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。     

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.     

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。     

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。     

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.     

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。     

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.     

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。     

STRUCTURE SYNTHESIS OF 4-DOF PARALLEL ROBOT MECHANISMS BASED ON SCREW THEORY

Structural synthesis for 4-DOF parallel manipulators using screw theory is systematically studied. Motion properties and constraint conditions of 4-DOF parallel manipulators according to the relationship between screw and reciprocal screw are analyzed. Mathematical expressions for constraint screws and twist screws of moving platform are constructed, and all possible limbs, which provide one or more force constraints, are enumerated. Finally, a parallel manipulator with 3-rotation-DOF and 1-translation-DOF is used as an example to describe the synthesis procedure for symmetrical and non-symmetrical 4-DOF parallel manipulators.     

少自由度并联机器人机构的静力分析

与6自由度并联机器人不同,少自由度并联机器人机构的支链不仅传递驱动力,同时还要向末端提供约束力,然而在对此类机构进行静力分析时,现有的研究都忽略了约束力的传递特性。为此,以微分流形理论为基础,分析指出少自由度并联机器人末端的完整力空间应包括驱动力子空间和约束力子空间,并以此为基础,利用虚功原理,给出一种建立此类机构输入与输出广义力间完整映射的方法。此完整力映射包括驱动力映射矩阵和约束力映射矩阵。通过计算这两个矩阵的条件数,可以分别分析此类机构驱动力和约束力的传递特性。该分析方法的物理意义和数学理论相统一,且概念清晰,便于深入理解少自由度并联机构静力传递的特性。最后,以3-UPU并联机器人机构为例进行实例分析。     

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。     

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。     

摆盘发动机动力平衡的优化设计

在对摆盘发动机进行动力学分析的基础上,通过确定设计变量、选择目标函数,给出约束条件,建立动力优化的数学模型.并以某一型号摆盘发动机为例,分别给出限定振动力和限定振动力矩两种约束条件下不同的目标函数,并用二次规划法对摆盘发动机动平衡进行优化,最后比较两种目标函数下的优化结果.结果表明,在保证下降百分比一定的情况下,利用限定振动力矩这一约束条件所得到的优化结果要好于限定振动力所得到的结果,从而更有利于控制发动机机架的振动和降低噪声.     

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。     

Maximum allowable load of mobile manipulators for two given end points of end effector

The aim of this paper is the formulation and numerical solution for finding the maximum dynamic load of mobile manipulators for a given two-end-point task. In fixed-base classical robots, the maximum allowable load is limited mainly by their joint actuator capacity constraints. However, besides actuator capacity constraints, kinematic redundancy and non-holonomic constraints should be considered for finding maximum dynamic payload of mobile manipulators, both of which arise from base mobility. The extended Jacobian matrix concept is used to solve the redundancy resolution and non-holonomic constraints. The problem is formulated as a trajectory optimisation problem, which fundamentally is a constrained nonlinear optimisation problem. Then, the iterative linear programming (ILP) method is utilised to solve the optimisation problem. Finally, by a numerical example involving a two-link manipulator mounted on a differentially driven wheeled base, use of the method is presented and the results are discussed.     

Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators

Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems.Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint space control and work space control.     

A methodology for actuator failure recovery in parallel manipulators

In this paper, the failure of parallel manipulators is examined considering the failure modes of manipulators. A methodology for investigating the effect of actuator/joint failures on the force/moment capabilities of manipulators is presented, and the criteria for full and partial recovery from these failures are established. The proposed methodology is valid for both planar and spatial parallel manipulators; in the case study and simulation, the planar manipulators are used as an example.     

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.     

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．