（節(jié)選）外文翻譯---新型二自由度平動并聯(lián)機器人的結(jié)構(gòu)和運動學分析

1、<p>　　附錄（一） 英文文獻</p><p>　　Structure and kinematic analysis of </p><p>　　a novel 2-DOF translational parallel robot</p><p>　　Chen Tao1．Wu Chao2 and Liu xiujun2**</p><

2、p>　　( 1. School of Application Science and Technology．Harbin University of Science</p><p>　　And Technology，Harbin l50080,China；2. Department of Precision Instruments．Tsinghua University, Beijing 100084, C

3、hina)</p><p>　　Accepted on February 13, 2007</p><p>　　Abstract This paper addresses the analysis of a novel parallel robot with 2 translational degrees of freedom (DOFs). The robot can position

4、a rigid body in a plane with constant orientation. The kinematic structure of the robot is first described in detail, Some kinematic problems, such as the inverse and forward kinematics, velocity, and singularity are the

5、n analyzed. The working and assembly modes are discussed. Since it is the most important index to design a robot , the workspace of the robo</p><p>　　Keywords： parallel robot, degree of freedom, kinematics w

6、orkspace. </p><p>　　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 spe

7、cified position and orientation of a moving platform so as to test tire wear and. tear. Based on this principle, Stewart designed a platform used as an aircraft simulator in 1965. In 1978, Hunt made a systematic study of

8、 robots with parallel kinematics, in which the spatial 3-RPS (R-revolute joint，P-prismatic jo</p><p>　　The parallel robots with 6 DOFs possess the ad-vantages of high stiffness, low inertia, and large payloa

9、d capacity. However, they suffer the problems of relatively small useful workspace and design difficulties .Their direct kinematics possess a very difficult problem. The same problem of parallel robots with 2 and 3 DOFs

10、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</p><p>　　The most famous plana

11、r 2-DOF parallel robots are the well-known five-bar mechanism with prismatic actuators or revolute actuators. In the case of the robot with revolute actuators, the mechanism consists of five re volute pairs and the two j

12、oints 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 joints are usually actuated.

13、The output of the robot is the translat</p><p>　　This paper introduces a novel planar translational parallel robot with simple kinematic structure. The robot can position an objective with constant orientati

14、on. Some kinematic problems, such as inverse and forward kinematics, workspace and singularity are discussed.</p><p>　　1Description of the 2-DOF TPR and its topological architectures</p><p>　　1

15、.1Architecture description</p><p>　　The 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.

16、Leg 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 t

17、he revolute joints in leg 1 are normal to those of the joints in leg 2. The two joints attached to the end-eff</p><p>　　As introduced previously，other TPRs have at least one parallelogram in their structures

18、. 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 th

19、e new TPR is not symmetric in its workspace. Additionally, the new TPR is likely to need more occupying space.</p><p>　　(a) the CAD model (b) the schematic</p><p>　　Fig.1 The 2-

20、DOF translational parallel robot</p><p>　　1.2Capability</p><p>　　Here, an expression like is used to describe the capability of an object j. In , and express the translation and rotation of t

21、he object, 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;

22、 indicates that the object can rotate about the y-axis.</p><p>　　Observing only leg 1, the capability of the end-effector in the leg can be expressed as . Letting leg 1 alone, the capability of the end-effe

23、ctor with leg 2 can be written as Then, the intersection of and is ， i. e,,</p><p><b>　　(1)</b></p><p>　　which describes the capability of the robot, i.e., the translations of th

24、e end-effector along the x and y axes. This means the end-effector has two purely translational degrees of freedom with respect to the base.</p><p>　　It is noteworthy that the capability analysis method used

25、 above cannot be applied to all parallel robots.</p><p>　　2Kinematics analysis</p><p>　　2.1Inverse kinematics</p><p>　　As illustrated in Fig. 1(b), a reference frame :O-xy is fix

26、ed 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 ，

27、and vectors as the position vectors of points in frame .The geometric parameters of the robot are ，，，，，and the distance from point to the guideway is ,where and and are dimensional parameters, and and non-dimens

28、</p><p><b>　　(2)</b></p><p>　　The vectors of in the fixed frame can be written as</p><p><b>　　(3)</b></p><p>　　where is the actuated input fo

29、r leg 1. Vector in the fixed frame can be written as</p><p><b>　　(4)</b></p><p>　　The inverse kinematics problem of leg 1 can be solved by writing the following constraint equation

30、</p><p><b>　　(5)</b></p><p><b>　　that is</b></p><p><b>　　(6)</b></p><p>　　Then, there is</p><p><b>　　(7)</b>

31、;</p><p><b>　　where</b></p><p><b>　　(8)</b></p><p>　　For leg 2，it is obvious that</p><p><b>　　s = x(9)</b></p><p>　　in

32、 which s is the input of leg 2. From Eqs. (8) and (9), we can see that there are two solutions for the inverse kinematics of the robot. Hence, for a </p><p>　　given robot and for prescribed values of the pos

33、ition 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) should be 1. This configuration is called the

34、 “ + ” working mode. When , the corresponding configuration is referred to as the “一” working mode.</p><p>　　2.2Forward kinematics</p><p>　　The forward kinematic problem is to obtain the outpu

35、t with respect to a set of given inputs. From Eqs. (6) and (9),one obtains</p><p><b>　　(11)</b></p><p><b>　　and</b></p><p>　　x = s(12)</p><p>　

36、　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

37、 is referred to as the up-configuration. These two kinds of configurations correspond to two kinds of assembly modes of the robot.</p><p>　　3Singularity analysis</p><p>　　4Workspace analysis&l

38、t;/p><p>　　5Conclusion and future work</p><p>　　In 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 wh

39、ile maintaining a constant orientation. The proposed robot has potential application in light industry. The inverse and forward kinematics problems’ workspace* and singularity are presented here.</p><p>　　Th

40、e future work will focus on the kinematic design based on the workspace concept, the development of the computer-aided design of the robot based on the proposed design methodology, the development of the robot prototype,

41、 and the experience research of the prototype.</p><p>　　References：</p><p>　　[1]Stewart D.A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers,1965(180)

42、:371-386</p><p>　　[2]Hunt KH. Structural kinematics of in-parallel-actuated robotarms. ASME Journal of Mechanism, Transmission and Automation in Design,1983,105:705-712</p><p>　　[3]Merlet JP. Pa

43、rallel Robots. London: Kluwer Academic Publishers,2000</p><p>　　[4]Liu XJ.Mechanical and kinematics design of parallel robotic mechanisms with less than six degrees of freedom.Post-Doctoral Research Report (

44、in Chinese),Tsinghua University,Beijing,2001</p><p>　　[5]Tsai LW and Stamper R.A parallel manipulator with only translational degrees of freedom.In: Proceedings of ASME 1996 Design Engineering Technical Conf

45、erence,Irvine,CA,1996,paper 96-DETC-MECH-1152</p><p>　　[6]Siciliano B.The tricept robot:inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm.Robotica,1999,17:437-445</p&

46、gt;<p>　　[7]Liu XJ,Wang QM and Wang J.Kinematics, dynamics and dimensional synthesis of a novel 2-DoF translational manipulator. Journal of Intelligent & Robotic Systems,2005,41:205-224</p><p>　　[

47、8]Clavel R.DELTA: a fast robot with parallel geometry.In: Proceedings of 18th Int. Symp. on Industrial Robot,Sydney,1988,91-100</p><p>　　[9]Collaborative Research Centers (SFB),SFB 562-Robotic systems for ha

48、ndling and assembly:Seitentitel:PORTYS,http://www.tu-braunschweig.de/sfb562/galerie/portys,2007-2-13</p><p>　　[10]Liu XJ and Wang J. Some new parallel mechanisms containing the planar four-bar parallelogram.

49、 International Journal of Robotics Research,2003,22:717-732</p><p>　　[11]Huang T, Li Z,Li M,et al. Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-andplace

50、operations. Journal of Mechanical Design,2004,126:449-455</p><p>　　[12]Sarrus PT.Note sur la Transformation des Mouvements Rctilignes Alternatifs,en Mouvements Circulairs; et Reciproquement.Comptes Rendus He

51、bdomadaires des Seances de l' Academie des Sciences,1853,36:1036-1038</p><p>　　附錄（二） 英文文獻翻譯</p><p>　　新型二自由度平動并聯(lián)機器人的結(jié)構(gòu)和運動學分析</p><p>　　陳濤1，吳超2，劉學軍2**</p><p>　　(1. 應(yīng)用科

52、學和技術(shù)學院，哈爾濱理工大學，哈爾濱150080，中國;</p><p>　　2. 精密儀器系，清華大學，北京100084，中國)</p><p>　　2007年2月13日，接受</p><p>　　摘要:本文對一種新型的二自由度并聯(lián)機器人進行分析。機器人可以放置在一個固定方向的平面剛體。首先詳細介紹了機器人的運動結(jié)構(gòu)，然后分析了一些運動的問題，如正向和逆向的運動學

53、，速度，和奇異點。對工作和裝配方式進行了討論。因為對于設(shè)計機器人它是個重要的指標，本文對機器人的工作空間做了系統(tǒng)的研究。以可達工作空間和奇異性的分析為基礎(chǔ)，描述機器人末端效應(yīng)可以達到在實踐中被定義的區(qū)域。本文的結(jié)果將對機器人的設(shè)計和應(yīng)用非常有用。</p><p>　　關(guān)鍵詞：并聯(lián)機器人，自由度，運動學工作空間。</p><p>　　并聯(lián)機器人的概念設(shè)計，可以追溯到高夫建立的基本原則，一個閉

54、環(huán)的運動結(jié)構(gòu)，可以生成指定的位置和方向的移動平臺，以測試輪胎的磨損。基于這個原則，1965年斯圖爾特設(shè)計了一個用作飛機模擬器的平臺。 1978年，亨特對并聯(lián)機器人作了系統(tǒng)的研究，其中空間3-RPS（R–轉(zhuǎn)動關(guān)節(jié)，P-移動關(guān)節(jié)，和S-球形關(guān)節(jié)）并聯(lián)機器人是典型的一個。自那時以來，并聯(lián)機器人被眾多研究者廣泛研究。</p><p>　　6自由度并聯(lián)機器人具有高剛度，低慣量，大載荷能力。然而，他們受到相對較小的

55、有益的工作空間的問題和設(shè)計上的困難。他們的正向運動有一個非常困難的問題。在一個封閉的形式下2和3自由度并聯(lián)機器人也有同樣的問題。.眾所周知，并聯(lián)機器人中有3種類型的奇異點。一般來說，一個6自由度并聯(lián)機器人所有的奇異點并不是都能被容易地發(fā)現(xiàn)。而對于2或3自由度的并聯(lián)機器人，奇異點總是可以很容易確定。由于這樣的原因，少于6自由度的并聯(lián)機器人，尤其是2和3自由度并聯(lián)機器人，在工業(yè)應(yīng)用方面已經(jīng)越來越吸引更多的研究者的關(guān)注。在這些設(shè)計中，三自由度

56、平動并聯(lián)機器人在工業(yè)應(yīng)用中一直起著重要的作用。例如，三角洲（DELTA）機器人的設(shè)計是由一個擁有36項專利的家庭來承擔的。蔡（Tsai）的機器人，每三條腿構(gòu)成一個平行四邊形，是第一個解決支原體鏈問題的設(shè)計。這種并聯(lián)機器人在工業(yè)界廣泛應(yīng)用，比如拾取和放置的應(yīng)用，并聯(lián)機器和醫(yī)療設(shè)備。</p><p>　　最有名的平面2自由度并聯(lián)機器人是眾所周知的五桿棱柱驅(qū)動器或旋轉(zhuǎn)驅(qū)動器的機制。在帶有旋轉(zhuǎn)驅(qū)動器的機器人的情況下，該機

57、制由五個轉(zhuǎn)動副和兩個固定在底座上被啟動的關(guān)節(jié)組成，而在帶有棱柱驅(qū)動器的機器人的情況下，該機制包括三個轉(zhuǎn)動副和兩個柱狀關(guān)節(jié)，通常柱狀關(guān)節(jié)是被啟動的。機器人的輸出是一個末端執(zhí)行器上一個點的平移運動。這意味著在任何時刻末端執(zhí)行器的方向也會改變。因此，一些2自由度平動并聯(lián)機器人（TPR）的版本已披露。其中一個版本已被應(yīng)用于德國SFB高速的精確的拾放操作。在2001年，另一個2自由度的TPR已提出的5軸機床的概念設(shè)計。TPR的結(jié)構(gòu)，運動學和動力學

58、進行了詳細討論。最近，一個帶有旋轉(zhuǎn)驅(qū)動器的2自由度的TPR被采用。參考文獻陳述的TPR已經(jīng)用于龍門機床的設(shè)計中，用的是龍門式結(jié)構(gòu)，而不是用傳統(tǒng)的串行鏈，以此來提高其剛度和慣性特征。然而，所有這些TPRS包括至少一個平行四邊形，從而增加了制造的難度和影響精度。</p><p>　　本文介紹了一種新型的可以用簡單的運動結(jié)構(gòu)的平動并聯(lián)機器人。機器人定位一個恒定方向的目標。討論了一些運動學問題，如逆向和正向運動學，工作空

59、間和奇異點。</p><p>　　1 自由度TPR及其拓撲結(jié)構(gòu)描述</p><p><b>　　1.1體系結(jié)構(gòu)描述</b></p><p>　　新型二平動自由度并聯(lián)機器人，其原理圖如圖1所示。機器人的末端執(zhí)行器通過兩只運動腿部1和2連接到底座。腿1包括三個轉(zhuǎn)動關(guān)節(jié)和腿的2個轉(zhuǎn)動關(guān)節(jié)和一個氣缸，或三蝸殼接頭和一個棱柱關(guān)節(jié)-在每一個回合，重新蝸殼

60、接頭相互平行。軸的轉(zhuǎn)動關(guān)節(jié)的腿1是正常的關(guān)節(jié)的腿2。雙關(guān)節(jié)連接的末端放在相鄰兩邊的平方。運動鏈的機器人是指作為rrr-rrc（c-cylinder聯(lián)合）或rrr-rrrp，可以看到，如果該接頭固定，該機器人機構(gòu)盟友著名的Sarrus機制。</p><p>　　據(jù)介紹，其他TPRS在其結(jié)構(gòu)中至少有一個平行四邊形的結(jié)構(gòu)。這里提出的TPR沒有還原。這使得制造更容易。然而，相比TPRS在REFO中提出的， [9,10]

61、，TPR研究在這里有一些缺點。例如，新的TPR的性能在其工作區(qū)中是不對稱的。此外，新的TPR可能需要更多的占用空間。</p><p>　　（a）模型 （b）示意圖</p><p>　　圖1 二自由度平動并聯(lián)機器人 </p><p><b>　　1.2 能力</b></p>&

62、lt;p>　　在這里，表達像是分別用來描述對象j的能力。在，和分別表示對象的平移或旋轉(zhuǎn)。如果中的元素是等于0，則沒有這樣的平移或旋轉(zhuǎn)。如果它等于1，則有能力。例如，表示對象沒有沿x-axis 翻譯；表示對象可以關(guān)于y-axis軸旋轉(zhuǎn)。</p><p>　　只觀察1只腿，結(jié)束在腿部效應(yīng)的能力，可以表示為。僅讓腿1，腿2的最終效應(yīng)的能力，可以寫成。然后，和的交集是，即</p><p>&

63、lt;b>　?。?）</b></p><p>　　它描述了機器人的能力，例如，沿X和Y軸的翻譯最終效應(yīng)。這意味著最終效應(yīng)有兩個純粹的平移自由度方面的基礎(chǔ)。值得注意的是，上面使用的能力分析方法并不適用于所有的并聯(lián)機器人。</p><p><b>　　2 運動學分析</b></p><p><b>　　2.1逆運動學&

64、lt;/b></p><p>　　如圖1（b）所示，參照系：O-xy是固定的連接點一個移動的參照系：附加到最終效應(yīng)，是參考點的最終效應(yīng)。向量被定義在坐標系中點的位置向量，向量為在的位置向量。機器人的幾何參數(shù)為，，，，，從點到導(dǎo)軌的距離是, 和三維參數(shù)，和無量綱參數(shù)。點，在固定的幀的位置，表示為向量</p><p><b>　?。?）</b></p>

65、<p>　　可以在固定的參照系的載體寫成</p><p><b>　?。?）</b></p><p>　　其中為驅(qū)動的輸入腿1。在固定的幀的矢量可以寫成</p><p><b>　?。?）</b></p><p>　　腿部1的逆運動學問題解決了下面的約束方程的寫法</p>

66、<p><b>　?。?）</b></p><p><b>　　這是</b></p><p><b>　?。?）</b></p><p><b>　　然后，有</b></p><p><b>　?。?）</b></p&

67、gt;<p><b>　　這里</b></p><p><b>　?。?）</b></p><p>　　對于腿2，這里很明顯</p><p>　　s=x （9）</p><p>　　其中S是輸入的腿2。從式（8）和（9）我們可以看到，機器人的逆運動學有兩種解決方案。因此，對于一個

68、給定的機器人和規(guī)定值的位置的最終效應(yīng)，所需的驅(qū)動輸入，可直接由式（7）和（9）計算。為了獲得配置如圖1所示，參數(shù)在（8）式中應(yīng)為1。這種配置被稱為“+”的工作模式。當，相應(yīng)的配置被稱為“ - ”工作模式。</p><p><b>　　2.2 正向運動學</b></p><p>　　正向運動學問題獲得輸出就成立一個給定的輸入。環(huán)境質(zhì)量標準。（6）和（9），一個獲得<

69、;/p><p><b>　?。?1）</b></p><p><b>　　與</b></p><p>　　x=s （12）</p><p>　　其中 和。因此，機器人正向運動也有兩個解決方案。如圖1所示，這是記下配置的參數(shù)或響應(yīng)配置參數(shù)。當被稱為配置為最多配置。這兩種配置對應(yīng)兩個種機器人的組裝模式

70、。</p><p><b>　　3 奇異性分析</b></p><p><b>　　4 工作空間分析</b></p><p>　　5 結(jié)論和未來的工作</p><p>　　在本文提出了一種新型二平動自由度機器人的建議。機器人的一個特點是，它可以放置在二維平面上的剛體，同時保持一個恒定的方向。該

71、機器人具有潛在的應(yīng)用在輕工業(yè)。這里介紹了逆向和正向運動學問題的工作空間和奇異性。</p><p>　　今后的工作將集中在工作區(qū)的概念為基礎(chǔ)的運動設(shè)計，提出設(shè)計方法，開發(fā)的機器人原型，原型的經(jīng)驗研究為基礎(chǔ)的機器人計算機輔助設(shè)計的發(fā)展。</p><p>　　References：</p><p>　　[1]Stewart D.A platform with six de

72、grees of freedom. Proceedings of the Institution of Mechanical Engineers,1965(180):371-386</p><p>　　[2]Hunt KH. Structural kinematics of in-parallel-actuated robotarms. ASME Journal of Mechanism, Transmissio

73、n and Automation in Design,1983,105:705-712</p><p>　　[3]Merlet JP. Parallel Robots. London: Kluwer Academic Publishers,2000</p><p>　　[4]Liu XJ.Mechanical and kinematics design of parallel roboti

74、c mechanisms with less than six degrees of freedom.Post-Doctoral Research Report (in Chinese),Tsinghua University,Beijing,2001</p><p>　　[5]Tsai LW and Stamper R.A parallel manipulator with only translational

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