（節(jié)選）外文翻譯---新型二自由度平動(dòng)并聯(lián)機(jī)器人的結(jié)構(gòu)和運(yùn)動(dòng)學(xué)分析

1、<p>　　附錄（一） 英文文獻(xiàn)</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(xiàn)翻譯</p><p>　　新型二自由度平動(dòng)并聯(lián)機(jī)器人的結(jié)構(gòu)和運(yùn)動(dòng)學(xué)分析</p><p>　　陳濤1，吳超2，劉學(xué)軍2**</p><p>　　(1. 應(yīng)用科

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

53、，速度，和奇異點(diǎn)。對(duì)工作和裝配方式進(jìn)行了討論。因?yàn)閷?duì)于設(shè)計(jì)機(jī)器人它是個(gè)重要的指標(biāo)，本文對(duì)機(jī)器人的工作空間做了系統(tǒng)的研究。以可達(dá)工作空間和奇異性的分析為基礎(chǔ)，描述機(jī)器人末端效應(yīng)可以達(dá)到在實(shí)踐中被定義的區(qū)域。本文的結(jié)果將對(duì)機(jī)器人的設(shè)計(jì)和應(yīng)用非常有用。</p><p>　　關(guān)鍵詞：并聯(lián)機(jī)器人，自由度，運(yùn)動(dòng)學(xué)工作空間。</p><p>　　并聯(lián)機(jī)器人的概念設(shè)計(jì)，可以追溯到高夫建立的基本原則，一個(gè)閉

54、環(huán)的運(yùn)動(dòng)結(jié)構(gòu)，可以生成指定的位置和方向的移動(dòng)平臺(tái)，以測試輪胎的磨損?；谶@個(gè)原則，1965年斯圖爾特設(shè)計(jì)了一個(gè)用作飛機(jī)模擬器的平臺(tái)。 1978年，亨特對(duì)并聯(lián)機(jī)器人作了系統(tǒng)的研究，其中空間3-RPS（R–轉(zhuǎn)動(dòng)關(guān)節(jié)，P-移動(dòng)關(guān)節(jié)，和S-球形關(guān)節(jié)）并聯(lián)機(jī)器人是典型的一個(gè)。自那時(shí)以來，并聯(lián)機(jī)器人被眾多研究者廣泛研究。</p><p>　　6自由度并聯(lián)機(jī)器人具有高剛度，低慣量，大載荷能力。然而，他們受到相對(duì)較小的

55、有益的工作空間的問題和設(shè)計(jì)上的困難。他們的正向運(yùn)動(dòng)有一個(gè)非常困難的問題。在一個(gè)封閉的形式下2和3自由度并聯(lián)機(jī)器人也有同樣的問題。.眾所周知，并聯(lián)機(jī)器人中有3種類型的奇異點(diǎn)。一般來說，一個(gè)6自由度并聯(lián)機(jī)器人所有的奇異點(diǎn)并不是都能被容易地發(fā)現(xiàn)。而對(duì)于2或3自由度的并聯(lián)機(jī)器人，奇異點(diǎn)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(jī)器人，尤其是2和3自由度并聯(lián)機(jī)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(jì)中，三自由度

56、平動(dòng)并聯(lián)機(jī)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(jī)器人的設(shè)計(jì)是由一個(gè)擁有36項(xiàng)專利的家庭來承擔(dān)的。蔡（Tsai）的機(jī)器人，每三條腿構(gòu)成一個(gè)平行四邊形，是第一個(gè)解決支原體鏈問題的設(shè)計(jì)。這種并聯(lián)機(jī)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(jī)器和醫(yī)療設(shè)備。</p><p>　　最有名的平面2自由度并聯(lián)機(jī)器人是眾所周知的五桿棱柱驅(qū)動(dòng)器或旋轉(zhuǎn)驅(qū)動(dòng)器的機(jī)制。在帶有旋轉(zhuǎn)驅(qū)動(dòng)器的機(jī)器人的情況下，該機(jī)

57、制由五個(gè)轉(zhuǎn)動(dòng)副和兩個(gè)固定在底座上被啟動(dòng)的關(guān)節(jié)組成，而在帶有棱柱驅(qū)動(dòng)器的機(jī)器人的情況下，該機(jī)制包括三個(gè)轉(zhuǎn)動(dòng)副和兩個(gè)柱狀關(guān)節(jié)，通常柱狀關(guān)節(jié)是被啟動(dòng)的。機(jī)器人的輸出是一個(gè)末端執(zhí)行器上一個(gè)點(diǎn)的平移運(yùn)動(dòng)。這意味著在任何時(shí)刻末端執(zhí)行器的方向也會(huì)改變。因此，一些2自由度平動(dòng)并聯(lián)機(jī)器人（TPR）的版本已披露。其中一個(gè)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(gè)2自由度的TPR已提出的5軸機(jī)床的概念設(shè)計(jì)。TPR的結(jié)構(gòu)，運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)

58、進(jìn)行了詳細(xì)討論。最近，一個(gè)帶有旋轉(zhuǎn)驅(qū)動(dòng)器的2自由度的TPR被采用。參考文獻(xiàn)陳述的TPR已經(jīng)用于龍門機(jī)床的設(shè)計(jì)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(gè)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(yùn)動(dòng)結(jié)構(gòu)的平動(dòng)并聯(lián)機(jī)器人。機(jī)器人定位一個(gè)恒定方向的目標(biāo)。討論了一些運(yùn)動(dòng)學(xué)問題，如逆向和正向運(yùn)動(dòng)學(xué)，工作空

59、間和奇異點(diǎn)。</p><p>　　1 自由度TPR及其拓?fù)浣Y(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(dòng)自由度并聯(lián)機(jī)器人，其原理圖如圖1所示。機(jī)器人的末端執(zhí)行器通過兩只運(yùn)動(dòng)腿部1和2連接到底座。腿1包括三個(gè)轉(zhuǎn)動(dòng)關(guān)節(jié)和腿的2個(gè)轉(zhuǎn)動(dòng)關(guān)節(jié)和一個(gè)氣缸，或三蝸殼接頭和一個(gè)棱柱關(guān)節(jié)-在每一個(gè)回合，重新蝸殼

60、接頭相互平行。軸的轉(zhuǎn)動(dòng)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(yùn)動(dòng)鏈的機(jī)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(jī)器人機(jī)構(gòu)盟友著名的Sarrus機(jī)制。</p><p>　　據(jù)介紹，其他TPRS在其結(jié)構(gòu)中至少有一個(gè)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(diǎn)。例如，新的TPR的性能在其工作區(qū)中是不對(duì)稱的。此外，新的TPR可能需要更多的占用空間。</p><p>　?。╝）模型 （b）示意圖</p><p>　　圖1 二自由度平動(dòng)并聯(lián)機(jī)器人 </p><p><b>　　1.2 能力</b></p>&

62、lt;p>　　在這里，表達(dá)像是分別用來描述對(duì)象j的能力。在，和分別表示對(duì)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(duì)象沒有沿x-axis 翻譯；表示對(duì)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(jī)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(gè)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(jī)器人。</p><p><b>　　2 運(yùn)動(dòng)學(xué)分析</b></p><p><b>　　2.1逆運(yùn)動(dòng)學(xué)&

64、lt;/b></p><p>　　如圖1（b）所示，參照系：O-xy是固定的連接點(diǎn)一個(gè)移動(dòng)的參照系：附加到最終效應(yīng)，是參考點(diǎn)的最終效應(yīng)。向量被定義在坐標(biāo)系中點(diǎn)的位置向量，向量為在的位置向量。機(jī)器人的幾何參數(shù)為，，，，，從點(diǎn)到導(dǎo)軌的距離是, 和三維參數(shù)，和無量綱參數(shù)。點(diǎn)，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(dòng)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(yùn)動(dòng)學(xué)問題解決了下面的約束方程的寫法</p>

66、<p><b>　　（5）</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(duì)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(jī)器人的逆運(yùn)動(dòng)學(xué)有兩種解決方案。因此，對(duì)于一個(gè)

68、給定的機(jī)器人和規(guī)定值的位置的最終效應(yīng)，所需的驅(qū)動(dòng)輸入，可直接由式（7）和（9）計(jì)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(dāng)，相應(yīng)的配置被稱為“ - ”工作模式。</p><p><b>　　2.2 正向運(yùn)動(dòng)學(xué)</b></p><p>　　正向運(yùn)動(dòng)學(xué)問題獲得輸出就成立一個(gè)給定的輸入。環(huán)境質(zhì)量標(biāo)準(zhǔn)。（6）和（9），一個(gè)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(jī)器人正向運(yùn)動(dòng)也有兩個(gè)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(dāng)被稱為配置為最多配置。這兩種配置對(duì)應(yīng)兩個(gè)種機(jī)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(dòng)自由度機(jī)器人的建議。機(jī)器人的一個(gè)特點(diǎn)是，它可以放置在二維平面上的剛體，同時(shí)保持一個(gè)恒定的方向。該

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