Investigation of balancing problem for a planar mechanism using genetic algorithm

In this study, optimal balancing of a planar articulated mechanism is investigated to minimize the shaking force and moment fluctuations. Balancing of a four-bar mechanism is formulated as an optimization problem. On the other hand, an objective function based on the sub-components of shaking force and moment is constituted, and design variables consisting of kinematic and dynamic parameters are defined. Genetic algorithm is used to solve the optimization problem under the appropriate constraints. By using commercial simulation software, optimized values of design variables are also tested to evaluate the effectiveness of the proposed optimization process. This work provides a practical method for reducing the shaking force and moment fluctuations. The results show that both the structure of objective function and particularly the selection of weighting factors have a crucial role to obtain the optimum values of design parameters. By adjusting the value of weighting factor according to the relative sensitivity of the related term, there is a certain decrease at the shaking force and moment fluctuations. Moreover, these arrangements also decrease the initiative of mechanism designer on choosing the values of weighting factors.     

Optimum dynamic balancing of planar parallel manipulators based on sensitivity analysis

This paper addresses the optimum dynamic balancing of planar parallel manipulators exemplified with a 2 DOF parallel manipulator articulated with revolute joints. The dynamic balancing is formulated as an optimisation problem such that while the shaking force balancing is accomplished through analytically obtained balancing constraints, an objective function based on the sensitivity analysis of shaking moment with respect to the position, velocity and acceleration of the links is used to minimise the shaking moment. Sets of optimisation results corresponding to various combinations of the elements of the objective function are evaluated in order to quantify their influence on the resulting shaking moment, ground forces and the driving torques. The results prove that the proposed optimisation approach can be used to completely eliminate the shaking force and to minimise the shaking moment transmitted to the frame of the parallel mechanism. For parallel manipulators or mechanisms with higher degrees of freedom, for which it is virtually impossible to obtain shaking force balancing conditions analytically, we propose an alternative constrained optimisation procedure. This procedure is based on the fact that while the magnitude of either the shaking force or the shaking moment can be bounded through including a set of constraints in the optimisation algorithm, the sensitivities of the other, either those of the shaking force or the shaking moment, can be minimised.     

平面连杆机构摆动力完全平衡的质量矩替代法

改进了建立平面（连杆）机构摆动力完全平衡条件的质量矩替代法。其基本思路是利用质量矩替代将平面连杆机构摆动力完全平衡问题,简化为二副构件的质量矩替代和平面开链的摆动力完全平衡问题。着重导出了二副构件及平面开链的质量矩替代条件与公式,由这些替代条件与公式可直接构造出一般平面机构的摆动力完全平衡条件;最后以一平面六杆机构为例说明了该方法的应用。     

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.     

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.     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

封闭周转轮系动态优化设计

利用BP神经网络极强的非线性映射功能 ,成功地建立了封闭周转轮系的设计变量与模态柔度之间非线性映射的 3层BP神经网络模型 ,解决了动态优化设计时目标函数难以建立的难题 ,使非常复杂的动态优化问题变得十分简单。利用本文所提出的混合离散变量遗传算法对封闭周转轮系进行了动态优化设计 ,并对优化后的设计方案进行了动态特性分析 ,通过对比可以看出 ,优化后的设计方案不但动态特性有了较大提高 ,其重量也有所下降     

平面轨迹输出柔顺机构的形状优化

2自由度平面柔顺机构具备工作空间,可以作为微动机器人载体,通过控制两个独立输入实现可控的平面运动轨迹输出。为改善设计方案的可加工性,研究该柔顺机构拓扑图轮廓提取后的形状优化问题。将柔顺机构抽象成杆件和结点形式,基于拓扑学连通性原理,提出机构区域连通性判定条件,构造窗口平移扫描式机构结点搜索算法,获得设计区域内的柔顺机构结点,在此基础上,建立杆件搜索算法,找出各杆件,实现对柔顺机构的轮廓抽象。对轮廓抽象后的柔顺机构进行轮廓重构,将其轮廓表示为简单曲线的拼接,以曲线参数作为优化变量,通过敏度分析提取关键尺寸,以柔顺机构实际输出和期望输出间的误差作为目标函数,建立轮廓曲线尺寸优化模型,得到柔顺机构的最优轮廓,从而在保持柔顺机构输出性能的前提下明显改善设计方案的可加工性。算例验证了所提形状优化方法的有效性。     

利用遗传算法进行电动栏杆弹簧平衡系统的优化设计

弹簧平衡系统是电动栏杆机产品设计的关键技术之一，直接决定栏杆机的功率消耗指标．对产品的可靠性和寿命影响很大。为解决此关键技术，本文就能同步平衡栏杆正弦规律变化的阻力矩的弹簧平衡系统，提出了优化设计的教学模型．目标函数，利用具有很强优化能力和广泛适应性的遗传算法．用VB编程求解后得出了满意的优化数据，有效地支持了实际的产品设计。同时弹簧平衡系统的数学模型有普连实用性．还可以根据设计变量不同建立新的目标函敛．对关心的变量进行优化；对非正弦变化的负载阻力矩的平衡也可应用本设计的优化方法，有推广价值。     

全 R 副空间连杆机构摆动力和摆动力矩的完全平衡

提出了利用质量配重和惯性配重实现全Ｒ副空间连杆机构摆动力和摆动力矩完全平衡的质量动替代法。其基本思路是通过质量动替代的途径，将空间闭链机构摆动力和摆动力矩的完全平衡转化为空间树状链摆动力和摆动力矩的完全平衡。文中导出了ＲＲ构件的质量动替代的条件与公式以及空间树状链摆动力和摆动力矩完全平衡的条件，由此可简便地直接构造出任意全Ｒ副空间闭链机构摆动力和摆动力矩的完全平衡条件。最后讨论了Ｂｅｎ－ｎｅｔ机构摆动力和摆动力矩的完全平衡条件及其实现方法。     

Reducing undesirable vibrations of planar linkage mechanism with joint clearance

An optimization design method is presented to reduce the undesirable vibrations caused by clearance for planar linkage mechanism. A clearance joint is defined and considered a contact/impact force constraint. Contact and impact force models for the clearance joint are established using a normal contact force model based on Hertz model with energy loss and a tangential friction model based on modified Coulomb model with dynamic friction coefficient, respectively. In view of the clearance joint, dynamic equations and optimization method for a planar four-bar mechanism are then presented as an application example. The optimization aims to minimize the maximum absolute acceleration peaks of the mechanism by determining the link lengths of the planar linkage mechanism. Finally, the optimization design is solved by a generalized reduced gradient algorithm. Results show evident decrease in vibration peaks of the mechanism and obvious reduction in the contact forces in the clearance joint, which contribute to a good performance of planar linkage mechanism systems.     

全R副空间连杆机构摆动力完全平衡的质量静替代法

提出了全Ｒ副空间连杆机构摆动力完全平衡的一种新方法──质量静替代法，其基本思想是通过质量静替代的途径，将空间闭链机构摆动力的完全平衡转化为空间开链摆动力的完全平衡．导出了ＲＲ构件的质量静替代公式与空间开链摆动力的完全平衡条件，由此可直接构造出任意多环全Ｒ副空间连杆机构摆动力的完全平衡条件，不再需要进行繁琐的公式推导．最后以一种单自由度两环空间连杆机构为例。导出了其摆动力的完全平衡条件．     

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.     

DYNAMIC DESIGN OF VARIABLE SPEED PLANAR LINKAGES

A method for improving dynamic characteristics of planar linkages by actively varying the speed function of the input link is presented. Design criteria and constraints for the dynamic design of variable speed planar linkages are developed. Both analytical and optimization approaches for determining suitable input speed functions to minimize the driving torque, the shaking moment, or both simultaneously of planar linkages, subject to various design requirements and constraints, are derived. Finally, some examples are given to illustrate the design procedure and to verify its feasibility.     

Feasible parameter design spaces for force and root-mean-square moment balancing an in-line 4R 4-bar synthesized for kinematic criteria

The paper contains application oriented additions to the theory developed by Berkof and Lowen for root-mean-square (RMS) shaking moment optimization of a force balanced in-line 4R 4-bar linkage. The theory is extended to the problem of force-RMS moment balancing by mass redistribution when all link length ratios are fixed to satisfy kinematic design criteria. Feasible parameter design spaces and parameter inter-relationship monographs are presented. These aid in the selection of numerical values for five of the eight design parameters so that the three balancing equations can be solved for physically realistic values of the remaining three parameters.     

基于Matlab遗传算法对2K -H(NGW) -Z混合轮系的优化设计

以2K- H(NGW) -Z混合轮系体积减少进行目标优化,根据轮系的机构确定设计变量和约束条件,建立数学模型;基于Matlab软件运用遗传算法对其机构进行优化计算,使优化后的各项参数更符合实际要求,最终得出理想的优化设计方案.     

混合驱动平面五连杆机构优化设计与迭代学习控制

对混合驱动平面五连杆机构进行了优化设计和轨迹跟踪迭代学习控制研究.首先,以伺服电机角加速度波动最小为目标函数,应用遗传算法对混合驱动平面五连杆机构参数进行优化设计;其次,对混合驱动平面五连杆机构进行轨迹跟踪指数变增益D型和闭环PD型迭代学习控制研究;最后,结合实例进行混合驱动平面五连杆机构轨迹跟踪数值仿真.结果表明,迭...     

免疫遗传算法在智能桁架结构振动主动控制系统优化设计中的应用

研究智能桁架结构中主动构件的配置和反馈增益的同步优化问题.基于有限元法,建立智能桁架结构的机电耦合有限元模型.根据结构的最大耗散能理论,建立智能桁架结构中主动构件的位置和反馈增益的同步优化的目标函数.最后,采用免疫遗传算法解决这一个同时含有离散和连续变量的优化设计问题,并通过一个平面16杆智能桁架结构的振动主动控制系统的优化设计和数值仿真,表明所提出的优化设计方法和优化算法的有效性.     

含 R、P 副空间连杆机构摆动力完全平衡的质量矩替代法(Ⅰ)──质量矩替代

提出了含Ｒ、Ｐ副空间连杆机构摆动力完全平衡的质量矩替代法，将含Ｒ、Ｐ副空间连杆机构摆动力的完全平衡简化为ＲＲ构件、ＰＲ－ＲＲ构件组、全Ｒ副空间开链的质量矩替代。本文着重导出了ＲＲ构件、ＰＲ－ＲＲ构件组、全Ｒ副空间开链的质量矩替代条件与公式。由这些质量矩替代条件与公式，按照本文第（二）部分给出的含Ｒ、Ｐ副空间连杆机构摆动力完全平衡条件的构造步骤，可直接构造出一般含Ｒ、Ｐ副空间机构的摆动力完全平衡条件，使得这类机构摆动力完全平衡条件的建立过程大为简化。     

基于遗传算法的交互式齿轮优化设计方法研究

常规的齿轮设计方法通常需要花费大量时间，通过数次试算才能得到一个较好的设计结果，采用一般的非线性和线性优化方法注解起来也比较困难。为此，本文以渐开线标准直齿圆柱齿轮为例，提出了一种基于遗传算法的交互式优化设计方法，对于设计原始数据，设计要求及设计过程中的经验型中间结果采用交互式输入，而对其他主要设计变量采用遗传算法进行优化。