Extensions to the theory of balancing frame forces in planar linkages

This paper presents extensions to the theory of force-balancing planar linkage mechanisms given in [1]. It incorporates (i) a technique for checking whether a linkage can be fully force-balanced using counterweights alone, (ii) a formula that defines the minimum number of counterweights needed for a full force-balance, and (iii) a criterion for selecting what is likely to be the optimum counterweight set. The linkages may be multi degrees-of-freedom and may contain both revolute and prismatic joints.     

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.     

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.     

利用可视化技术进行平面四杆机构的轨迹综合

四杆机构的轨迹综合是一个较复杂的机构设计问题,这里采用可视化屏幕拟合技术很好地解决了此问题,并使拟合误差达μm级。     

Static balancing of planar articulated robots

Static balancing for a manipulator’s weight is necessary in terms of energy saving and performance improvement. This paper proposes a method to design balancing devices for articulated robots in industry, based on robotic dynamics. Full design details for the balancing system using springs are presented from two aspects: One is the optimization for the position of the balancing system; the other is the design of the spring parameters. As examples, two feasible balancing devices are proposed, based on different robotic structures: The first solution consists of linkages and springs; the other consists of pulleys, cross mechanisms and (hydro-) pneumatic springs. Then the two solutions are compared. Pneumatic, hydro-pneumatic and mechanical springs are discussed and their parameters are decided according to the requirements of torque compensation. Numerical results show that with the proper design using the methodology presented in this paper, an articulated robot can be statically balanced perfectly in all configurations. This paper therefore provides a design method of the balancing system for other similar structures.     

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.     

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.     

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.     

A general mass balancing method for complex planar mechanisms

The 1968 work by Berkof and Lowen provided a new perspective in the balancing of machines by using “linearly independent vectors” for the complete shaking force balancing of simple mechanisms. As logical extensions of their work, methods presented in this paper allow the complete balancing of complex mechanisms for shaking force or shaking moment (which inherently satisfies the shaking force criteria). These methods further allow the satisfaction of user specified non-zero values of the dynamic properties of the mechanism including driving torque, shaking momentum, shaking force, or combinations of these. The formulation provides, by direct non-iterative computation, redistribution of the mass content of the system in the most general sense to enhance the operating smoothness of the total system. These synthesis results are addressable by all designers since their uniform mathematical formulation can be packaged in compact interactive computational programs for all conceivable dynamic properties to be considered for balancing.     

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.     

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.     

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.     

任意复杂多回路平面机构及操作手奇异分析的模块法

提出了求解任意复杂多回路平面连杆机构及操作手奇异位置分析的模块法。即一个复杂机械可看作是由输入一个或多个零自由度的基本运动键组成,对这些数量有限的基本运动链进行奇异分析,然后将灾看作是复杂机构和操作手奇异分析的基本模块;仅当一个基于运动键达到奇异位置时,复杂机构即处于奇异位置。还得到了任意复杂多回咱平面机构产生奇异位置的奇异性条件总数的计算公式。因此,该方法可求解所有复杂的多回路平面机构及操作手的     

A novel approach for the rigid body guidance synthesis of planar RRPR linkages

Journal of Mechanical Science and Technology - This paper demonstrates that the maximum number of poses that can be exactly reached by a planar RRPR linkage is four, while the design for five poses...     

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。     

Three and four precision point kinematic synthesis of planar linkages

Dyads modelled by complex numbers are presented in several different equation forms for three prescribed positions of either motion, path generation with prescribed timing or function generation. Different strategies are suggested depending on how the free choices are best utilized. Interactive computer techniques are suggested for both the three and four prescribed position cases. Several examples are presented to help illustrate each of the design situations.     

平面机构综合动力平衡新方法

本文研究了平面多杆机构振动力、振动力矩和输入转矩的求解；并经过归纳分析，得到了一种综合动力平衡的有效方法；最后给出了一个六杵破碎机构的平衡算例，结果表明比法是较为合理和可行的。     

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.