Kinematics analysis and solution of the active/passive forces of a 4SPS+SPR parallel machine tool

A 5-dof 4SPS+SPR parallel machine tool with four SPS-type active legs and one SPR-type active leg is proposed. Its inverse kinematics is analysed by using an analytic approach and a CAD variation geometry approach. Some analytic formulae for solving the active/passive forces are derived by adopting a vector approach. First, a simulation mechanism of the 4SPS+SPR parallel machine tool is created and some kinematic characteristics are analysed. Second, the formulae for solving its inverse kinematics and the Jacobian matrix are derived and a reachable workspace is constructed. Third, the poses of the active/passive forces are analysed and an active/passive force transformation matrix and the analytic formulae for solving the active/passive forces of the 4SPS+SPR parallel machine tool are derived. The analytic results are verified by the simulation mechanism.     

空间并联机构运动学与动力学逆解的模块化计算方法

应用模块化计算方法研究了空间并联机构的运动学与动力学逆解,计算效率能够满足实时控制的要求。通过对各类支链运动学及动力学逆解的分析,应用牛顿-欧拉法并引入拉格朗日乘子建立了空间并联机构的动力学逆解模型,提出了空间并联机构运动学与动力学逆解模块化计算软件的系统构架。结果表明该方法适用于各类非冗余空间并联机构的运动学与动力学逆解的自动建模和可重构设计,并给出了一种新型并联机构的分析实例。     

3SPS+1PS髋关节并联仿生试验系统工作空间优化

为使人工髋关节试验系统具有仿生模拟人体髋关节运动特性的能力,不但要使其能模拟髋关节各种运动形式,而且其运动输出空间应完全覆盖实际人体髋关节的运动范围,这也使得对其运动空间进行深入分析成为必要。针对作为髋关节并联仿生试验系统核心运动模块的3SPS+1PS并联机构,利用四元数法建立其逆/正解运动学模型,基于动平台三点构造法构建了3SPS+1PS并联机构的量纲统一速度Jacobian矩阵,分别比较了该矩阵条件数在不同运动空间及结构参数下的取值变化情况,得到条件数平均值与机构定、动平台上球副中心连线长度比值、球副许用转角及动平台中心位置高度等参数之间关系,优化了机构结构参数,进而得到了运动性能良好的运动空间区域。髋关节并联仿生试验系统运动空间的研究对其运动路径规划、动态特性分析及控制系统设计具有重要的意义。     

Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator(represented by Lie bracket)is deduced.Further,Newton-Euler’s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.     

一种新型四自由度并联平台机构及其位置分析

提出了一种能实现空间三维移动和绕 z轴转动的并联机器人机构模型——空间4- TRT并联机构。文中采用螺旋理论分析了它能实现空间三维移动和绕 z轴转动的机构学原理 ,计算了它的自由度 ;给出了其位置反解的方法 ,推导出了位置正解的封闭方程 ,并进行了数值验证。     

DESIGN FEATURES OF A PARALLEL TESTING PLATFORM FOR SIMULATING KINEMATIC CHARACTERISTICS OF HIP JOINT

To simulate the movement of a human during daily activities, such as walking, running, squatting, and kneeling, a novel parallel hip joint simulator whose key movement component is a 3SPS + 1PS parallel manipulator with four degrees of freedom (DOF) was proposed. SPS denotes the spherical-prismatic-spherical leg, and PS denotes the prismatic-spherical leg where only the prismatic joint is actuated and hence underlined. Firstly, the formulae for solving the inverse kinematics of the 3SPS + 1PS parallel manipulator were derived based on the unit quaternion method. Then, the parallel hip joint simulator was designed and finally developed by means of constructing the mechanical module, control module, hydraulic loading module, and data transmission module. In addition, three linear actuators are driven by the scheduled inverse displacement trajectories to enable the moving platform to output rotations about the Z-, Y-, and X-axes for representing flexion/extension, abduction/adduction, and external/internal rotations of the human hip joint. Simultaneously, the hydraulic loading module represents the dynamic loading as described by ISO 14242 Part-1 acting on the hip joint during the kinematic experiment. The kinematic experiment and dynamic loading experiment show that the fitting curves of the experimental results are consistent with the designed movement and loading trajectories. All these illustrate that the developed 3SPS + 1PS parallel hip joint simulator with effective design of all modules can substantially represent the designed movement and loading trajectories. The developed hip joint simulator can provide more reliable tribology test data for artificial prosthesis of hip joint.     

基于2TIR机构串并联机器人位置分析及仿真

根据串联机构和并联机构的特点,设计了一种串并联机器人新机型。通过对该机器人机构运动特征分析,求出了其位置正反解析解,并将用PRO/E建立的虚拟样机导入到ADAMS软件中进行了位置的动态仿真,验证了理论分析的正确性。该机器人动平台具有三个平移和一个转动自由度,与具有同样运动特性的并联机构相比,该机器人机构的工作空间大,转动自由度运转灵活。同时,该机器人机构的运动学正反解求解容易,便于实现实时控制。该机器人机构可应用于工业机器人、中医推拿机器人等领域。     

新型平面三自由度冗余并联机构的动力学分析

提出了一种新型平面三自由度冗余并联机构,推导出该机构的运动学逆解,利用牛顿-欧拉法建立了该机构封闭形式的动力学模型,分析表明驱动冗余可以有效地消除奇异位形,最后给出了该机构动力学逆解的数值仿真实例。     

Kinematics and dynamics analysis of a novel serial-parallel dynamic simulator

A serial-parallel dynamics simulator based on serial-parallel manipulator is proposed. According to the dynamics simulator motion requirement, the proposed serial-parallel dynamics simulator formed by 3-RRS (active revolute joint-revolute joint-spherical joint) and 3-SPR (Spherical joint-active prismatic joint-revolute joint) PMs adopts the outer and inner layout. By integrating the kinematics, constraint and coupling information of the 3-RRS and 3-SPR PMs into the serial-parallel manipulator, the inverse Jacobian matrix, velocity, and acceleration of the serial-parallel dynamics simulator are studied. Based on the principle of virtual work and the kinematics model, the inverse dynamic model is established. Finally, the workspace of the (3-RRS)+(3-SPR) dynamics simulator is constructed.

     

6—3型Stewart平台并联机构的运动学正解

针对6—3型Stewart平台并联机构运动学正解的问题,提出了一种新型的快速数值解法,该数值法能得到一个精确的惟一解。该方法主要是利用了6—3型Stewart平台的运动学反解的一些特性,得到一个有关杆长的微变量与动平台的微变量之间的线性方程式。再通过叠加杆长的连续的微小变量,得到6—3型Stewart平台的运动学正解。最后以反解为已知条件,通过算例进行了验证。同时采用Mathematica符号软件来提高求解位姿的计算效率。     

基于结构降耦的一类低耦合度新型3T1R并联机构的拓扑设计

四自由度的可实现SCARA型（三平移一转动）输出运动的并联机构,与三自由度的Delta机构相比,因其本身的拓扑结构复杂,导致运动学正解以及动力学计算复杂,从而使其新机型的研究和开发应用相对困难;而降低这些机构的耦合度（简称结构降耦）可直接降低机构运动学、动力学求解的难度。根据笔者提出的机构结构降耦方法,对笔者最近提出的一类5个耦合度值κ为2且具有较好实用价值的SCARA型新型并联机构进行了结构降耦优化,得到了耦合度较低（降为κ=1）但自由度和动平台输出运动类型均保持不变的10个SCARA新机型,而这10个低耦合度（κ=1）机构的运动学正解及动力学正反解,可用一维搜索法方便求得数值解,或从易导出的1个一元高次代数方程求得封闭解,为其进一步构型拓扑优化、设计及应用研究奠定了基础。     

基于遗传算法的新型六自由度并联机器人运动学分析

运动学位置正解和位置逆解是对并联机器人其它性能进行分析的基础,位置正解也是并联机器人研究中的一个难点。本文采用遗传算法对一种新型六自由度并联机器人的运动学位置正解和位置逆解进行了求解,并且利用灰色关联分析对求解结果进行了分组,得到了Stewart并联机器人的5组位置正解实解。实例表明该方法简单、方便、具有通用性,是求解并联机器人运动学问题的一种新策略。     

Kinematics and dynamics analysis of the 3PUS-PRU parallel mechanism module designed for a novel 6-DOF gantry hybrid machine tool

A hybrid kinematic machine (HKM) tool with the respective advantages of serial and parallel mechanism is a significant direction for the innovation and development of current advanced sophisticated manufacturing equipment. This paper considers the configuration design, kinematics analysis and dynamics analysis of a 1-translational-3-rotational (1T3R) parallel manipulator, which acts as the main movement module of a novel 6-DOF reconfigurable HKM. The key parallel manipulator with 4 DOFs is composed of one middle PRU kinematic chain and three identical PUS kinematic chains. First, complete kinematics characteristics, including position, velocity, acceleration and jerk, are deeply analyzed by a vector analysis approach. Reachable position workspace and orientation workspace were derived through the workspace boundary search method. Furthermore, complete inverse dynamics model of the 3PUS-PRU parallel manipulator was formulated by virtue of the virtual work principle with considering the inertial and gravitational properties of struts. Finally, a driving power and energy consumption model of each actuated motor under the prescribed trajectory were obtained, resulting in the decouple contribution of each motion part correspondingly. This systematic and rigorous methodology aims at laying a solid theoretical and technical foundation for configuration design and performance analysis of this homologous type HKM.

     

6－UPS型并联机构的刚体动力学模型

建立了6－UPS型并联机构的动力学模型。为了能使动力学模型包含所有构件的重力和惯性力,以6－UPS并联机构的支链为研究对象,运用D－H方法建立了各构件的坐标系,推导了支链的运动学反解的解析方程,并给出了各个构件的速度、加速度与动平台的速度、加速度的映射关系。然后用牛顿－欧拉方法推导了6－UPS并联机构的动力学模型,为支链中各个构件支反力的求解和整个机构的动力学分析奠定了基础。最后以并联机床为例,运用动力学模型进行了实际计算并绘制了连杆驱动力的变化曲线。     

具有连续转轴的新型3-UPU并联机构的运动特性分析

提出了一种新型3-UPU对称并联机构,该机构具有两个转动自由度和一个移动自由度（2R1T）。基于单叶双曲面几何性质,证明了该机构在任意位形下始终关于一个中间平面对称及机构自由度的非瞬时性;进而发现该机构动平台具有可绕其中间对称平面内任意直线做连续转动的特性,并通过仿真进行验证;采用一种新的两转动机构的姿态矩阵的求解方法,推导了该机构的运动学反解,并进一步分析了其工作空间。研究结果为该类机构的应用提供了理论参考。     

平面柔性并联机器人动力学建模

利用有限元理论研究柔性并联机器人动力学建模的理论和方法,分析各支链的弹性位移及其耦合关系,建立柔性并联机器人系统的运动约束条件和动力约束条件。综合考虑构件的分布质量、集中质量以及杆件的剪切变形、弯曲变形、拉压变形和横向位移的影响,运用运动弹性动力学理论和Lagrange方程,推导出平面柔性并联机器人的动力学方程。以平面3-RRR柔性并联机器人为例,说明该动力学模型能正确反映柔性并联机器人的弹性振动特性,杆件的弹性变形对机器人动平台的位置误差和方向误差具有重要影响。     

新型串并联中医推拿机器人研究

研究了中医推拿中常用的滚法、按法、揉法、推法等手法的运动学及动力学特征,获得完成各推拿手法的运动输出矩阵和施力方向。提出一种能满足推拿要求的基于三自由度并联机构新型串并联中医推拿机器人机型。对该机型中的三自由度并联机构进行了分析,求出其运动学正反解的解析解。系统讨论了该并联机构的推拿范围及转动能力,为扩大该机器人的推拿范围提供依据。该串并联机器人机构综合了串并联机构的优点,不仅能模拟中医推拿常用的几种手法,而且结构简单、位置分析求解容易、解耦性强,易于实时控制。     

3-CRR 并联机构动力学分析与仿真

以机构支链的动力学为基础,推导3-CRR并联机构的动力学方程。在SolidWorks软件中建立机构的虚拟模型并在CosmosMotion模块中进行动力学仿真。通过动力学方程和仿真两种方法分别计算机构完成规定运动所需要的驱动力,比较发现计算结果基本一致,证明了两种方法的一致性与准确性,为机构的设计制造和动力学控制提供了理论基础。     

柔索驱动并联机器人动力学建模与数值仿真

柔索驱动并联机器人采用柔索代替连杆作为驱动元件,并结合了并联机构和柔索驱动的优点。500 m口径大射电望远镜(Five-hundred meter aperture spherical radio telescope, FAST)粗调系统通过6根索长的协调变化使馈源舱作跟踪射电源的6自由度运动,其工作特点与并联机器人类似,因此可被看作柔索驱动并联机器人。基于此,根据FAST 5 m缩比试验模型,首先应用悬链线解析表达式推导出柔索两端固定时索端拉力与索长之间的关系,用于求解特定长度的驱动柔索对处于某一位姿的馈源舱的作用力。其次,对该舱索系统进行逆运动学分析,采用拉格朗日方程建立柔索驱动并联机器人的逆动力学模型。最后,针对FAST 5 m缩比模型的设计方案进行动力学仿真,数值结果表明该动力学建模是合理的。