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.

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.

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.

Forward Position Analysis of 5-DOF Parallel Mechanism

A systematic method for the forward kinematics of a five degrees of freedom （5-DOF） parallel mechanism with the legs＇ topology 4-UPS/UPU, is developed. Such mechanism is composed of a movable platform connected to the base by four identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DQF of the movable platform. Three translational and two rotational DOFs can be achieved. Firstly, a set of polynomial equations of forward position analysis is formulated based on the architecture of the mechanism. Then the system of equations is degraded from five-dimensional to three-dimensional by means of analytic elimination. Method of least squares and Gauss-Newton algorithm are used to construct the objective function and to solve it, respectively. Example shows that through 4-time iteration within 16 ms the ohjective, function converaes to the provided error tolerance. 10^-4.

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.

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.

Architecture Singularity Analysis of 4-U■S/U■U 5-DOF Parallel Mechanism

Architecture singularity of a parallel mechanism with five degrees of freedom (DOF) is analyzed. Such mechanism consists of a movable platform connected to the base by five active limbs. Four of them are identical 6-DOF limbs and the last one has the same DOF as the specified DOF of the movable platform. Based on the kinematics analysis, two categories of architecture singularities for such mechanism are proposed. Then the sufficient condition for each singularity is researched. Results show that the mechanism is singular when it employs each category of the proposed architecture, provided that it satisfies the corresponding sufficient condition. It can be concluded that the proposed two categories of architecture singularities should be avoided with the following dimensional synthesis of such mechanism.

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.

Dynamic Modeling and Analysis of 5‑PSS/UPU Parallel Mechanism with Elastically Active Branched Chains

To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.

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.

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.

5-DOF混联机器人设计与运动学分析

针对现有2R1T并联机构并不能很好地满足航空航天工业制孔稳定性的问题,设计了一种全新的两转一移并联机构3SPU-PU,并基于此并联机构设计了2-DOF转头,构造了5-DOF混联机器人,可用于某型飞机座舱盖制孔。首先,利用修正的G-K公式计算了3SPU-PU并联机构的自由度;其次,利用子结构综合的方法对所设计的五自由度混联机器人进行了逆运动学分析;运用ADAMS仿真分析与MATLAB理论计算对运动学分析理论模型进行了验证;最后,利用有限元分析方法对混联机器人进行了静力学分析。结果表明,所设计的混联机器人刚度大、质量轻,能更好地满足制孔稳定性的需求,研究结果也为混联机器人的样机研制、动力学分析及实时控制打下了理论基础。

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。

Accuracy Analysis for 6-DOF PKM with Sobol Sequence Based Quasi Monte Carlo Method

To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions,can prevail traditional Monte Carlo method with up to 98. 59% and 98. 25% enhancement for computational precision of pose error statistics.Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.

基于单开链和方位特征集的5-DOF串并联构型综合

根据单开链和方位特征集设计了一种5自由度串并联机器人,并对5自由度串并联机器人并联机器人的运动学,对并联机构的位置逆解和动平台速度进行分析。运用Adams软件对设计的5自由度串并联机器人进行仿真分析,并验证机构的可行性。结果表明,该机构具有运动比较平稳、工作空间大等特点,对5自由度串并联机构多驱动器控制提供了参考依据。

Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms

A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displacement analysis of this mechanism is developed.When the six vertices of the top platform are in a quadratic curve,this mechanism becomes singular.This new theoretical result is confirmed with a numerical example.

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。

Design and Analysis of a Novel 2T2R Parallel Mechanism with the Closed-loop Limbs

This paper presents a novel four degrees of freedom(DOF) parallel mechanism with the closed-loop limbs, which includes two translational(2 T) DOF and two rotational(2 R) DOF. By connecting the proposed parallel mechanism with the guide rail in series,the 5-DOF hybrid robot system is obtained, which can be applied for the composite material tape laying in aerospace industry. The analysis in this paper mainly focuses on the parallel module of the hybrid robot system. First, the freedom of the proposed parallel mechanism is calculated based on the screw theory. Then, according to the closed-loop vector equation, the inverse kinematics and Jacobian matrix of the parallel mechanism are carried out. Next, the workspace stiffness and dexterity analysis of the parallel mechanism are investigated based on the constraint equations, static stiffness matrix and Jacobian condition number. Finally, the correctness of the inverse kinematics and the high stiffness of the parallel mechanism are verified by the kinematics and stiffness simulation analysis, which lays a foundation for the automatic composite material tape laying.

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。