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.     

基于变胞铰链的并联机构结构设计与构型分析

为了拓展变胞机构的种类,提出了一种变胞运动单元,该变胞单元采用三个旋转关节,并且三个旋转关节可以通过位置调节形成等效球铰、虎克铰以及转动副。与传统的锁定运动副来实现变胞功能的变胞单元相比,此变胞单元三种构型的切换只需对轴线位置调整,无需额外增加关节锁死电机。通过研究由线矢量构成的螺旋系统的相关性,揭示了变胞运动单元构态变化的基本原理。提出了可用于构造新型变胞并联机构的支链构型设计方法,并基于螺旋的互易性分析了各支链构型所必须满足的几何约束条件。提出了两种变胞并联机构,通过不同的支链装配形式可将其从6自由度构型转换为3自由度构型,并对支链安装形式进行改进,构造出了具有3自由度平移模式和3自由度转动模式的并联机构。对变胞支链作为中心支链组装而成的并联机构的构型及对应的运动类型进行了分析,获得了六种不同构型的并联机构。     

DYNAMIC MODELING OF METAMORPHIC MECHANISM

The concept of metamorphic mechanism is put forward according to the change of configurations from one state to another. Different configurations of metamorphic mechanism are described through the method of Huston lower body arrays. Kinematics analyses for metamorphic mechanism with generalized topological structure, including the velocity, angular velocity, acceleration and angular acceleration, are given. Dynamic equations for an arbitrary configuration, including close-loop constraints, are formed by using Kane's equations. For an arbitrary metamorphic mechanism, the transformation matrix of generalized speeds between configuration ζ and ζ+1 is obtained for the first time. Furthermore, configuration-complete dynamic modeling of metamorphic mechanism including all configurations is completely established.     

Analysis for a planar 3 degree-of-freedom parallel mechanism with actively adjustable stiffness characteristics

A planar three degree-of-freedom parallel manipulator has been extensively studied as the fundamental example of general parallel manipulators. It is proven from previous work (Kim, et. al., 1996) that when three identical joint compliances are attached to the three base joints of the mechanism in its symmetric configurations, this mechanism possesses a completely decoupled compliance characteristic at the object space, which is the important operational requirement for an RCC device. In this work, we are concerned with the adjustability of the output compliance matrix of this mechanism, by employing redundancy on either joint compliances or on actuators. Two approaches are suggested to achieve this purpose. In the first approach, the stiffness modulation is achieved through purely redundant passive springs or decoupled feedback stiffness gains. In the second approach, stiffness modulation is achieved through antagonistic actuation of the system actuators. General stiffness models are derived for both cases. Based on these stiffness models, stiffness modulation algorithms are formulated. The capability of actively adjustable stiffness will be very effective in several robotic applications.     

具有关节柔性和臂柔性的机器人操作受限物体的动力学建模

针对具有柔性关节和柔性臂的机器人操作受作业环境约束这种情况,基于绝对坐标建立了系统的动力学模型。根据物体与作业环境的约束关系,推导出系统的正动力学模型。以期望的被操作物体的轨迹和所期望的物体与环境的作用力为边界条件,推导出了系统的逆动力学模型。对于给定的任务,所提出的逆动力学模型可求出柔性机器人的理想输入。而所提出的正动力学模型可用于数值仿真。通过对具有三柔性关节和三柔性臂的机器人臂进行仿真,验证了该方法的有效性。     

Synthesis of a mechanism for the stabilisation of a radar antennaSynthèse d'un mécanisme pour la stabilisation d'une antenne de radar

A mechanism designed to stabilise radar antennae on sea-going vessels is analysed geometrically and equations derived which relate the mechanism parameters with the vessel attitude. The analysis is developed to give a method by which configurations of the mechanism may be selected which are compatible with the maximum pitch and roll of the vessel. Further development of the analysis yields a method of synthesis which enables desired kinematic conditions to be achieved. Examples of compatibility and of synthesis are given.     

Joint reactions in rigid body mechanisms with dependent constraints

The problem of calculating joint reaction forces in rigid body mechanisms with dependent constraints is discussed. Two essentially different reasons of constraint dependency are considered: the existence of redundant constraints and singular configuration of the mechanism. It is known that if constraint equations are dependent, the constraint reaction forces cannot be uniquely determined. In this paper it is shown that despite the fact that all of the constraint reactions cannot be uniquely determined, selected single constraint reactions or selected groups of reactions can be specified uniquely. Conditions, which must be fulfilled to obtain unique values of selected reaction forces in the presence of dependent constraints, are presented and proven. The concept of direct sum, known from linear algebra, is exploited. These purely mathematical conditions form a basis for numerical methods that enable detection of constraints with uniquely solvable reactions. Three different numerical methods are proposed. These methods are confined to constraint Jacobian matrix analysis, thus they can be easily implemented in a multibody software. Finally, two examples of detection of constraints with uniquely solvable reactions are presented.     

On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints

The uniqueness of simulated motion of an overconstrained rigid body mechanism with joint friction is studied. The investigated issue originates in the problem of joint reactions solvability. It is known that in case of redundant constraints existence the constraint reaction forces cannot be — in general — uniquely determined. It can be proved, however, that — under certain conditions — selected reactions can be specified uniquely. Analytical and numerical methods for reactions solvability analysis are available. It is shown in this paper that indeterminacy of normal reactions results in indeterminacy of friction forces, and moreover, non-uniqueness of friction forces results in non-uniqueness of simulated motion. A method of finding these joints, for which friction forces are unique, is presented. It is also proved that if only uniquely solvable friction effects are introduced, then simulated motion of the mechanism is unique, otherwise it is not. Finally, examples of dynamic analysis of overconstrained mechanisms with joint friction are presented; unique and non-unique results are obtained.     

驱动支链完全解耦的可重构踝关节康复并联机构型综合

基于术后6～12周内的前、中、后期踝关节扭伤的康复运动需求,提出具有三种康复运动模式的可重构踝关节康复并联机构。首先,针对胫距关节和距下关节的轴线运动特征,研究踝关节康复运动切换机理和“双心”特性,提出符合踝关节自由度和轴线运动特性的六种融合支链;根据构型约束支链的选取方案,筛选出四种无约束支链。其次,基于旋量理论对六种融合支链进行过约束设计,验证符合实际需求的融合支链;根据传递力旋量与动平台运动轴线关系,提出一种驱动支链完全解耦优化方法,得到三种无约束驱动支链以及十二种机构构型,使得机构在三种康复模式中实现完全解耦。最后,通过ADAMS仿真验证机构的三种运动分支及完全解耦的正确性。可重构踝关节康复机器人依据患者康复需求采取对应康复模式,适用范围广,针对性强,控制简单。     

Synthesis and stiffness modeling of XYZ flexure parallel mechanisms with large-motion and decoupled kinematic structure

This paper systematically studies structure synthesis and dimension optimization of XYZ flexure parallel mechanisms (FPMs) with large-motion and decoupled kinematic structure. Different from structure synthesis of rigid-body mechanisms, structure synthesis of flexure mechanisms is constrained by the limitations inherent in flexure mechanisms. These limitations are investigated and summarized as the structure constraints. With consideration of these structure constraints, the configurations of the decoupled XYZ-FPMs are synthesized using the Screw Theory. The synthesized XYZ-FPMs also possess large motion range, due to integration of a new type of large-motion prismatic joint designed in this paper. The stiffness models of the synthesized XYZ-FPMs are formulated. A 3-PPP XYZFPM is developed as the case of the studies of structure synthesis and stiffness modeling.     

Analysis of a planar 3 degree-of-freedom adjustable compliance mechanism

In this work, a planar three degree-of-freedom parallel mechanism as another type of assembly device which utilizes joint compliances is proposed. In order to generate the desired operational compliance characteristics at RCC point, these joint compliances can be adjusted either by properly replacing the joint compliances or by actively controlling stiffness at joints. The operational compliance matrix for this mechanism is obtained explicitly by symbolic manipulation, and its operational compliance characteristics are examined. It is found that the RCC point exists at the center of the workspace when the mechanism maintains symmetric configurations. Compliance characteristics and its sensitivity of this mechanism are analyzed with respect to the magnitude of the diagonal compliance components and two different matrix norms by measuring compliance sensitivity. It is expected that the analysis results provide the designer with a helpful information to determine a set of optimal parameters of this RCC mechanism.     

空间两弹簧系统的力逆解

讨论了空间两弹簧系统的力逆解问题。空间两弹簧系统是由两根弹簧并行地将空间一点（即两根弹簧的公共球铰中心）与固定平台相联而成,这两根弹簧分别通过转动副和球副与固定平台相联。其力逆解即对于给定的公共球铰中心所作用外力,求解该系统处于静力平衡时的所有构形。文中建立了该系统的力逆解方程组,并用连续法对其进行了求解。算例表明该空间两弹簧系统的力逆解最多具有１０组解。     

面向在轨装配的八索并联机构构型设计与工作空间分析

针对大型空间结构的在轨装配任务,提出了由八根绳索驱动的索并联机构,具有结构简单、质量轻、工作空间大的特点;针对绳索并联机构的构型综合问题,定义了出线点和绳索与中心执行器连接点的关联矩阵,在此基础上考虑约束条件综合出了八索并联机构的18种有效构型;计算了不同构型的力封闭工作空间以及针对在轨装配任务时的力螺旋可行工作空间,以工作空间体积为指标筛选出了最佳构型;分析了绳索拉力范围以及绳索与中心执行器连接点的位置变化对机构力螺旋可行工作空间的影响,并且对连接点的位置参数进行了优化。     

A multilevel calibration technique for an industrial robot with parallelogram mechanism

This paper presents a multilevel calibration technique for improving the absolute accuracy of an industrial robot with a parallelogram mechanism (ABB IRB2400). The parallelogram structural error is firstly modeled based on the partial differential of the position function of a general four-bar linkage and the linearization of the position constraints of the parallelogram mechanism, the model coefficients are fitted from experimental data. Secondly, an absolute kinematic calibration model is established and resolved as a linear function of all the kinematic parameters, as well as the base frame parameters and tool parameters. Finally, contrary to most other similar works, the robot joint space (rather than Cartesian space) is divided into a sequence of fan-shaped cells in order to compensate the non-geometric errors, the positioning errors on the grid points are measured and stored for the error compensation on the target points. After the multilevel calibration, the maximum/mean point positioning errors on 284 tested configurations (evenly distributed in the robot common workspace) are reduced from 1.583/0.420 mm to 0.172/0.066 mm respectively, which is almost the same level as the robot bidirectional repeatability.     

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a...     

Topology and kinematic analysis of color-changing ball

The color-changing ball has two stable configurations. Its mechanism is a multiple loop and polygonal mechanism. This paper investigates the mechanism typology and analyzes its structure and configurations during motion. A three-legged mechanism is extracted from this mechanism. The kinematics model of the mechanism is presented and singularity is discussed. The paper further decomposes the mechanism and investigates the platform structure of the intersection between loops. This leads to investigation of the offset of joint intersection at the intersection and its relevant geometry and kinematics. The paper further focuses on the configuration change between two states of the mechanism and investigates kinematics and singularity between two configurations. Based on the analysis, simulation of the color-changing ball is carried out. The topology and kinematics analysis in this paper helps the analysis of this kind of polyhedral linkage mechanism with radial motion. The research could potentially lead to the development of kinematics for design of this kind of mechanism.     

Dimensional synthesis of a novel 5-DOF reconfigurable hybrid perfusion manipulator for large-scale spherical honeycomb perfusion

A novel hybrid perfusion manipulator (HPM) with five degrees of freedom (DOFs) is introduced by combining the 5PUS-PRPU (P, R, U, and S represent prismatic, revolute, universal, and spherical joint, respectively) parallel mechanism with the 5PRR reconfigurable base to enhance the perfusion efficiency of the large-scale spherical honeycomb thermal protection layer. This study mainly presents the dimensional synthesis of the proposed HPM. First, the inverse kinematics, including the analytic expression of the rotation angles of the U joint in the PUS limb, is obtained, and mobility analysis is conducted based on screw theory. The Jacobian matrix of 5PUS-PRPU is also determined with screw theory and used for the establishment of the objective function. Second, a global and comprehensive objective function (GCOF) is proposed to represent the Jacobian matrix’s condition number. With the genetic algorithm, dimensional synthesis is conducted by minimizing GCOF subject to the given variable constraints. The values of the designed variables corresponding to different configurations of the reconfigurable base are then obtained. Lastly, the optimal structure parameters of the proposed 5-DOF HPM are determined. Results show that the HPM with the optimized parameters has an enlarged orientation workspace, and the maximum angle of the reconfigurable base is decreased, which is conducive to improving the overall stiffness of HPM.     

ADAMS约束问题讨论

机构存在冗余约束时,ADAMS会在计算时自动解除一些约束,从而使被解除约束的自由度上不会计算构件间的作用力.冗余约束应在进行动力学分析前被手动解除,以获得更精确的结果数据.     

Optimal trajectory generation for biped robots walking up-and-down stairs

This paper proposes an optimal trajectory generation method for biped robots for walking up-and-down stairs using a Real-Coded Genetic Algorithm (RCGA). The RCGA is most effective in minimizing the total consumption energy of a multi-dof biped robot. Each joint angle trajectory is defined as a 4-th order polynomial of which the coefficients are chromosomes or design variables to approximate the walking gait. Constraints are divided into equalities and inequalities. First, equality constraints consist of initial conditions and repeatability conditions with respect to each joint angle and angular velocity at the start and end of a stride period. Next, inequality constraints include collision prevention conditions of a swing leg, singular prevention conditions, and stability conditions. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot model that consists of seven links in the sagittal plane. The optimal trajectory is more efficient than that generated by the Modified Gravity-Compensated Inverted Pendulum Mode (MGCIPM). And various trajectories generated by the proposed GA method are analyzed from the viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.     

基于运动精度可靠性的平面四杆机构优化设计

以具有杆长尺寸和铰链间隙误差的平面四杆机构为对象 ,运用微小位移线性迭加原理 ,对机构的输出运动误差进行了可靠性分析 ;建立了以杆长误差和铰链间隙的均方差为设计变量 ,满足运动精度可靠度和设计变量上下限要求为约束条件 ,使机构制造加工费用极小化为目标函数的优化设计数学模型 ;利用外点法和 Powell方向加速法求解 ,获得了令人满意的设计结果