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。     

含 R、P 副空间连杆机构摆动力完全平衡的质量矩替代法(Ⅱ)一般步骤

在文［１］的基础上，本文着重给出了含Ｒ、Ｐ副空间连杆机构摆动力完全平衡条件的构造步骤，按照该步骤，由文［１］所给出的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，可直接构造出含Ｒ、Ｐ副空间连杆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。最后以一两环含Ｒ、Ｐ副空间连杆机构为例，具体说明了用质量矩替代法构造含Ｒ、Ｐ副空间连杆机构的摆动力完全平衡条件的过程。     

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。     

弹性机构动力平衡的有效新方法

从改善弹性机构动力特性的角度研究了机构弹性动力平衡的本质问题。提出了附加弹性元件的新方法，有效地解决了弹性机构震动力、震动力矩、输入扭矩波动和运动副反力的平衡难题。首次推导出具有弹性元件的弹性连杆机构动力学方程，从理论上阐述了此平衡方法的有效性。仅用附加一根扭簧的简单方法实现了平面四杆机构的弹性动力平衡，效果明显。     

Shaking force balancing of planar linkages with force transmission irregularities using balancing idler loopsVollständiger trägheitskraftausgleich von ebenen koppelgetrieben mit ungleichmässiger kraftübertragung durch schleifen

The article first shows 4-bar, 6-bar and 8-bar planar mechanisms with force transmission irregularities in which an unbalanceable shaking force is generated by a link or by a group of links that have connections to the fixed link through pairs permitting linear freedoms only. Complete shaking force balancing of such mechanisms with force transmission irregularities using the method of linearly independent mass vectors and the concept of balancing idler loops in presented. Design equations for the complete shaking force balancing of some 4-bar, 6-bar and 8-bar mechanisms with force transmission irregularities are given. A numerical example is included.     

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.     

The complete shaking force balancing of a spatial linkageПoлнoe ypaвнoвeшивaниe peзyльтиpyюшeй cил инepции пpocтpaнcтвeнныx мexaнизмoв нин-xин-чэнь

The equations for complete shaking force balancing of an open-loop spatial chain consisting of pairs without sliding freedom, a single loop spatial n-bar linkage with R-R link consisting of pairs without sliding freedom, as well as a single loop spatial n-bar linkage with only one P pair are derived in this paper. For a single loop n-bar linkage with R-S link, the equations of complete shaking force balancing are derived also, if the mass center of the R-S link has some constraint. In the examples, the equations of complete shaking force balancing of Bennett, RRRSR, RRPSR and RRSRR linkages are given.     

剑杆织机新型引纬机构的震动力完全平衡

针对一种由共轭凸轮机构、空间连杆机构和齿轮机构组合而成的新型剑杆织机引纬机构，通过有效分离，将其中的共轭凸轮作为两个盘形转子单独进行了平衡，其余构件整体上作为空间机构运用线性无关向量法一并进行了平衡，从而实现了整个机构的震动力完全平衡。     

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．     

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。     

平面连杆机构摆动力与摆动力矩完全平衡的质量动替代法

在机构平衡中首次提出质量动替代法。首先对质量动替代法的力学特性做了探讨,然后利用此方法对四杆机构和Stephenson型六杆机构的摆动力和摆动力矩进行了完全平衡。     

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.     

平面连杆机构摆动力与摆动力矩优化平衡研究

提出了平面连杆机构摆动力与摆动力矩优化平衡的新方法，并用其对平面铰链四杆、六杆机构以及曲柄滑块机构摆动力与摆动力矩的最优平衡问题进行了研究，平衡效果较为理想。由于本文只需求解一个线性方程组就可得到最优平衡方案，因此具有较大实用价值。     

Partial balancing of the shaking force of a spatial 4-bar RCCC linkage by the optimization methodчacтичнoe ypaвнoвeщивaниe peзyльтиpyющeй cилы инepции пpocтpaнcтвeннoгo чeтыpexзвeннoгo мexaнизмa

In order to obtain partial balancing of the shaking force of a spatial 4-bar RCCC linkage, three counterweights are attached to moving links of the RCCC linkage respectively and optimal vectors of the position of the counterweights are computed by optimization procedure BFS or BFGS (Broyden-Fletcher-Goldfarb-Shanno), which is a variable metric method. In this way, the RMS norm of the shaking force of the RCCC linkage is reduced by half.     

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.     

平面连杆机构摆动力和摆动力矩的完全平衡

本文利用质量分布和附加两种惯性配重相结合的方法,实现了平面多杆机构摆动力摆动力矩的完全平衡。这两种惯性配重是定轴齿轮机构（简称为齿轮机构）惯性配重和行星机构惯性配重。笔者先以一种六杆机构为例,说明一般多杆机构力与力矩完全平衡的条件推导过程。本文的重点是根据上述理论进一步提出了铰链多杆机构的分解平衡法,即把该类机构分解成若干个铰链四杆机构和双杆组来分别平衡,从而明显简化了平衡方程的推导过程。     

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.     

滑阀真空泵的振动控制

对滑阀真空泵振动控制进行探讨。针对泵振动的主要激励源，提出在泵的外部和内部实现的动平衡措施。为了获得优化配重，发展了分别采用幅值最小二乘拟合和分力最小二乘拟合，来拟合滑阀杆产生的惯性力的方法。理论分析和实验结果表明，所提出的动平衡措施易于实现，可使泵的振动有明显下降。     

平面机构综合优化目标函数加权系数的确定

本文将平面机构作用的机座系统抽象为三自由度强迫振动系统，研究振动力Ｘ、Ｙ分量，振动力矩与系统响应之间关系。发现进行综合优化平衡时，加权系数大小与系统的固有属性（质量、刚度）有关。从而解决了综合优化目标函数加权系数数值的确定问题。与传统方法相比，文中所述目标函数构造方法可有效减小系统的振动响应。     

Kineto-elastodynamic balancing of 4R-four bar mechanisms combining kinematic and dynamic stress considerations

When a mechanism runs at high speed and has elastic links, its links vibrate under the action of forces present on the mechanism. The acceleration field resulting from the vibration of the links develops additional interia forces called kineto-elastodynamic (KED) inertia forces. The present paper takes into account the contribution of the KED inertia forces towards the shaking force and shaking moment while balancing planar mechanisms. Combining kinematic design and dynamic stress considerations an optimal kinematic design of the mechanism satisfying the given aim and optimal cross-sectional areas of the links were determined such that the shaking force trasmitted to the foundations due to the combined effect of rigid-body inertia forces and KED inertia forces is a minimum.