A complex solution framework for the kinetostatic synthesis of a compliant four-bar mechanism

This paper presents a systematic solution framework for the kinetostatic synthesis of compliant four-bar mechanisms. The goal of the kinetostatic synthesis is to find feasible compliant mechanism solutions for a given set of kinematic and force/energy specifications. Similar to the synthesis of rigid body linkages, we first classify kinetostatic synthesis problems into three major categories: function, motion and path generations. The kinetostatic synthesis equations are derived by combining the kinematic synthesis and static equilibrium equations. We then propose a comprehensive framework based on polynomial solvers for obtaining solutions to these synthesis equations. When kinematic and static equations are decoupled, we solve first kinematic equations independently and then solve static equations for springs' stiffness. While they are coupled, we transform them into a polynomial form and solve them simultaneously with polynomial solvers. For this case a parameter continuation is devised to avoid computing for the junk solutions. At last, three representative examples are provided to demonstrate the solution process and verify the solution framework.     

全方位六足步行机的运动设计

本文对六足步行机的全方位运动步态进行了探讨, 提出了基于静态稳定性考虑的最佳步态的选择方案.就横向运动六足步行机的广义三角步态, 分析了其静态稳定裕量、爬坡能力、越沟能力等运动性能, 并给出了采用广义三角步态的横向运动六足步行机总体几何参数CAD的实例.     

Analytical study of the stability of a two-ball automatic balancer

A ball-type automatic balancer, which consists of several balls moving on a circular orbit, can effectively reduce the imbalance vibrations of an optical-disk drive. Under proper working conditions, the balls can counter-balance the imbalance of a disk by positioning the appropriate angles relative to the mass center of the disk. These particular positions are referred to as the perfect balancing positions. The proper working conditions depend on the stability of the perfect balancing positions. Much work has been done to determine the stability of the equilibrium positions numerically for some specific values of the system parameters. This paper, in contrast, analytically studies the stability characteristics of the equilibrium positions under several conditions. A theoretical model of an optical-disk drive packed with a two-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange's equations. The closed-form formulae and the existence conditions for the equilibrium positions are presented. Experiments are conducted to verify the theoretical model. The stability of each equilibrium position is determined by Routh's criterion. Finally, general guidelines on the stability of the equilibrium positions are proposed.     

Maximum load for toruslike shells

Maximum loads for toruslike shells with constant thickness loaded with an axial force, internal pressure, and a bending torque are calculated. The rigid plastic body model, the Tresca yield condition, and the plastic yield law associated with it are used. Application of the finite element method for calculation of the maximum load on a shell is considered. A significant increase in the characteristic deformation of a shell is used as a criterion. The corresponding formulas for maximum loads are obtained based on the kinematic method of the limit equilibrium theory. The difference between the obtained results and the static solution does not exceed 3%.     

基于虚拟样机技术和灵敏度分析的地面火炮射击稳定性优化研究

传统的火炮设计和分析均基于“平面、对称和静平衡”三个基本假设,实际上是一种静态的分析方法,尽管在工程实践中引入了多种经验符合系数,但是火炮分析结果和试验的一致程度不能令人满意。这是因为火炮的射击过程是一个动力学过程,需要采用动力学分析方法。虚拟样机技术的出现为火炮射击稳定性研究提供了新的方法,文中在建立火炮动力学模型的基础上,通过选取火炮结构参数对火炮射击稳定性进行研究,利用虚拟样机分析高低机刚度和阻尼、大架刚度和阻尼、土壤介质刚度和阻尼、后坐质量偏心和耳轴位置偏心对火炮射击稳定性的影响。通过引入改进的相对灵敏度分析公式,解决具有不同量纲的影响因素的比较问题,进而确定影响火炮射击稳定性的重要结构参数。针对目前优化技术存在的局限性,以火炮射击稳定性为目标,采用优化子空间的逐层优化方法对火炮射击稳定性进行研究,找到一组使火炮稳定性最优的结构参数,证明虚拟样机技术对火炮系统动态特性仿真的可行性和优越性。最后,展望了虚拟样机技术在武器装备领域应用的前景。     

移动型3-UPU并联机构静态稳定性分析

使用最小势能原理,对刚性支撑3-UPU并联机构进行了静态稳定性分析。稳定性分析中,将并联机构的连杆分解为包含油液在内的三部分,通过建立并联机构的Lagrange势能函数,得到反映机构静态稳定性的Hessian矩阵,并由此提出了机构不同稳定性状态的比较判据。分析和计算表明,在工作空间中,移动型3-UPU并联机构在由几何构型所确定的工作空间中的静平衡基本上稳定。     

A novel methodology to study the singularity of spatial parallel mechanisms

In this paper, a novel methodology to study the singularity of spatial parallel mechanisms is presented. With the theory of reciprocal screws, we make a thorough analysis of the kinematic screws of each branch mechanism. According to the physical meaning of the inverse screws of kinematic screws, we introduce the static equilibrium equations to gain a novel methodology to study the singularities of the dynamic mechanisms. Through the novel methodology, we obtain universal criteria that the mechanism will be singular.     

Optimization of a quasi-zero-stiffness isolator

The frequency range over which a mount can isolate a mass from a vibrating base (or vice versa) is often limited by the mount stiffness required to support the weight of the mass. This compromise can be made more favourable by employing non-linear mounts with a softening spring characteristic such that small excursions about the static equilibrium position result in small dynamic spring forces and a correspondingly low natural frequency. This paper concerns the force-displacement characteristic of a so-called quasi-zero-stiffness (QZS) mechanism which is characterised by an appreciable static stiffness but very small (theoretically zero) dynamic stiffness. The mechanism studied comprises a vertical spring acting in parallel with two further springs which, when inclined at an appropriate angle to the vertical, produce a cancelling negative stiffness effect. Analysis of the system shows that a QZS characteristic can be obtained if the system’s parameters (angle of inclination and ratio of spring stiffnesses) are opportunely chosen. By introducing the additional criterion that the displacement of the system be largest without exceeding a desired (low) value of stiffness an optimal set of parameter values is derived. Under sufficiently large displacements the stiffness of the QZS mechanism can eventually exceed that of the simple mass-spring system and criteria for this detrimental scenario to arise are presented.     

Synchronous Group Operation of Robots with Arbitrary Manipulator Kinematics

Russian Engineering Research - When an object is being transported by two robots of arbitrary structure, it must be stabilized around the static equilibrium position in the event of kinematic and...     

A sequentially-defined stiffness model of the knee

A new procedure is proposed to obtain a stiffness model of the knee, i.e. a model of the joint when static external loads are applied to the tibia and femur. A sequential approach is used to generalise a kinematic model of the passive motion of the articulation previously presented by the authors. The procedure is devised in such a way that the restraining function of the articular components which guide the passive motion of the joint is preserved after generalisation. As a result, the new stiffness model can replicate the passive motion with the same accuracy as the previous kinematic model, and it can also replicate the relative motion of the tibia and femur when the knee is loaded by static external loads. The proposed procedure is applied to a specimen and the relevant stiffness model is devised. The motion of the model under several loading conditions is then compared with the original motion of the specimen and with data obtained from the literature, in order to show the accuracy of the model and the potential of the proposed procedure.     

A consistent approach to linear stability of thin-walled beams of open section

This paper presents a stability criterion for thin-walled beams of curvilinear section, based on the positive definiteness of the second variation of the potential energy. The internal stresses are derived according to a shell model which incorporates the kinematic restraints of thin-walled beams. In addition to the classical terms of the potential energy, the geometric effects of an applied torque, as well as flexural-extensional and torsional-extensional coupling terms, are accounted for.     

Static and kinematic limit analysis of orthotropic strain-hardening pressure vessels involving large deformation

This paper analytically investigates plastic limit pressure of orthotropic strain-hardening cylindrical vessels under internal pressure. It is an interesting problem to illustrate the interaction between strengthening and weakening behavior during the deformation process. The Voce hardening law and Hill's yield criterion were adopted in the paper. A sequence of static and kinematic limit analysis problems were performed by updating the yield criterion and the deformed configuration. The equality relation between the greatest lower bound and the least upper bound was confirmed explicitly. Accordingly, exact solutions of plastic limit pressure were developed with an integral term. Particularly, exact closed-form solutions were obtained for certain values of the hardening exponent of the Voce hardening law. Finally, numerical efforts were also made for rigorous validations.     

弹性曲柄滑块机构的运动精度可靠性分析

将弹性曲柄滑块机构的杆长、截面尺寸、铰链间隙、质量密度、弹性模量等几何、物理参数均视为随机变量,对机构输出运动进行了静态和动态误差分析。应用微小位移的线性叠加原理分别对静态、动态误差进行了综合,建立了机构输出运动精度可靠性分析模型。通过算例,考察了机构输出运动精度可靠度的影响因素,结果表明随着机构转速的提高,机构的动态弹性变形将成为影响机构运动精度可靠性的主要因素。     

用拓扑特性矩阵辨识运动链的同构体及机架变换研究

基于运动链的基本环路及环路中构件、运动副的互相连接关系，建立了描述平面和空间运动链及机构的拓扑特性矩阵，对平面、空间运动链及机构的同构体辨识问题进行了研究。由于拓扑特性矩阵较常用于同构体辨识的邻接矩阵、关联矩阵等矩阵的元素少，而且可以通过比较拓扑特性矩阵的对应行列的元素直接进行同构体的辨识，因此，应用拓扑特性矩阵辨识同构体是更简便和高效的。给出了应用拓扑特性矩阵辨识同构体的方法、步骤及流程图，并给出了较典型的辨识例子（包括空间运动链），证明了该方法的正确性和高效性。同时还应用拓扑特性矩阵对运动链的机架变换问题进行了研究。     

Computer method for kinematic analysis of lower-pair mechanisms—II position problemsEine neue methode zur analyse von mechanismen teil 2: Positionsprobleme

In the first part of this study, a new method for solving the problem of kinematic analysis was presented, based on the concepts of “basic coordinates” and “link constraint equations”. In this second part, these same concepts are used to solve the problems of initial position, finite displacements and static equilibrium position of a mechanism with springs between its links. The proposed algorithms are elementary in their formulation and of exceptional efficiency in their performance. The methods describes are based on the solution of a problem of mathematical programming. Several examples are presented, giving an idea of the potential of said algorithms.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

Kinetostatic modelling of a 3-PRR planar compliant parallel manipulator with flexure pivots

Flexure pivots are widely used in long stroke complaint parallel manipulators (CPMs) for their large deformation capacity. However the parasitic motion caused by the flexure pivots cannot be neglected as the rotation angle gets large, which will finally affect the absolute positioning accuracy of the manipulators. In this paper, a modelling approach to calculate the nonlinear kinetostatics of a long stroke planar CPM with flexure pivots is proposed, in which the parasitic motion of the flexure joints are taken into account. The displacement constraint equations and the static equilibrium equations of the CPM are established under the deformed configuration. Finite element analysis (FEA) shows the accuracy and efficiency of the nonlinear kinematic model (NLKM) for both the inverse and forward kinematic analysis. Moreover, the prediction accuracy of the CPM’s kinematic behavior has been improved more than 20 times by employing the NLKM compared with the conventional kinematic model (CKM).     

摆线齿轮连杆机构的函数综合

应用复数法给出了摆线（内摆线和外摆线）齿轮连杆机构的函数综合方程，并用连续（同伦）法进行求解，它不需要选取初值就可求出全部解。最后本文给出了数值实例，求出了满足给定设计要求的全部机构，并给出了这些机构的图形显示，通过对它们进行运动分析，以从中优选设计方案。     

Kinetostatic modeling and analysis of an exechon parallel kinematic machine(PKM) module

As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton’s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system’s deflections. The platform’s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.     

双摇杆假肢膝关节的运动学与动力学分析

膝关节是人体正常运动的重要部位.为了满足下肢截肢患者恢复正常运动功能的需求,设计了一款双摇杆机构的假肢膝关节.首先,建立了下假肢的简化模型,通过对模型的运动学分析,获得了相关关节角度、角速度、角加速度等参数.通过动态静力分析法对双摇杆的各个杆件进行动力学分析,最终得到输出阻尼力与驱动力矩之间的平衡方程.通过Adams仿...