Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.     

隔振对象重量变化对准零刚度隔振器隔振性能的影响

本文主要研究隔振对象重量变化对一类准零刚度隔振器隔振性能的影响,并给出了新的研究结果.文中使用欧拉屈曲梁构建负刚度调节结构并设计了隔振系统的平衡位置可调机构.假设系统有轻微的过载和超载,推导了系统的动力学方程并进行求解,定义了非线性隔振系统的力传递率及位移传递率来评价系统的隔振性能.对线性隔振系统,超载会让隔振频率略微降低,共振放大峰略微增大.对于准零刚度隔振系统,力传递率和线性系统类似,但是对于位移传递率,过载会导致系统固有频率和共振放大峰均升高,反而不利于隔振.研究结果可以对此类隔振系统的使用场合以及对过载和轻载的选择有工程指导意义.     

分段阻尼隔振系统的动力学特性分析

针对传统线性隔振器在降低共振峰值的同时会牺牲隔振性能的矛盾,设计了一种含分段阻尼的隔振器.首先,采用移动凸轮变阻尼装置,通过凸轮廓线的设计使系统的垂向阻尼系数的受振动位移大小控制并呈现分段线性特征,分析了该装置的阻尼特性.然后将分段阻尼装置应用于隔振器中,建立了含分段阻尼的积极隔振系统模型及其动力学方程,通过能量等效原理求出了分段阻尼系统的等效线性阻尼系数,求解了简谐力激励下系统响应的理论解,并用四阶龙格-库塔法数值仿真验证了理论解的正确性.最后研究了分段阻尼隔振系统的动态特性,分析了主要参数对幅频响应特性与力传递率特性的影响.结果表明,通过合理的参数选择,分段阻尼隔振器可兼顾无阻尼隔振器与线性阻尼隔振器的优点,既能有效降低系统的共振峰值,又能保证高频区域的优秀隔振性能,为新型非线性隔振器的设计提供了理论依据.     

一种基于电磁—空气弹簧的非线性隔振器理论与实验研究

本文提出一种主要由空气弹簧和永磁体所组成的具有准零刚度特性的非线性隔振器.首先,通过分析空气弹簧和磁体的受力特性,建立隔振器力-位移关系和刚度-位移关系,揭示隔振器静态力学特性,并分析隔振器参数对系统刚度的影响规律.然后,采用谐波平衡法计算隔振器力传递率特性.结果表明,通过在适当范围内调节系统阻尼比或激励幅值,所提出的非线性隔振器在隔振频率范围内优于普通空气弹簧隔振器.最后,通过实验验证隔振器的隔振性能.该研究可为小振幅甚至微振动系统的振动隔离提供新的参考.     

低频大幅隔振器设计及实验

为了突破传统隔振器刚度和承载能力之间的矛盾,需要隔振器具有高的静态刚度,低动态刚度的特性.如今的准零刚度隔振器技术可以实现低频微幅隔振,但是对于大幅振动,隔振效果并不明显甚至失效,因此突破宽幅隔振成为隔振领域亟待解决的问题.为此,我们利用多稳态折纸通过并联装配的方式,构造具有宽幅零刚度区间的折纸型隔振器,以解决传统隔振器振动抑制幅值较低的问题.本文建立了宽零刚度隔振器模型,提出宽幅零刚度的设计方法,并通过动力学分析分析了模型的隔振效果.最后搭建试验样机,验证了理论的正确性.这种设计打破了传统准零刚度隔振器单点准零的设计准则,能够在一个大幅范围内保证稳定性,同时实现零刚度,极大拓宽了隔振器的适用范围.这种设计理念能够被用在新隔振材料设计和航空、船舶等大幅低频动态环境中.     

A novel active vibration isolator applied for micro-gyro by array of deposited electrodes

Micro-gyroscopes are usually driven into resonance so that the sensitivity and resolution can be enhanced. However, if any substantial vibration of the gyroscope base, over which the seismic proof mass is seated, was present, then the preset resonant frequency would be altered and the performances of the gyroscopes could be much degraded. In this paper, an innovative three degree-of-freedom (DOF) isolation system is proposed to attenuate the undesirable vibrations caused by the ambient environments. The mathematic model of the proposed 3-DOF micro-machined isolation system is established and analyzed such that the transfer function of transmissibility is obtained. The pull-in instability and associated pull-in voltage for the actuators of the isolation system are numerically unveiled so that the interval of the applied voltage to generate the electrostatic control force can be set to ensure the stability of the suspension system. In addition, a fuzzy logic proportion and derivative (PD) controller is synthesized for disturbance rejection. Five sensing electrodes, in cooperation with the isolator, are used to provide the feedback signals of the relative displacements of the proof mass with respect to the base, i.e., pitch, yaw and lateral linear displacement. Ten tuning electrodes are utilized to generate the required electrostatic forces to preserve the seismic proof mass from external disturbance. In comparison with the traditional PD action, the proposed fuzzy logic PD control strategy is verified by intensive simulations to illustrate its superior vibration isolation capability.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

Research on the inertia matching of the Stewart parallel manipulator

With the development of the parallel manipulator, inertia matching as an essential factor to realize good potentials of the parallel manipulator is taken serious gradually. However, neither definite inertia index nor inertia matching method has been proposed so far. In this paper, the above issues are discussed by taking the Stewart parallel manipulator as a study object. Firstly, adopting limb Jacobian matrices, the concise algebraic expression of the joint–space inertia matrix of the Stewart parallel manipulator is deduced, based on the dynamic modeling. Next, on the basis of the coupling analysis of the joint–space inertia matrix, the inertia index of the parallel manipulator, the Joint-Reflected Inertia, is proposed. Then, the practical inertia matching principles of the Stewart parallel manipulator are concluded on the basis of simulations, considering multiple factors, such as mechanical resonance frequency, acceleration torque and dynamic performance. Finally, the available range of the motor inertia is deduced, and the inertia matching of the Stewart parallel manipulator is finished as the case study. The inertia index and inertia matching method suggested in this paper can be further used in other parallel manipulators for dynamic analysis and motion system design.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

TriM: An Ultra-Accurate High-Speed Six Degree-of-Freedom Manipulator Using Planar Stepper Motors

In this paper, we propose a novel six degree-of-freedom positioning system. This mechanism is a tripod structure with inextensible limbs actuated at the base by two-dimensional linear stepper motors (other types of actuators may also be utilized). This manipulator has a closed-chain kinematic structure. Both the direct and the inverse kinematics of the manipulator are presented in detail. While the inverse kinematics are obtained in closed form, the direct kinematics can not be solved in closed form and an algorithm is provided for numerically computing the direct kinematic solution. A detailed dynamic model of the positioning system is also provided. The dynamics of the actuators (Sawyer motors) are also included in the dynamic modeling. The design of the tripod manipulator (TriM) included a kinematic optimization of the system parameters to maximize the manipulator workspace. The proposed manipulator achieves large range of motion in all the 6 degrees of freedom. Furthermore, high resolution and high speed motion may be achieved in all axes due to the actuators used and the direct-drive nature of the manipulator. This work was supported in part by NSF under grants ECS-9977693 and ECS-0501539. An earlier version of this paper was presented at the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, Oct. 2003.     

仿生隔振器设计方法研究进展

基于仿生学的思想,通过模仿生物系统的结构几何构成特性,创新优化隔振模型是当今隔振领域的热门问题.本文基于仿生灵感来源的不同,对现有的仿生隔振器进行了系统的分类,并对不同设计原理的仿生隔振器恢复力本构与隔振性能做了详细的阐述和对比,旨在通过隔振器隔振频带的横向对比厘清几何构型与可调参数的影响,以此厘清隔振器几何设计和隔振性能的关系.并且,本文展望了未来仿生隔振器的发展前景和研究方向.     

Kinematics,dynamics and dimensional synthesis of a novel 2-DoF translational manipulator

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. In this paper, a novel 2-degree-of-freedom (DoF) parallel manipulator, which has two translational DoFs, is proposed. It is characterized by the fact that the output of the manipulator is two planar DoFs of a rigid body, while its orientation remains constant. The inverse and forward kinematics can be described in closed form. The velocity equation, singularity, and workspace of the manipulator are presented. In addition the inverse dynamics problem of the device is investigated employing the Lagrange multipliers approach. The dimensional synthesis based on the workspace and conditioning indices is presented. The proposed manipulator can be applied to the field of machine tools or used as the mobile base for a spatial manipulator. The results of the paper are very useful for the design and application of the new manipulator.     

消隔组合X型减振器设计与动力学分析

本文将一种X型结构与线性弹簧阻尼减振器相结合构成一种兼具消振和隔振性能的新型X型减振器.基于拉格朗日方法建立单自由度线性振子耦合消隔组合X型减振器系统的动力学方程,应用谐波平衡法得到系统稳态响应的近似解析解,并通过Runge Kutta法得到系统的数值解验证解析解的正确性.讨论了不同的基础激励下新型X型减振器对系统的响应幅值以及位移传递率的减振效果.此外,分析了不同参数对系统的幅频响应曲线以及位移传递率的影响.研究结果表明,新型X型减振器不仅可以将线性刚度转化为非线性刚度,还可以为系统提供负刚度,拥有优秀的消振和超低频隔振性能.     

舰船概念设计中振动预报方法

以带有双层隔振装置的舰船模型为对象,利用MSC Nastran的有限元分析方法以及试验手段,对其隔振性能进行研究.将船体与双层隔振装置作为一个系统,建立三维有限元振动分析模型;以降低船体结构振动能量为目标,对发动机激励作用下的双层隔振装置与船体的振动特性进行分析;通过有限元分析方法和试验两方面的研究与对比,为舰船的减振降噪的初期概念设计提供快速预报方法.     

双层混合隔振系统隔振效果评价与实验研究

为了对双层混合隔振系统进行全面评价,提出了一种全新的双层混合隔振系统隔振效果评价方法.该方法将混合隔振的评价指标定义为被动隔振指标与主动隔振指标之和,并在自行研制的磁悬浮隔振器上进行隔振实验.实验结果表明,该评价方法简便易行,能够准确地反映被动和主动隔振对不同频段隔振的贡献以及两者之间的相互影响,为进一步优化双层混合隔振器的设计提供了可靠依据.     

Inverse dynamic analysis and simulation of a platform type of robot

This article presents an algorithm to solve the inverse dynamics for platform type of manipulators using Newton-Euler equations of motion. We found that the inverse dynamics of the system is governed by thirty-six linear equations. The number of these simultaneous equations can be reduced to six, if a proper sequence is taken. The relationships between the actuating forces and the shape of the structure are analyzed. Based on the algorithm, computer code for simulation was developed. Three cases were studied. As a result, configurations which minimize the actuating forces are suggested. It is also found that the fluctuation of the driving forces is lesser when the path is closer to the center of the base. These results are believed to be useful in the design and control of this type of manipulating devices.     

Shock and vibration isolation of laptop hard disk drive using rubber mount

Hard disk drives (HDDs) in laptop personal computers (PCs) are subject to impact-induced failure, as well as to operational vibrations. Elastic mounts with cushioning materials are often used to minimize the likelihood of failure in such cases. In this paper, we analyze the dynamic characteristics and shock response of the vibration isolation systems supporting HDDs. Anti-vibration performance is investigated via position error signal and acceleration transmissibility. Shock response is obtained from a lumped parameter model, based on the nonlinearity of the rubber mounts. Based on the results, we propose guidelines for shock and vibration isolation systems, including a dual rubber mount design.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

一类非线性隔振器振动传递特性分析

非线性输出频率响应函数是由Volterra级数发展而来的一个新概念.对一类具有反对称阻尼特性的隔振器,通过该概念推导出了振动传递性与系统非线性参数之间的显式解析关系；进而系统地研究了非线性阻尼参数对隔振器的力传递性能和位移传递性能的影响.研究结果表明,虽然非线性隔振器在受正弦信号激励下会出现高次倍频分量,但对于其传递性...     

Dynamic Modeling and Inverse Optimal PID with Feed-forward Control in <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Framework for a Novel 3D Pantograph Manipulator

This paper affords dynamic modeling and control for a new 3D pantograph manipulator. The new manipulator possesses pure decoupled translational motions and it is characterized by large workspace to size ratio, high speed, rigidity, and accuracy. Euler-Lagrange first type method is used to get the dynamic model. However, the resulted dynamic model is too complex to be used in model-based control techniques. Therefore, a simplified nominal plant is proposed. It allows the inverse dynamic solution efficiently. However, an explicit form of the nominal Coriolis and centrifugal matrix cannot be obtained due to the complicated kinematic terms. Considering these dynamic characteristics as well as the required robust trajectory tracking performance of the manipulator, a new controller is proposed. The new controller is called inverse optimal PID with Feed-Forward Control which is designed in H_∞ framework. The new controller has the following merits; robustness, optimality, simple implementation, and efficient execution without the need of explicit forms of dynamic matrices. The extended disturbance in the proposed controller is smaller than that in the inverse optimal PID control (IPID) and contains one type of error contrary to the nonlinear robust motion controller (NRIC). The performance of the proposed controller is compared with those of IPID and NRIC controllers for different trajectories and payloads. The dynamic simulation results via co-simulation of MSC-ADAMS® and MATLAB®/Simulink software prove the robustness of the proposed controller against speed/payload variations. The proposed controller is found to have higher performance compared with IPID and NRIC controllers. These results assure the feasibility of the 3D pantograph manipulator with the proposed controller for pure translational tracking applications.