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.     

Dynamic simulation and choice of generalized coordinates for a free-floating closed-chain planar manipulator

Free-floating manipulators are inherently different from fixed-base planar manipulators due to conservation of linear and angular momentum. In this paper, we present simulation studies of a free-floating closed-chain planar manipulator. A fundamental question which an analyst is faced with during dynamic simulation of closed-chain mechanisms is how to choose the generalized coordinates during simulation. The independence of coordinates is dependent on the instantaneous properties of the governing constraints. For free-floating manipulators, this question becomes even more difficult due to the presence of constraints of momentum conservation. The objectives of this paper are to: (a) present a modular algorithm to build a rigid-body dynamic model of a free-floating closed-chain planar manipulator such that the instantaneous properties of the constraints can be easily studied; and (b) examine the momentum and closure constraints to build an algorithm for selection and switching of the generalized coordinates during simulation. In this algorithm, the free-floating manipulator is broken into component subsystems and the equation of constraint on these subsystems. This algorithm clearly describes the instantaneous properties of the constraints during the motion of the mechanism and helps in the selection of the generalized coordinates. The simulation results with this dynamic model and the algorithm for switching of coordinates are presented.     

Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

In order to accurately model compliant mechanism utilizing plate flexures, qualitative planar stress (Young’s modulus) and planar strain (plate modulus) assumptions are not feasible. This paper investigates a quantitative equivalent modulus using nonlinear finite element analysis (FEA) to reflect coupled factors in affecting the modelling accuracy of two typical distributed- compliance mechanisms. It has been shown that all parameters have influences on the equivalent modulus with different degrees; that the presence of large load-stiffening effect makes the equivalent modulus significantly deviate from the planar assumptions in two ideal scenarios; and that a plate modulus assumption is more reasonable for a very large out-of-plane thickness if the beam length is large.     

基于BP神经网络的平面机构连杆运动综合

针对要求实现连杆运动位置数目大于机构的精确点数目的平面连杆机构的综合问题,提出了利用BP神经 网络的综合方法。首先,将连杆的运动映射为映射空间的一条曲线,利用二维实数的傅里叶变换提取曲线的傅里 叶描述,然后,在大量的机构运动仿真的基础上,将连杆运动的映像曲线的傅里叶描述作为BP神经网络的输入, 相应的机构的几何参数作为网络的输出,训练BP网络。研究结果表明,训练后的神经网络不仅对连杆机构运动 综合问题能够做出正确的反应,而且具有其他方法所不具有的优点。     

极坐标下逐点比较法的直线插补

在旋臂式结构的机械加工装置中采用极坐标图形插补具有很多优点.结合旋臂式数控切割机床,采用逐点比较法的原理,对极坐标系统下的直线插补理论及其算法做了详细的探讨,并给出了递推公式和程序框图.还对如何采用MCS-51单片机编程实现作了简单介绍.     

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.     

6-SPS型并联机构的混合坐标动力学建模

研究6-SPS型并联机构的动力学建模方法,提出了一种新颖的混合坐标动力学建模方法,根据6-SPS型并联机构特点,以四元数和笛卡尔坐标来定义6根支杆和动平台的方位及位置坐标,然后运用第一类拉格朗日方程建模方法建立了6-SPS型并联机构动力学模型,所建立的动力学模型形式简洁,体现了并联机构各向同性的特点,而且又发挥了四元数在数值计算上的优越性,因此具有适合计算机大规模编程计算的优点.     

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.     

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 the multi-link five-point suspension system in point coordinates

In this paper, a numerical algorithm for the kinematic analysis of a multi-link five-point suspension system is presented. The kinematic analysis is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the joints. Geometric constraints are introduced to fix the relative positions between the points belonging to the same rigid body. Position, velocity and acceleration analyses are carried out. The presented formulation in terms of this system of coordinates is simple and involves only elementary mathematics. The results of the kinematic analysis are presented and discussed.     

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.     

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     

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.     

Explorative statistical analysis of planar point processes in microscopy

Basic methods of explorative statistical analysis for stationary and isotropic planar point processes are briefly and informally reviewed. At the explorative level, planar point patterns may be characterized in terms of the intensity, the K-function and the pair correlation function. These second-order functions enable one to classify a given point process as completely random, clustering or repulsive. The repulsive behaviour may be quantified by an estimate of the hard-core distance. In the exploratory approach, the statistics are essentially free from model assumptions. Second-order spatial functions have been estimated to characterize genuine planar point processes in the macroscopic domain, for example in forestry, geography and epidemiology. For light microscopy and transmission electron microscopy, two situations are distinguished, which may be summarized as the genuine planar case and the stereological case. In the genuine planar case, a direct interpretation of the results of spatial statistics is feasible. Here, monolayers in cell culture, intramembranous particles on freeze fracture specimens and amacrine cells of the retina are mentioned as examples. In the stereological case, point patterns are generated by sections through 3D structures. Here the observed point patterns may arise as the centres of sectional profiles of particles, or as centres of sectional profiles of spatial fibre processes. In both situations, exploratory spatial point process statistics allow a quantitative characterization of sectional images for the purposes of group comparisons and classification. Moreover, for spatial fibre processes it has recently been shown that the observed pair correlation function of the centres of the fibre profiles is an estimate of the reduced pair correlation function of the fibre process in 3D. Hence for fibre processes a stereological interpretation of point process statistics obtained from sections is an additional option.     

Dynamic modeling of flexible-links planar parallel robots

This paper presents a finite element-based method for dynamic modeling of parallel robots with flexible links and rigid moving platform. The elastic displacements of flexible links are investigated while considering the coupling effects between links due to the structural flexibility. The kinematic constraint conditions and dynamic constraint conditions for elastic displacements are presented. Considering the effects of distributed mass, lumped mass, shearing deformation, bending deformation, tensile deformation and lateral displacements, the Kineto-Elasto dynamics (KED) theory and Lagrange formula are used to derive the dynamic equations of planar flexible-links parallel robots. The dynamic behavior of the flexible-links planar parallel robot is well illustrated through numerical simulation of a planar 3-RRR parallel robot. Compared with the results of finite element software SAMCEF, the numerical simulation results show good coherence of the proposed method. The flexibility of links is demonstrated to have a significant impact on the position error and orientation error of the flexible-links planar parallel robot.