KINEMATICS OF 3-DOF PYRAMID MANIPULATOR BY PRINCIPAL SCREWS

0　ＩＮＴＲＯＤＵＣＴＩＯＮＯｎｅｗｈｏｌｅｃｅｎｔｕｒｙａｇｏＢａｌｌ[1] ｐｕｂｌｉｓｈｅｄｈｉｓｃｌａｓｓｉｃａｌｗｏｒｋ ,ｉｎｗｈｉｃｈｈｅｓｔｕｄｉｅｄｔｈｅｓｃｒｅｗｔｈｅｏｒｙ .Ｈｕｎｔ[2 ] ｄｉｓｃｕｓｓｅｄａｌｌｔｈｅｓｃｒｅｗｓｙｓｔｅｍｓ .Ｔｈｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆａｌｌｔｈｅｓｃｒｅｗｓｏｆａｓｃｒｅｗｓｙｓｔｅｍｉｎｔｈｒｅｅ ｄｉｍｅｎｓｉｏｎｓｐａｃｅｉｓｒｅｇｕｌａｒ .Ｆｏｒａｔｈｉｒｄ ｏｒｄｅｒｓｃｒｅｗｓｙｓｔｅｍ ,ｔｈｅａｘｅｓｏｆａｌｌｔｈｅｓｃｒｅｗ…     

Gough-Stewart并联机构奇异轨迹的性质识别

基于Gough-Stewart并联机构奇异轨迹的解析表达式，推导出了该并联机构在主截面上的奇异轨迹，并对此奇异轨迹的性质进行了识别。研究结果表明，Gough-Stewart并联机构在相互平行的主截面上的奇异轨迹总是一个二次多项式，包括四对相交直线、一条抛物线及双曲线束。对奇异的几何特性进行了研究。     

A generalised approach to point-to-point motion of multi-DOF parallel manipulators illustrated with TMPM

The work presented in this paper describes a novel approach to the computation of the point-to-point motion of multi-degree-of-freedom parallel mechanisms. The common technique for solving for the inverse kinematics of parallel mechanisms is through intense computations and complex vector transformations. One obvious drawback of this method is the fact that the solution method varies with the type of mechanism being used. In this paper, a generalised alternative approach is presented, which avoids the problems encountered in the available techniques, for solving for the inverse kinematics of parallel manipulator systems. The proposed approach uses a fuzzy system as a general black box model to solve for the joint angles of the desired pose when the position and orientation of the parallel manipulator end-effector are given in advance. Since optimal membership functions are difficult to achieve using the experience of system designers, genetic algorithms are used instead and applied to the fuzzy rules set to optimise the search procedure. To verify the proposed scheme, a three degree-of-freedom parallel manipulator is analysed and the simulation results are very encouraging.     

Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS) of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.     

一种所有转轴均连续的五自由度混联机器人机构

根据两转一移并联机构两转动自由度转轴的分布,提出构造五自由度混联机器人机构构型的新思路,基于2-RPU&UPR并联机构构造一种新型五轴混联机器人机构。建立2-RPU&UPR并联机构的位置正反解模型,由于该并联部分存在两条连续转轴,可将其等效成一个三自由度串联机构RPR,进而将整个混联机器人机构等效为一个四自由度串联机构RPRR和一个移动平台的组合进行分析,根据这两部分位姿之间的解耦性,建立了混联机器人完整的位置正反解模型,并用加工球面轨迹的算例验证了所建运动学模型的正确性。提出的5自由度混联机器人所有转动自由度均具有连续转轴,能够得到解析的位置模型表达式,能够很容易实现轨迹规划与运动控制,具有良好的应用前景。     

Mass determination and sensitivity based on resonance frequency changes of the higher flexural modes of cantilever sensors

Micro- and nanocantilevers are increasingly employed as mass sensors. Most studies consider the first flexural mode and adsorbed masses that are either discretely attached or homogeneously distributed along the entire length of the cantilever. We derive general expressions that allow for the determination of the total attached mass with any mass distribution along the cantilever length and all flexural modes. The expressions are valid for all cantilevers whose flexural deflection can be described by a one-dimensional function. This approach includes the most common types of microcantilevers, namely, rectangular, picket, and V-shaped. The theoretical results are compared with experimental data up to the fourth flexural mode obtained from thermal noise spectra of rectangular and V-shaped cantilevers.     

空间4R冗余度机械臂容错空间分析

针对空间4R冗余度机械臂活动关节工作空间进行了定量研究,并且对其容错空间做了进一步探讨。首先推导出空间4R冗余度机械臂不同关节锁定时工作空间的解析表达式,并且根据表达式对工作空间进行了三维造型;然后,进一步分析了机械臂的D-H参数对工作空间的影响;最后,给出3 sigm a型机械臂容错空间的计算方法及三维造型,分析了其容错空间的影响因素。研究结果表明:当机械臂结构参数一定时,一个活动关节(关节2)在一定范围内锁定,工作空间不变,并且此锁定范围与结构参数一一对应;机械臂的臂长之和一定时,各机械臂长度越接近,机械臂的工作空间越大;机械臂关节2偏置的存在使机械臂工作空间不会出现薄壳,另一活动活动关节(关节3)的偏置的存在也可以增大工作空间;关节工作空间增大,容错空间也会相应增大。     

Development of a redundant anthropomorphic hydraulically actuated manipulator with a roll–pitch–yaw spherical wrist

The demand for redundant hydraulic manipulators that can implement complex heavy-duty tasks in unstructured areas is increasing; however, current manipulator layouts that remarkably differ from human arms make intuitive kinematic operation challenging to achieve. This study proposes a seven-degree-of-freedom (7-DOF) redundant anthropomorphic hydraulically actuated manipulator with a novel roll–pitch–yaw spherical wrist. A hybrid series–parallel mechanism is presented to achieve the spherical wrist design, which consists of two parallel linear hydraulic cylinders to drive the yaw/pitch 2-DOF wrist plate connected serially to the roll structure. Designed as a 1R PRRR-1S PU mechanism (“R”, “P”, “S”, and “U” denote revolute, prismatic, spherical, and universal joints, respectively; the underlined letter indicates the active joint), the 2-DOF parallel structure is partially decoupled to obtain simple forward/inverse kinematic solutions in which a closed-loop subchain “R PRR” is included. The 7-DOF manipulator is then designed, and its third joint axis goes through the spherical center to obtain closed-form inverse kinematic computation. The analytical inverse kinematic solution is drawn by constructing self-motion manifolds. Finally, a physical prototype is developed, and the kinematic analysis is validated via numerical simulation and test results.     

关于任意机械系统动力学方程的结构

本文给出了任意机械系统（完整、非完整的约束,含有各类运动副的开、闭或混合链系统）动力学显式方程。其中,含约束反力的动力学显式方程乃是Newton-Euler方法与动力学普遍方程（虚功原理）的统一形式;提出了动力学等效分解模型,在一定意义上将系统动力学方程试为若班干子系统在特定运动输入下的运动学关系的某种叠加与组合;给出了动力学方程生成的计算量与系统结构单元的划分层次及其拓扑结构特征之间的关系。从而进一步提示了系统动力学、运动学与结构学之间的内在联系。     

带闭链的五自由度工业机器人动力学解析模型

提出了一种建立带闭链的工业机器人动力学解析模型的方法。设想将闭式链的某一非主动关节的运动副断开 ,其运动关系用约束方程来代替 ,形成带有附加约束的等效系统 ,然后基于 Kane动力学方程 ,导出了显式形式的动力学方程。并将部分变量处理为符号量 ,其余变量处理为数字量 ,从而获得了动力学解析模型中各模型矩阵元素的数字 -符号表达式 ,并给出一实例进行说明     

Constraint-force-based approach of modelling compliant mechanisms: Principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.     

Analytical model for estimating intersegmental forces exerted on human lower limbs during walking motion

Existing methods for evaluating the intersegmental forces acting on the human lower limbs during walking generally measure the ground reaction force exerted on the feet using force plates and estimate the intersegmental forces using an inverse dynamics approach. However, force plates are inconvenient and expensive. Accordingly, the present study proposes an approach for evaluating the intersegmental forces without the need for force plates by modeling the human lower limbs as a seven-link manipulator system. In the proposed approach, the intersegmental forces are derived directly from the analytical model using Newton–Euler theory based on the posture information obtained from a system of gyroscopes and accelerometers during walking motion. The results obtained from the analytical model are compared with the experimental data obtained using load cells. It is found that the estimated results are in good agreement with the measured results. Thus, the basic validity of the proposed analysis system is confirmed.     

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a...     

Obtaining configuration space and singularity maps for parallel manipulators

The aim of this paper is to describe a general methodology to obtain the entire set of positions that a parallel manipulator can reach and the workspace regions where the robot is controllable. The workspace is computed using a hybrid analytical-discrete procedure. Next the singularity maps are traced by carrying out a kinematic analysis of the positions obtained. To perform the latter a systematic method has been introduced to obtain the corresponding Jacobian matrices. The result of the whole process is the computation of singularity-free workspace regions, associated with certain working and assembly modes. After that, strategies to enlarge the accessible space are easier to plan and implement. This methodology is based on disassembling the manipulator into a mobile platform and a set of kinematic chains.     

按照性能指标进行机构优化设计

提出了一个根据给定相关性能(如精度和工作空间),设计6自由度并联机构的可靠方法。该方法采用了区间分析理论及其算法,不仅可以分析末端执行件定位精度的测量误差,也能够得到设计参数的取值区间。只要并联机构的几何参数满足这些求得的设计参数区间,该并联机构必然达到相关的性能要求。利用本文的算法,应用于一个6自由度的并联机构设计。本文通过对该并联机构搜索空间的分析,比较了设计参数和阈值对计算结果和效率的影响。     

A method of verifying force-closure condition for general cable manipulators with seven cables

This paper introduces a systematic method of verifying the force-closure condition for general 6-DOF cable-driven manipulators with seven cables. Force-closure is defined as that the inverse dynamics problem has a feasible solution for any external wrench exerted on the end-effector. For any given configuration of a 7-cable manipulator, the method can easily determine, by examining the Jacobian matrix of the manipulator, whether a solution of all-positive cable forces exists. The necessary and sufficient conditions of the proposed method are mathematically proven. The paper also addresses the application of the proposed method for determination of the force-closure workspace. As a numerical example, the shape, boundary, dimensions, and volume of the force-closure workspace of a 6-DOF, 7-cable manipulator are discussed.     

一类3-3 Stewart平台的正向运动学闭式解

针对 Stewart平台机器人的结构特点 ,提出一种新的姿态描述 ,这种描述直观、简便 ;并对一类 3- 3RSR并行机器人进行几何分析 ,给出一种新的解法 ;应用 Mathe-m atica软件编程进行符号运算得到该类平台的闭式解 ,闭式解便于实现实时控制。同时用算例进行校验 ,结果表明计算速度快 ,为实时控制和实际应用创造了条件。     

基于区间对分搜索法的并联机构位置正解问题求解

针对并联机构的位置正解问题 ,提出一种基于区间对分搜索法的数值迭代计算方法。该算法通过对并联机构约束方程解空间的不断细分 ,得到非线性约束方程所有解的收敛域空间 ,然后通过Newton迭代方法计算问题的所有近似解。与一般点迭代方法相比 ,该算法的收敛性不依赖于初始条件的选取 ,并且能够一次得到问题的所有近似解。文中对 6自由度Stewart平台进行了仿真计算。     

线驱动拟人臂机器人逆向运动学分析

基于最新人臂仿生理论和并联机器人研究的成果,提出一种线驱动7-DOF冗余手臂的设计方案.线驱动机构具有高刚度、高精度、高负载能力的优点,可以克服常规串联机构的缺点.介绍这种新型线驱动拟人臂机器人具体的结构,利用旋量理论描述机器人运动,在绳索张力条件的约束下,分析肩关节的工作空间.针对7-DOF机器人的逆运动学求解问题,先采用关节速度再分配法求关节速度逆解;然后与Paden-Kahan子问题法相结合,取得具有冗余控制的位置逆解,求出在给定位姿时各关节角的角度;再由关节角与绳长的关系解出各关节处驱动绳索的长度,并分析肩关节运动对腕、肘关节的耦合影响.最后在ADAMS下进行仿真,采用直线插补算法,动画图形实时显示机器人的运动情况,证明逆向运动学算法的正确性.     

Closed loop control of the planar flexible manipulator via Youla-Kucera parameterization

This work treats the problem of controlling a flexible robotic manipulator. The case study is a planar manipulator with a single flexible arm together with a clamped-free end and a tip lumped mass. To control the angular position of the flexible arm using an actuator, a controller method is developed which is based on Youla-Kucera parameterization. The main challenge in this approach is to obtain a Youla parameter with infinity dimensions. This parameter is approximated by a subspace with finite dimensions which makes the problem tractable. The developed approach exhibit advanced theoretical properties and good numerical convergence. In this paper, two sets of orthogonal bases such as FIR and Laguerre bases are used for system identification. The results of the present case study indicate that the proposed method is very efficient and robust for the time-continuous instances. The characteristics of an optimization problem are finally formulated for larger systems with hundreds of variables and solved with the interior point method.