外文翻译---新型二自由度平动并联机器人的结构和运动学分析

1、.附录（一） 英文文献Structure and kinematic analysis of a novel 2-DOF translational parallel robotChen Tao1Wu Chao2 and Liu xiujun2*( 1. School of Application Science and TechnologyHarbin University of ScienceAnd Technology，Harbin l50080,China；2. Department of Precision InstrumentsTsinghua University, Beijin

2、g 100084, China)Accepted on February 13, 2007Abstract This paper addresses the analysis of a novel parallel robot with 2 translational degrees of freedom (DOFs). The robot can position a rigid body in a plane with constant orientation. The kinematic structure of the robot is first described in detai

3、l, Some kinematic problems, such as the inverse and forward kinematics, velocity, and singularity are then analyzed. The working and assembly modes are discussed. Since it is the most important index to design a robot , the workspace of the robot is studied systematically in this paper. Based on the

4、 analysis of reachable workspace and singularity, a kind of workspace concept characterizing the region that the end-effector of the robot can reach in practice is defined. The results of this paper will be very useful for the design and application of the robot.Keywords： parallel robot, degree of f

5、reedom, kinematics workspace. The conceptual design of parallel robots can be dated back to the time when Gough established the basic principles of a device with a closed-loop kinematic structure that can generate specified position and orientation of a moving platform so as to test tire wear and. t

6、ear. Based on this principle, Stewart designed a platform used as an aircraft simulator in 1965. In 1978, Hunt made a systematic study of robots with parallel kinematics, in which the spatial 3-RPS (R-revolute joint，P-prismatic joint, and S- spherical joint) parallel robot is a typical one. Since th

7、en, parallel robots have been studied extensively by numerous researchers.The parallel robots with 6 DOFs possess the ad-vantages of high stiffness, low inertia, and large payload capacity. However, they suffer the problems of relatively small useful workspace and design difficulties .Their direct k

8、inematics possess a very difficult problem. The same problem of parallel robots with 2 and 3 DOFs can be described in a closed form . As is well known, there are three kinds of singularities in parallel robots. Generally, not all singularities of a 6- DOF parallel robot can be found easily. For a pa

9、rallel robot with 2 or 3 DOFs, the singularities can always be identified readily. For such reasons, parallel robots with less than 6 DOFs, especially 2 and 3 DOFs, have increasingly attracted more and more researchers attention with respect to industrial applications. In these designs, parallel rob

10、ots with three translational CKDFs have been playing important roles in the industrial applications. For example, the design of the DELTA robot is covered by a family of 36 patents. Tsais robot，in which each of the three legs consists of a parallelogram, is the first de, sign to solve the problem of

11、 UU chain. Such parallel robots have wide applications in the industrial world, e. g., pick-and-place application, parallel kinematic machines, and medical devices.The most famous planar 2-DOF parallel robots are the well-known five-bar mechanism with prismatic actuators or revolute actuators. In th

12、e case of the robot with revolute actuators, the mechanism consists of five re volute pairs and the two joints fixed to the base are actuated, while in the case of the robot with prismatic actuators, the mechanism consists of three revolute pairs and two prismatic joints, in which the prismatic join

13、ts are usually actuated. The output of the robot is the translational motion of a point on the end-effector. This means the orientation of the end- effector is also changed at any moment. Accordingly, some versions of the 2-DOF translational parallel robot (TPR) have been disclosed. One of them has

14、been applied in precise pick & place operations at high speed at SFB in German, In 2001, another 2-DOF TPR has been proposed for the conceptual design of a 5-axis machine tool, The structure, kinematics and dynamics of the TPR were discussed in de- tail, Recently, a 2-DOF TPR with revolute actua

15、tors was introduced. The TPR presented in Ref. 4 has been used in the design of a planer machine tool with a gantry structure instead of a traditional one with serial chains to improve its stiffness and inertia characteristics. However* all of these TPRs consist of at least of one parallelogram, whi

16、ch increases the difficulty of manufacturing and affects the accuracy.This paper introduces a novel planar translational parallel robot with simple kinematic structure. The robot can position an objective with constant orientation. Some kinematic problems, such as inverse and forward kinematics, wor

17、kspace and singularity are discussed.1Description of the 2-DOF TPR and its topological architectures1.1Architecture descriptionThe novel 2-DOF translational parallel robot and its schematic are shown in Fig. 1. The end-effector of the robot is connected to the base by two kinematic legs 1 and 2. Leg

18、 1 consists of three revolute joints and leg 2 two revolute joints and one cylinder joint, or three re volute joints and one prismatic joint- In each leg, the re volute joints are parallel to each other. The axes of the revolute joints in leg 1 are normal to those of the joints in leg 2. The two joi

19、nts attached to the end-effector are put in the adjacent sides of a square. The kinematic chain of the robot is denoted as RRR-RRC (C-cylinder joint) or RRR-RRRP, One may see that, if the P joint is fixed, the robot is actually the famous Sarrus mechanism.As introduced previously，other TPRs have at

20、least one parallelogram in their structures. The TPR proposed here has no parallelogram. This makes the manufacturing easier. However, compared with the TPRs presented in Refs. 9,10，the TPR studied here has some disadvantages. For example, the performance of the new TPR is not symmetric in its works

21、pace. Additionally, the new TPR is likely to need more occupying space.(a) the CAD model (b) the schematicFig.1 The 2-DOF translational parallel robot1.2CapabilityHere, an expression like is used to describe the capability of an object j. In , and express the translation and rotation of the object,

22、respectively. If an element in is equal to 0, there is no such a translation or rotation. If it is equal to 1, there is the capability. For example, means that the object has no translation along the x-axis; indicates that the object can rotate about the y-axis.Observing only leg 1, the capability o

23、f the end-effector in the leg can be expressed as . Letting leg 1 alone, the capability of the end-effector with leg 2 can be written as Then, the intersection of and is ， i. e, (1)which describes the capability of the robot, i.e., the translations of the end-effector along the x and y axes. This me

24、ans the end-effector has two purely translational degrees of freedom with respect to the base.It is noteworthy that the capability analysis method used above cannot be applied to all parallel robots.2Kinematics analysis2.1Inverse kinematicsAs illustrated in Fig. 1(b), a reference frame :O-xy is fixe

25、d to the base at the joint point and a moving reference frame ： is attached to the end-effector, where is the reference point on the end-effector. Vectors are defined as the position vectors of points in the frame ，and vectors as the position vectors of points in frame .The geometric parameters of t

26、he robot are ，and the distance from point to the guideway is ,where and and are dimensional parameters, and and non-dimensional parameters. The position of point in the fixed frame is denoted as vector (2)The vectors of in the fixed frame can be written as (3)where is the actuated input for leg 1. V

27、ector in the fixed frame can be written as (4)The inverse kinematics problem of leg 1 can be solved by writing the following constraint equation (5)that is (6)Then, there is (7)where (8)For leg 2，it is obvious thats = x(9)in which s is the input of leg 2. From Eqs. (8) and (9), we can see that there

28、 are two solutions for the inverse kinematics of the robot. Hence, for a given robot and for prescribed values of the position of the end-effector, the required actuated inputs can be directly computed from Eqs. (7) and (9). To obtain the configuration as shown in Fig. 1, parameter a in Eq. (8) shou

29、ld be 1. This configuration is called the “ + ” working mode. When , the corresponding configuration is referred to as the “一” working mode.2.2Forward kinematicsThe forward kinematic problem is to obtain the output with respect to a set of given inputs. From Eqs. (6) and (9),one obtains(11)andx = s(

30、12)where and . Therefore , there are also two forward kinematic solutions for the robot. The parameter corresponds to the configuration shown in Fig. 1, which is denoted as the down-configuration. When the configuration is referred to as the up-configuration. These two kinds of configurations corres

31、pond to two kinds of assembly modes of the robot.3Singularity analysis4Workspace analysis5Conclusion and future workIn this paper , a novel 2-DOF translational robot is proposed. One characteristic of the robot is that it can position a rigid body in a 2D plane while maintaining a constant orientati

32、on. The proposed robot has potential application in light industry. The inverse and forward kinematics problems workspace* and singularity are presented here.The future work will focus on the kinematic design based on the workspace concept, the development of the computer-aided design of the robot b

33、ased on the proposed design methodology, the development of the robot prototype, and the experience research of the prototype.References：1Stewart D.A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers,1965(180):371-3862Hunt KH. Structural kinematics of in-pa

34、rallel-actuated robotarms. ASME Journal of Mechanism, Transmission and Automation in Design,1983,105:705-7123Merlet JP. Parallel Robots. London: Kluwer Academic Publishers,20004Liu XJ.Mechanical and kinematics design of parallel robotic mechanisms with less than six degrees of freedom.Post-Doctoral

35、Research Report (in Chinese),Tsinghua University,Beijing,20015Tsai LW and Stamper R.A parallel manipulator with only translational degrees of freedom.In: Proceedings of ASME 1996 Design Engineering Technical Conference,Irvine,CA,1996,paper 96-DETC-MECH-11526Siciliano B.The tricept robot:inverse kine

36、matics, manipulability analysis and closed-loop direct kinematics algorithm.Robotica,1999,17:437-4457Liu XJ,Wang QM and Wang J.Kinematics, dynamics and dimensional synthesis of a novel 2-DoF translational manipulator. Journal of Intelligent & Robotic Systems,2005,41:205-2248Clavel R.DELTA: a fas

37、t robot with parallel geometry.In: Proceedings of 18th Int. Symp. on Industrial Robot,Sydney,1988,91-1009Collaborative Research Centers (SFB),SFB 562-Robotic systems for handling and assembly:Seitentitel:PORTYS,http:/www.tu-braunschweig.de/sfb562/galerie/portys,2007-2-1310Liu XJ and Wang J. Some new

38、 parallel mechanisms containing the planar four-bar parallelogram. International Journal of Robotics Research,2003,22:717-73211Huang T, Li Z,Li M,et al. Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-andplace operations. Journal of Mechanical Desig

39、n,2004,126:449-45512Sarrus PT.Note sur la Transformation des Mouvements Rctilignes Alternatifs,en Mouvements Circulairs; et Reciproquement.Comptes Rendus Hebdomadaires des Seances de l' Academie des Sciences,1853,36:1036-1038附录（二） 英文文献翻译新型二自由度平动并联机器人的结构和运动学分析陈涛1，吴超2，刘学军2*(1. 应用科学和技术学院，哈尔滨理工大学，哈尔

40、滨150080，中国;2. 精密仪器系，清华大学，北京100084，中国)2007年2月13日，接受摘要:本文对一种新型的二自由度并联机器人进行分析。机器人可以放置在一个固定方向的平面刚体。首先详细介绍了机器人的运动结构，然后分析了一些运动的问题，如正向和逆向的运动学，速度，和奇异点。对工作和装配方式进行了讨论。因为对于设计机器人它是个重要的指标，本文对机器人的工作空间做了系统的研究。以可达工作空间和奇异性的分析为基础，描述机器人末端效应可以达到在实践中被定义的区域。本文的结果将对机器人的设计和应用非常有用。关键词：并联机器人，自由度，运动学工作空间。并联机器人的概念设计，可以追溯到高夫建立的

41、基本原则，一个闭环的运动结构，可以生成指定的位置和方向的移动平台，以测试轮胎的磨损。基于这个原则，1965年斯图尔特设计了一个用作飞机模拟器的平台。 1978年，亨特对并联机器人作了系统的研究，其中空间3-RPS（R转动关节，P-移动关节，和S-球形关节）并联机器人是典型的一个。自那时以来，并联机器人被众多研究者广泛研究。6自由度并联机器人具有高刚度，低惯量，大载荷能力。然而，他们受到相对较小的有益的工作空间的问题和设计上的困难。他们的正向运动有一个非常困难的问题。在一个封闭的形式下2和3自由度并联机器人也有同样的问题。.众所周知，并联机器人中有3种类型的奇异点。一般来说，一个6自由

42、度并联机器人所有的奇异点并不是都能被容易地发现。而对于2或3自由度的并联机器人，奇异点总是可以很容易确定。由于这样的原因，少于6自由度的并联机器人，尤其是2和3自由度并联机器人，在工业应用方面已经越来越吸引更多的研究者的关注。在这些设计中，三自由度平动并联机器人在工业应用中一直起着重要的作用。例如，三角洲（DELTA）机器人的设计是由一个拥有36项专利的家庭来承担的。蔡（Tsai）的机器人，每三条腿构成一个平行四边形，是第一个解决支原体链问题的设计。这种并联机器人在工业界广泛应用，比如拾取和放置的应用，并联机器和医疗设备。最有名的平面2自由度并联机器人是众所周知的五杆棱柱驱动器或旋转驱动器的机

43、制。在带有旋转驱动器的机器人的情况下，该机制由五个转动副和两个固定在底座上被启动的关节组成，而在带有棱柱驱动器的机器人的情况下，该机制包括三个转动副和两个柱状关节，通常柱状关节是被启动的。机器人的输出是一个末端执行器上一个点的平移运动。这意味着在任何时刻末端执行器的方向也会改变。因此，一些2自由度平动并联机器人（TPR）的版本已披露。其中一个版本已被应用于德国SFB高速的精确的拾放操作。在2001年，另一个2自由度的TPR已提出的5轴机床的概念设计。TPR的结构，运动学和动力学进行了详细讨论。最近，一个带有旋转驱动器的2自由度的TPR被采用。参考文献陈述的TPR已经用于龙门机床的设计中，用的是

44、龙门式结构，而不是用传统的串行链，以此来提高其刚度和惯性特征。然而，所有这些TPRS包括至少一个平行四边形，从而增加了制造的难度和影响精度。本文介绍了一种新型的可以用简单的运动结构的平动并联机器人。机器人定位一个恒定方向的目标。讨论了一些运动学问题，如逆向和正向运动学，工作空间和奇异点。1 自由度TPR及其拓扑结构描述1.1体系结构描述新型二平动自由度并联机器人，其原理图如图1所示。机器人的末端执行器通过两只运动腿部1和2连接到底座。腿1包括三个转动关节和腿的2个转动关节和一个气缸，或三蜗壳接头和一个棱柱关节-在每一个回合，重新蜗壳接头相互平行。轴的转动关节的腿1是正常的关节的腿2。双关节连接

45、的末端放在相邻两边的平方。运动链的机器人是指作为rrr-rrc（c-cylinder联合）或rrr-rrrp，可以看到，如果该接头固定，该机器人机构盟友著名的Sarrus机制。据介绍，其他TPRS在其结构中至少有一个平行四边形的结构。这里提出的TPR没有还原。这使得制造更容易。然而，相比TPRS在REFO中提出的， 9,10，TPR研究在这里有一些缺点。例如，新的TPR的性能在其工作区中是不对称的。此外，新的TPR可能需要更多的占用空间。（a）模型 （b）示意图图1 二自由度平动并联机器人 1.2 能力在这里，表达像是分别用来描述对象j的能力。在，和分别表示对象的平移或旋转。如果中的元素是等于

46、0，则没有这样的平移或旋转。如果它等于1，则有能力。例如，表示对象没有沿x-axis 翻译；表示对象可以关于y-axis轴旋转。只观察1只腿，结束在腿部效应的能力，可以表示为。仅让腿1，腿2的最终效应的能力，可以写成。然后，和的交集是，即 （1）它描述了机器人的能力，例如，沿X和Y轴的翻译最终效应。这意味着最终效应有两个纯粹的平移自由度方面的基础。值得注意的是，上面使用的能力分析方法并不适用于所有的并联机器人。2 运动学分析2.1逆运动学如图1（b）所示，参照系：O-xy是固定的连接点一个移动的参照系：附加到最终效应，是参考点的最终效应。向量被定义在坐标系中点的位置向量，向量为在的位置向量。机

47、器人的几何参数为，从点到导轨的距离是, 和三维参数，和无量纲参数。点，在固定的帧的位置，表示为向量 （2）可以在固定的参照系的载体写成 （3）其中为驱动的输入腿1。在固定的帧的矢量可以写成 （4）腿部1的逆运动学问题解决了下面的约束方程的写法 （5）这是 （6）然后，有 （7）这里 （8）对于腿2，这里很明显s=x （9）其中S是输入的腿2。从式（8）和（9）我们可以看到，机器人的逆运动学有两种解决方案。因此，对于一个给定的机器人和规定值的位置的最终效应，所需的驱动输入，可直接由式（7）和（9）计算。为了获得配置如图1所示，参数在（8）式中应为1。这种配置被称为“+”的工作模式。当，相应的配置

48、被称为“ - ”工作模式。2.2 正向运动学正向运动学问题获得输出就成立一个给定的输入。环境质量标准。（6）和（9），一个获得 （11）与x=s （12）其中 和。因此，机器人正向运动也有两个解决方案。如图1所示，这是记下配置的参数或响应配置参数。当被称为配置为最多配置。这两种配置对应两个种机器人的组装模式。3 奇异性分析4 工作空间分析5 结论和未来的工作在本文提出了一种新型二平动自由度机器人的建议。机器人的一个特点是，它可以放置在二维平面上的刚体，同时保持一个恒定的方向。该机器人具有潜在的应用在轻工业。这里介绍了逆向和正向运动学问题的工作空间和奇异性。今后的工作将集中在工作区的概念为基础的

49、运动设计，提出设计方法，开发的机器人原型，原型的经验研究为基础的机器人计算机辅助设计的发展。References：1Stewart D.A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers,1965(180):371-3862Hunt KH. Structural kinematics of in-parallel-actuated robotarms. ASME Journal of Mechanism, Transmission and Automation in Design,1983