Configuration and Kinematics of a 3-DOF Generalized Spherical Parallel Mechanism for Ankle Rehabilitation

The kinematic equivalent model of an existing ankle-rehabilitation robot is inconsistent with the anatomical structure of the human ankle,which influences the rehabilitation effect.Therefore,this study equates the human ankle to the UR model and proposes a novel three degrees of freedom(3-DOF)generalized spherical parallel mechanism for ankle rehabilitation.The parallel mechanism has two spherical centers corresponding to the rotation centers of tibiotalar and subtalar joints.Using screw theory,the mobility of the parallel mechanism,which meets the requirements of the human ankle,is analyzed.The inverse kinematics are presented,and singularities are identified based on the Jacobian matrix.The workspaces of the parallel mechanism are obtained through the search method and compared with the motion range of the human ankle,which shows that the parallel mechanism can meet the motion demand of ankle rehabilitation.Additionally,based on the motion-force transmissibility,the performance atlases are plotted in the parameter optimal design space,and the optimum parameter is obtained according to the demands of practical applications.The results show that the parallel mechanism can meet the motion requirements of ankle rehabilitation and has excellent kinematic performance in its rehabilitation range,which provides a theoretical basis for the prototype design and experimental verification.

INVERSE KINEMATIC AND DYNAMIC ANALYSIS OF A 3-DOF PARALLEL MECHANISM

According to the structure character of the passive sub-chain of the 3TPS-TPparallel mechanism, the kinematic constraint equations of the movable platform are established,based on which the closed-form inverse kinematics formula of the parallel mechanism are presented.Through parting the spherical joints of the active sub-chains and using the force and momentequilibrium of both the active sub-chains and passive sub-chain, the constraint forces acting on theparted joints are determined. Subsequently, the analytic expressions of the actuator driving forcesare derived by means of the force equilibrium of the upper links of active sub-chains.

PERFORMANCE ANALYSIS AND KINEMATIC DESIGN OF PURE TRANSLATIONAL PARALLEL MECHANISM WITH VERTICAL GUIDE-WAYS

Performance analysis and kinematic design of the 3-PUU pure translational parallel mechanism with vertical guide-ways are investigated. Two novel performance indices, the critical slider stroke and the main section area of workspace, are defined; The expressions of two other indices, i.e. the global dexterity and global force transfer ratio are revised based on the main section of workspace. Using these indices, performance changes versus the varieties of dimensional parameters of mechanism are investigated in detail and the graphic descriptions of change tendencies of the performance indices are illustrated. By means of these obtained graphic descriptions, kinematic parameters for the 3-PUU pure translational parallel mechanism with better characteristics can be directly acquired.

FORWARD KINEMATICS ANALYSIS FOR A NOVEL 5-DOF PARALLEL MECHANISM USING TETRAHEDRON CONFIGURATIONS

Forward kinematics analysis of a novel 5-DOF parallel mechanism using tetrahedron configurations is presented. Such mechanism is suitable to many tasks requiring less than 6 DOFs. It consists of a movable platform connected to the base by five identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DOF of the movable platform, which leads to its legs＇ topology 4-UPS/UPU. Based on the tetmhedron geometry, both closed-form solution with an extra sensor and numerical method using iterative algorithm are employed to obtain the forward kinematics solutions of the mechanism. Compared with the conventional methods, the proposed closed-form solution has the advantages in automatically avoiding unnecessary complex roots and getting a unique solution for the forward kinematics. Finally, an example shows that the proposed numerical algorithm is so effective that it enables a real-time forward kinematics solution to be achieved and the initial value can be chosen easily.

Dynamic Modeling and Analysis of 4UPS-UPU Spatial Parallel Mechanism with Spherical Clearance Joint

Clearance between the moving joints is unavoidable in real working process. At present, many researches are mainly focused on dynamics of plane revolute joint in plane mechanism, but few on dynamics of spatial spherical joint clearance in spatial parallel mechanism. In this paper, a general method is proposed for establishing dynamic equations of spatial parallel mechanism with spatial spherical clearance by Lagrange multiplier method. The kinematic model and contact force model of the spherical joint clearance were established successively. Lagrange multiplier method was used to deduce the dynamics equation of 4 UPS-UPU mechanism with spherical clearance joint systematically. The influence of friction coefficient on dynamics response of 4 UPS-UPU mechanism with spherical clearance joint was analyzed. Non-linear characteristics of clearance joint and moving platform were analyzed by Poincare map, phase diagram, and bifurcation diagram. The results show that variation of friction coefficient and clearance value had little effect on stability of the mechanism, but the chaotic phenomenon was found at spherical clearance joint. The research has theoretical guiding significance for improving the dynamic performance and avoiding of chaos of parallel mechanisms including spherical joint clearance.

Analysis and Simulation of Kinematical Performances of Two Kinds of Parallel Mechanisms Based on the Plane Sprayer

Two kinds of 2-dof parallel mechanisms are proposed in this paper which can be used as the actuator for the plane sprayer. The direct and inverse kinematics solutions of the two kinds of mechanisms are derived on the end operating point and two workspaces are analyzed and compared. The kinematics models of the end operating point of two mechanisms are simulated by Matlab examples obtaining variation of kinematics parameters of these two mechanisms. The research of this paper provides the basis for the selection of mechanism, trajectory planning of the end operating point on the sprayer and often some practical value for trajectory analysis and structure design of the plane sprayer.

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with Kinematic Redundancy

The kinematic redundancy is considered as a way to improve the performance of the parallel mechanism.In this paper,the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy(3-DOF PM-KR)and the influence of redundant parts on the PM-KR are analyzed.Firstly,the kinematics model of the PM-KR is established.The inverse solutions,the Jacobian matrix,and the workspace of the PM-KR are solved.Secondly,the influence of redundancy on the PM-KR is analyzed.Since there exists kinematic redundancy,the PM-KR possesses fault-tolerant performance.By locking one actuating joint or two actuating joints simultaneously,the fault-tolerant workspace is obtained.When the position of the redundant part is changed,the workspace and singularity will be changed.The results show that kinematic redundancy can be used to avoid singularity.Finally,the simulations are performed to prove the theoretical analysis.

KINEMATIC ANALYSIS OF THE GENERAL SPATIAL 7R MECHANISM

The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref. [5]found a base for establishing an expert system of spatial mechanism analysis in the future.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

Error Analysis of Three Degree-of-Freedom Changeable Parallel Measuring Mechanism

A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.

Position, Singularity and Workspace Analysis of 3-PSR-O Spatial Parallel Manipulator

Although the parallel mechanisms have the advantages of high accuracy, velocity, stiffness, and payload capacity, the shortcomings of the space utilization and workspace limit the applications in the confined space. A novel 3 degrees of freedom spatial parallel manipulator 3-PSR-O（prismatic-spherical-revolute） is proposed, which possesses a compact architecture and extended workspace while maintaining the inherent advantages of the parallel mechanisms. The direct-inverse position, singularity and workspace are investigated. The mapping method is adopted in the position analysis, and the closed form solution is derived in the form of a six order equation. The singularity analysis of the mechanism is also carried out based on the geometrical constraints, including six singularity boundaries. A feature boundary, which is independent of the prismatic joints＇ stroke limit, is obtained by integrating the six singularity boundaries. According to the formation of the reachable workspace, a concept of basic workspace is also introduced and presented in the analytical way. By demarcating the basic workspace along the central height with the feature boundary, the reachable workspace can be derived and analyzed more efficiently. Finally, a comparative study on the space utilization between the 3-PSP parallel mechanism and the new mechanism is also presented. The area of feature boundary of the new mechanism is about 140% of the 3-PSP parallel mechanism, while its installation radius is only 1/2 of the 3-PSP parallel mechanism. The proposed parallel mechanism shows great space utilization, and is ideally suited for applications in confined space occasions such as immersion lithography, nano-imprint etc.

ANINVESTIGATION ON THE REPLACEMENT OF SPHERICAL PAIR BY CROSS-HEAD PAIR IN SPATIAL MECHANISMS

The spatial RSSR crank rocker mechanism is widely used in industry, but, the manufac-turing, mounting and lubrication of S pair are more complicate than R or C pair. This paperdeals with the replacement of S pair by cress-head pair and investigates the equivalence of thetwo mechanisms with output angular displacement and oscillating angle ψ, as the object func-tion. The synthesis in terms of velocity ratio K and ψ and the influence of the cross-headstructure on the replacement have also been discussed.

正解符号化且运动解耦的2T1R并联机构拓扑设计与分析

基于方位特征(POC)方程的并联机构设计理论与方法,设计了一种全部由低副组成、具有位置正解符号化且部分运动解耦的两平移一转动(2T1R)并联机构,并对机构的主要拓扑特征(POC、自由度、耦合度、运动解耦性)进行分析与计算;基于拓扑特征运动学建模原理,导出机构符号式位置正解和反解;同时,由位置反解分析了机构奇异性,基于符号式位置正解求解了机构工作空间;根据基于虚功原理的序单开链法,对该机构动力学性能进行分析,计算得施加在3个驱动副上的驱动力;最后,对该机构应用于无人机操作及其安全着陆的动作原理进行了概念设计阐述。

基于PCA/PSO的3T1R并联机构性能优化

根据少自由度并联机构应用广泛的优点,提出了一种3T1R并联机构,该机构具有构型简单、结构对称、定位精度高等特点,可应用于小范围的精密操作,或者是大范围的搬运、分拣以及喷涂等领域。基于方位特征方程的拓扑分析理论,对该并联机构完成了自由度种类以及数目的分析与验证;基于闭环矢量法完成了运动学模型建立,并通过位置正逆解算例验证了运动学的合理性。基于位置逆解方程利用极限边界搜索法分析了3T1R并联机构可达工作空间;通过速度分析建立了速度雅可比矩阵,并根据该矩阵分析机构的定位精度与可操作度性能指标。利用主成分分析(PCA)与粒子群算法(PSO)对3个性能指标进行优化设计,并对优化结果进行了分析,最终优化后可达工作空间体积从0.2933m3提高到0.4231m3,定位精度误差放大因子从15.5044减小至4.4308,可操作度指数从9.7027减小至1.3996。

一种用于汽车零部件分拣与传送并联机构的设计及动力学分析

为实现对汽车零部件的智能分拣与传送,提出了一种全铰链新型一平移一转动(1T1R)并联机构,其结构简单且部分运动解耦。首先,基于方位特征方程的拓扑设计理论和方法,设计、分析了一种2自由度1T1R并联机构;其次,基于拓扑特征运动学方法,求解出机构的符号式位置正解,并对该机构的工作空间、奇异性进行了计算;最后,运用基于虚功原理的序单开链法,求得其驱动力矩和子运动链(Sub Kinematic Chain,SKC)连接处的支反力。研究为汽车零部件并联机构设计研究奠定了基础。

3-SRR腿履式调姿救援机器人优化设计与试验

为实现在复杂环境下对处于不同位姿伤员的精准施救及稳定转运,文中提出了一种3-SRR腿履式调姿救援机器人机构,并进行运动学分析、机构优化设计及试验研究。首先,基于闭环矢量法对其进行运动学分析,得到救援机器人运动学反解;然后,基于迭代搜索算法,得到其救援作业空间与姿态空间,并基于单一变量法分析救援机器人机构尺寸参数对救援作业空间的影响;然后,以救援作业空间最大、姿态能力最强为优化目标函数,基于差分进化算法对机构尺寸参数进行优化;最后,研制原理样机并进行调姿能力试验,试验结果证明了方案的可行性与理论分析的正确性,为灾难救援提供一种可行的解决方案。

新型3-DOF 1T2R并联机构的运动学分析与尺度优化

移动和转动混合运动的并联机构具有很高的研究和应用价值。基于转移混合输出运动的机构适用范围广,但该类机构的设计比较困难。为了研发和推广转移混合运动的1T2R并联机构,基于平面五杆机构和一条无约束支链,设计了一种一平移两转动(1T2R)的并联机构。首先,根据方位特征(POC)方程对机构进行了拓扑结构分析,并计算了该机构的自由度;然后,对该并联机构进行了运动学建模,推导了其位置正反解的解析表达式,并基于雅可比矩阵分析了机构的奇异性,利用三维离散搜索法计算了机构的工作空间,给出了机构在工作空间中的灵巧度分布情况;最后,利用粒子群算法(PSO)对机构的工作空间和灵巧度进行了双重优化,同时探讨了无约束支链的布置角φ对机构工作空间和灵巧度的影响。研究结果表明:所设计的1T2R并联机构结构简单,具有位置解析解;优化后的机构的工作空间和灵巧度分别提升了93.47%,203.42%;当无约束支链的驱动方向与平面(2P-3R)机构垂直布置时,能够获得更好的运动性能。该结果为3-DOF 1T2R机构的实际应用奠定了理论基础。

运动冗余球面并联机构动力学建模与分析

为了改善传统非冗余3-RRR球面并联机构工作空间不足、工作空间内易产生奇异和干涉,以及性能不足的问题,笔者设计了具有运动冗余球面并联机构。根据闭环矢量法建立了机构位置逆解模型,推导出机构雅可比矩阵并进行奇异分析;采用数值搜索法分析该机构干涉区域和可达空间;根据虚功原理方法建立该机构动力学模型,得到ADAMS动力学仿真与驱动力矩理论分析结果仅相差0.4%;基于动力学模型进行驱动力矩分布优化,优化结果表明对于一般动平台轨迹,该机构所需平均驱动力矩相比于传统非冗余3-RRR球面并联机构小25.80%;最后进行样机搭建和运动学实验。研究结果表明该机构干涉空间和奇异位形相对于传统3-RRR球面并联机构显著减少,该机构在应用中更有优势。

三移一转并联机构运动学分析

为满足钢铁搬运行业的应用需求,提出了一种新型三移一转并联机构。该机构的每条分支包含驱动支链RPR和执行支链RPaPaR,其执行支链中的平行四边形铰链Pa具有封闭环结构特性,使机构有较大的刚度。借助螺旋理论分析了该并联机构的自由度。采用机构杆件之间的几何条件以及坐标变换求出机构的位置逆解,得到驱动杆件与动平台位姿的关系。根据钢铁搬运任务需求,使用五次多项式计算出动平台分段驱动函数,在仿真软件ADAMS中实现机构末端由初始到目标位置的轨迹规划,并由驱动杆的仿真数据与计算数据一致,验证了机构位置逆解数学模型的正确性。利用PID控制器搭建机构的位置控制模型,实现动平台的实际位置与理论位置轨迹的一致性。使用CAD变量几何法得到了机构的可达位置工作空间,并对其进行了分析,得出工作空间分布特点。

基于并联机构的抓书机械手设计与分析

为满足智慧图书馆存、取书的需求,本研究设计了一款专用于智慧图书馆的抓书机械手。根据实际抓书工况的需求,基于Soildworks软件设计出一款末端执行器,并对末端执行器进行有限元分析。对并联机构建立笛卡尔坐标系,最后基于蒙特卡洛法对工作空间进行仿真验证。本研究最终将设计所得的末端执行器与并联机构相结合,得到一款能够快速、稳定抓取书本的机械手。根据仿真结果可知,所设计的抓书机械手可达到实际工况要求。