刚性.     

基于自然方程式的平面四杆机构的综合

在连杆曲线以其特征参数分类的基础上,利用其特征参数的自然方程式,将创成曲线与理想曲线一致程度的判定问题,归结为曲线上的特征参数及自然方程式的一致程度的判定,进而用此方法进行了曲线创成机构综合,充分显示了该方法的有效适用性.     

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.     

Dynamic modelling of planar mechanisms using point coordinates

In the present study, the dynamic modelling of planar mechanisms that consist of a system of rigid bodies is carried out using point coordiantes. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then for the resulting equivalent system of particles, the concepts of linear and angular momentums are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.     

Dynamic balancing of planar mechanisms using genetic algorithm

This paper presents an optimization technique to dynamically balance the planar mechanisms in which the shaking forces and shaking moments are minimized using the genetic algorithm (GA). A dynamically equivalent system of point-masses that represents each rigid link of a mechanism is developed to represent link’s inertial properties. The shaking force and shaking moment are then expressed in terms of the point-mass parameters which are taken as the design variables. These design variables are brought into the optimization scheme to reduce the shaking force and shaking moment. This formulates the objective function which optimizes the mass distribution of each link. First, the problem is formulated as a single objective optimization problem for which the genetic algorithm produces better results as compared to the conventional optimization algorithm. The same problem is then formulated as a multi-objective optimization problem and multiple optimal solutions are created as a Pareto front by using the genetic algorithm. The masses and inertias of the optimized links are computed from the optimized design variables. The effectiveness of the proposed methodology is shown by applying it to a standard problem of four-bar planar mechanism available in the literature.     

RECDWELL-Computer aided design of six-link planar dwell mechanisms

Linkage-type dwell mechanisms are less expensive to manufacture and maintain, and can be superior to cams at high speed. They are also easily adjustable for satisfying variable output motion requirements. In spite of these advantages they have not found wide application. Part of the reason for this lack of popularity is the absence of proper design tools. The inspiration for this work stems from the need to bridge this technological gap. RECDWELL helps to design both circular-arc and straight-line dwell mechanisms using a technique which is simple, efficient and accurate.