外文翻译--具有2或3个自由度的对应机械手【中英文文献译文】
外文翻译-具有2或3个自由度的对应机械手【中英文文献译文】,中英文文献译文,外文,翻译,具有,拥有,具备,或者,自由度,对应,机械手,中英文,文献,译文
附录A译文具有2或3个自由度的对应机械手克里斯蒂安J.J.帕雷迪斯, H .本杰明K布朗,普拉迪普.科斯拉摘要为了更好的应用,机床工业的对应机械手获得了广泛的研究,然而,有限的工作空间,较差的灵活性,复杂对应机械手的难于设计,导致人们把目光投向于少于6个自由度的对应机械手,本篇论文描述了几个在自由度的数量和类型上都不相同的对应机械手,这些对应机械手可被用语对应运动机器,运动模拟器和工业机器人。关键词:对应机械手;对应运动机械;机器人引言允许一个刚体可相对于固定底座运动的机构,在许多领域扮演着许多非常重要的角色。一个刚体可以有几个平移和旋转与动,该平移和旋转与动称为刚体的自由度。刚体的自由度最多6个。也就是说,对于3个互相垂直的坐标轴的3个平移,和3个旋转。一个机器人包含一个系统,用以控制末端受动器的数个自由度。最近几年,有证据显示,工业机器人,因其灵活性,在应用上得到了推广。然而,普通的机器人却不能用来完成某些任务,因此,最近为了工业上的使用,其他类似的机构,包括对应机械手得到了发展。一种对应机械手,即一个由几个连接杆构成的封闭环机构,通常包含一个运动平台,若干下肢或腿,后者把运动平台连接到固定基础上。通常,下肢的数量等于自由度的数量。一个下肢受一个驱动装置控制,所有的驱动装置安装在固定基础上或其附近,对应机械手有时也称作平台机构,因为外部载荷能被各驱动装置分担,对应机械手具有较大的承载能力。它常用于要求精度高,刚性好,和承载能力大的场合,他们在航天和航行模拟器上都得到了广泛的应用,在机床工业的知名度也越来越大。图1平行操纵器的早期失效对应机械手概念的提出可追溯到1947年,那时,高夫创立了有一个封闭环的运动机构的基础原理,在那时,是为了在测试轮胎磨损时,控制运动平台的位置和方向。在1955年,他创立了一个模型(图1),在该模型里,受动器是一个六角平台。他的6个顶点,分别以球型铰链形式,与连接杆相连。连接杆的另一端,以通用的铰链连接,连接到基础上。6个线性驱动装置可调整连接杆的长度。斯图尔特,在1965年,设计了一个平台机构,作为一个飞行起模拟器(图1b),在其中,受动器是一个三角平台,它的顶点同样,用球型铰链连一连接杆,连接到支持机构上,每个支持机构喊又2个支撑杆,支撑机构是三角形布置。在1978年,亨特,以空间3-RPS对应机械手为例,对对应机械手的运动机制做了体统的研究。从那时起,又有很多人多次对对应机械手记性了广泛的研究。直到如今,所研究的大多数是6-自由度对应机械手,他们都有6个可伸缩的下肢。这些对应机械手具有高的刚度,低惯性,大的承载能力。然而,他们受到有限使用空间的限制,和难于设计的困扰。而且,对他们的运动也很难进行分析。因此,在工业领域,人们越来越关注少余个自由度的对应机械手。这篇论文引入了对应机械手的概念,机器分类。几扫了3种新对应机械手,新空间3-自由度对应机械手,新2-自由度平移平台,新平面3-自由度系列对应机构。2 机构的自由度机构的自由度是所需的独立参数,或输入的参数,目的是为了定义机构的结构。然而,如亨特和Lerbet所说:可动度的准则是很难定义的。典型的可动度公式忽略了某些自由度。现在,人们仍在使用Grubler的公式:M=d(n-g-1)+(1)式中,M可动度;D螺钉系统顺序数(对于平面和球型的运动,d=3;对于空间运动,d=6);n连接杆的数量,包括框架;j铰链的数量;fi第i个连接杆的自由度。3 对应机械手的分类一个刚体有6个自由度,对应机械手的自由度在2到6之间。自从第一个机械手设计开始,又推出了许多个有2到6个自由度的机械手。对文献所记载的87个驱动装置的调查显示,6个自由度的对应机械手占40%,5个自由度的占3.5%,4个自由度的占6%,3个自由度的占40%,余下的为2个自由度的。3.1 2-自由度对应机械手大多数现存的2个自由度的机械手是平面的,有2个平移自由度。这样的设计采用棱柱状的能移动的铰链。Mccloy提出了20个不同的组合。驱动器系统在地上的有6个,如图2所示。没有被动的棱柱铰链,任何一个驱动器也不承受另一个驱动器的重量。图2 平行操纵器的早期失效3.2 3-自由度对应接携手有许多3-自由度的机械手。这里只举几个典型的例子。图3a,平面3-移动铰链对应机械手。运动平台有3个平面自由度,沿X、Y轴的平移和Z轴的旋转。图3b,球面的3-铰链连接杆对应机械手。三个铰链连接杆汇交于一点。机构上任何一点的运动是绕共同焦点的旋转。图3c,3-RPS机械手,由亨特设计,有综合的自由度,很难定义。图3d,DELTA机械人,由Clave设计,由Demaurex公司和ABB,以IRB 340 Fpexpicker的名字推向市场,DELTA在工业上得到了广泛应用。图3e,有被动腿的机械手的例子,运动平台有4条腿,第4条腿是被动的,也是主要的,决定运动平台的运动,例如,本图显示的球坐标对应机械手。该对应机械手被Hannover大学的IFW用于机床设计。图3 一些三自由度平行操纵器3.3 4-自由度对应机械手对于一个4-自由度全对应机械手,d=6,n=10,g=12,M=4。把这些值代入公式(1),得出F=22/4,即每个腿有22/4的自由度。因此,实际上,不可能有4-自由度的全对应机械手。早期的4-自由度机构并不是全对应机械手,也就是说,机械手的每个连接杆配有两个驱动器或者有被动约束。3.4 5-自由度对应机械手5-自由度全对应机械手的F=29/5,所以,实际上,不可能有5-自由度的全对应机械手。由Austad提出的5-自由度对应机械手,实际上包含2个对应机械手。3.5 6-自由度对应机械手6-自由度对应机械手是最流行的,并得到广泛的研究。图4a显示的是一个典型的6-自由度对应机械手。大多数6-自由度对应机械手都有6个可伸缩的下肢。这些对应机械手具有高的刚度,低惯性,大的承载能力。然而,他们受相对小的可用空间限制和难于设计的困扰。而且,对它们的运动很难进行分析。也有一些奇特的链机械手,这些机械手被一个平面机构驱动,例如,4杆机构或5杆机构,或每条腿有两个驱动趋的,通常有3条腿。图4 大约六自由度平行操纵器4 对应机械手的评价高夫在1947年建立了如图1a所示的,有封闭环的运动机构的原理之后,推出了许多自由度数量和类型不同的对应机械手。图1b的结构是1965年由Steward设计的。图4a所示的通用机械手,从理论上讲,他的6个腿可以任意布置,设计成各种各样的6-自由度对应机械手,例如,图4b所示的,6条腿按3-2-1配置,结构紧凑,可用在微观系统。图4c所示的,是机械手按规定的方向运动自如,在工业上应用广泛。图4a所示的通用机械手,类似于Pierrot提出的,每对的两条腿互相平行。即使每一对的两条腿的输入是相同的,机械手自由度的数量也是不同的(机构不同所致)。与此相当的机械手显示在图5。该机械手输出的是3个平移,几乎是DELTA机器人的初型。驱动的连接杆可以按众所周知的,如图3d所示的,快速机器人DELTA的布置。DELTA有几个变体,例如,Pollard机构,Tsai机器人,如图3 f所示的,也是3-平移自由度对应机器人之一。虽然Tsai机器人与DELTA一样,也有3个平移,准确的说,他不是DELTA的变体。它们的设计观念是不同的,Tsai机器人是用来处理UPU链的问题的第一个设计。另一个3-平移自由度对应机器人Star是由Herve以群论为基础设计的。这些设计观念对设计新机械手提供了新的想法,后续的工作是,设计出把平移和旋转结合在一起的,自由度少于6个的机器人。例如,有不多的空间3-自由度机器人,把两个空间平移和一个旋转结合在一起,如下一节提出的。图5 空间三自由度1机械手5 新空间3-自由度对应机械手5.1 机械手结构图6(a)所示的空间三自由度并联机械手由一个底板、一个可移动平台和连接两个板的三个支腿组成。每个连接腿有四个自由度。三个支腿中的两个具有相同的链条,具有两个自由度关节(或两个1自由度关节)和两个1自由度关节。第三个支腿由一个平面四杆平行四边形和三个1自由度关节组成。每个支腿中的一个1自由度关节被启动。新空间3-自由度对应机械手,如图6(a)所示,包含:基础板运动平台(等腰三角形) 14腿 1 12 8铰链 15和3(被动) 13和11(被动) 16和5(被动)主动滑套 4 10 6导轨(固定的) 2 9 7运动平台的运动由3个滑套在导轨上滑动来实现。5.2 新空间3-自由度对应机械手的自由度当约束起作用时,,此机械手有3个自由度。腿1和12给出两个约束。即限制运动平套对Z轴的旋转和对X轴的平移。腿8的铰链5和16有2个平行轴。腿8给出一个约束,即限制对X轴的旋转。因此,3条腿结合在一起,限制了运动平台对X、Z轴的旋转,限制了对X轴的平移。因此,运动平台仅剩下3个自由度:即沿YZ轴的平移,和对Y轴的旋转。5.3 新空间3-自由度对应机械手的新颖之处和应用驱动腿8,如Star Like机器人,Tsai机械手和CaPaMan一样,采用一个平面的4-杆平行四边形结构,机构设计显得很有趣。这个独特的空间3-自由度对应机械手有3个特点:(a)仅有转动铰链,(b)把空间平移和旋转结合在一个对应机械手内,(c)绕Y轴转动的自由度具有灵活性。从实用角度,此设计使用与对应机床。由于少于6-自由度的对应机械手有低的可动度和好的适应性,越来越多的对应机床被作成混合结构,例如,Tricept和George机床,他们都是基于3-自由度对应机构。在将来,所提出的对应机械手将被应用与设计混合对应机床。该对应机构也能用于工业机器人,运动模拟器,或微机器人。图6a显示的设计,是约束过的,也就是说,加工的零件必须是高精度的。然而,球铰链可用容易加工的,精度较高上午转动铰链来代替。图6 新型空间三自由度并联多机5.4 新空间3-自由度对应机械手的逆运算逆运算即用输出平台的坐标计算输入变量的坐标。运动模型见图6b。输出平台的3个顶点用P1,P2,P3表示。基础平台的3个顶点用b1,b2,b3表示。固定球型参考系R:O-xyz,原点O在边b1b2中心,z轴垂直于基础平面,y轴沿b1,b2。另一个参考系,称为顶架,R:O-xyz,原点O在边P1P2的中心,z轴垂直于输出平台,y轴沿P1,P2。3个连接杆的长度L1,L2,L3,相等,为L,有时L3不等于L1,L2。假定,运动平台的笛卡儿参考系原点坐标在R:O-xyz是已知的,即 OR =(x y z)T (2)式中,x=0,方向由矩阵Q给出,Q= (3)式中,角度是输出平台对y轴的转角。P1,P2,P3在参考系R的坐标用向量P1R,P2R,P3R表示,p1R=(0 r 0)Tp2R=(0 r 0)Tp3R=(r 0 0)T (4)向量P1R,P2R,P3R用基础铰链在参考系R的位置向量定义, b1R=(0 R z1)T b2R=(0 R z2)Tb3R=(R 0 z3)T (5)向量P1R,P2R,P3R在参考系O-xyz可写为, pim=QpiR + OR (6)那么,对应机械手的逆运动能用下列限定公式求解,=L ,i=1,2,3 (7)因此,对于给顶的机械手,给顶的运动平台的方向值,需要的驱动器输入可从公式(7)直接计算出,z1=(8) z2=(9) = (10)从公式(8)-(10),可以看出对于一个对应机械手的给顶方位。有8个逆运算解。为了得到如图6的逆结构,公式中的三个“”符号都应该取“+”6 其他对应机构6.1 新2-自由度平移平台新型两自由度并联机构如图7a所示。机构示意图如图76所示,其中底座标记为1,移动平台标记为2。移动平台通过两个相同的支腿与底座相连。每个支腿由一个平面四杆平行四边形组成:第一支腿的连杆2、3、4和5,第二支腿的连杆2、6、7和8。每个平面四杆平行四边形中的关节都是转动副。连杆3和8由棱柱型执行机构驱动。平台运动是通过两个平行四边形传送到平台的连杆3和8的运动来实现的。由于四杆平面平行四边形的存在,移动平台相对于底座有两个纯平移自由度。由于在本设计中只需一个平面四杆平行四边形就可获得两个刚体自由度,因此系统受到了过度约束。采用两个平面四杆平行四边形来提高系统的刚度,使系统对称。目前,该机构正与中国齐齐哈尔第二刀具厂合作开发一种新型五轴机床。图7 新型平面二自由度并联机床图8 三自由度平面串并联机构6.2 平面3-自由度系列对应机构图8显示该机构运动平台有两条腿。右边的腿,下部与转动铰链连接,上部与被动转动铰链连接。被动铰链通过棱柱铰链与基础连接。左边的腿,完全不同于右边的,是一个可变的四边形,其一边是可伸缩的,目的是变更运动平台的方位。四条边,通过转动铰链互相连接。四边形与基础的连接是靠棱柱铰链。该机构正被用于与江东机床厂合作开发新型6-轴机床。7 结论这篇论文给出了对应机械手和其自由度的定义。讨论了三种类型的新对应机械手,新空间3-自由度对应机械手,新兴2-自由度平移平台,3-自由度平面系列对应机构,这些设计的后两个正被机床工业的开发设计所采用。确认作者感谢王爱民博士和李剑峰博士的讨论,感谢唐秀强博士对三自由度平面串并联机构的贡献。参考文献1 GoughV.E.对汽车稳定性、控制和轮胎性能研究论文的讨论做出了贡献.:Proc.汽车.Div.本月,马赫.1956:392一395.2 英国白厅通用轮胎试验机.;第九届国际汽车技术大会,伦敦,1962年,117:117一135.3 斯图尔特D.一个有六个自由度的平台;Proc.本月,机械.Eng.伦敦,1965年.180;371一386.4 寻找机构的运动学几何.牛津:克拉伦登出版社,1978年.5 Merlet J-P,平行机器人.伦敦;Kluwer学术出版社,2000年6 包络费米的刚体刚体组成的勒贝力学论文.1987年6月19日,巴黎.(中文)7 Merlet j.http:/www-sop.inria.fr coprin /运动队及其装备/ merlet merlet一eng.html, 2001.8 McCloy.D.serial-driven和并行驱动机械手的一些比较,Roboteca, 1990, 8: 355一3 fi2.9 Clavel R. DELTA:一个具有平行几何结构的快速机器人.;18 Int.计算机协会,工业机器人,1988年4月:91一100.10 本文介绍了一种新型混合机械手的结构和特点.布尔CR,莫利纳里-托萨蒂L,史密斯KS,合编.平行运动机械,斯普林拉格伦敦有限公司,1999;3 fi5一376.11 Arm设备.IPN,不.6月4日,WO 87.03239.1987.12 平行机器人和微型机器人.ISRAM 96年,蒙彼利埃1996:535 542.13 Pierrot F.机器人褶皱与leger平行;概念建模等命令.蒙彼利埃;蒙彼利埃第二大学,1991年4月24日.(中文)14 波拉德液位控制装置.美国专利2286571,1942年6月16日15 蔡立伟,印模师R.只有平动自由度的并联机械手.在,ASM1996设计工程技术会议,欧文,加州,1996,96-DETC-MECH-1152.16 群数学与并联机构,In;imac马夫Int.电脑.论机器人、机电一体化与制造系统,神户,日本,1992;459一464.17 刘新军,王杰,王立平,等.提出了一种新的空间三自由度并联机器人1n.IFAC移动机器人技术研讨会,Jejudo岛,韩国,2001:309一314.18 Ceccarelli我是一个新3d.o . f .空间并联机构、机制和机器理论,1997年,32(8):895一902.19 刘新军,王俊,王立平,等.一种新型五轴龙门式混合机床的概念设计.;ISAMT 2001年,南京,2001:493一496.20 王杰,唐,段国,等.一种新型平面三自由度并联机床的设计方法.;学报2001年IEEE机器人与自动化国际会议上,韩国,首尔2001年2448一2453.附录B外文文献Parallel Mechanisms with Two or Three Degrees of FreedomChristiaan J.J. Paredis, H. Benjamin Brown, Pradeep K. KhoslaAbstractParallel manipulators for the machine tool Industry have been studied extensively for various industrial applications. However, limited useful workspace areas, the poor mobility, and design difficulties of more complex parallel manipulators have led to mare interest in parallel manipulators with less than six degrees of freedom (DoFs). Several parallel mechanisms with various numbers and types of degrees of freedom are described in this paper, which can be used in parallel kinematics machines, motion simulators, and industrial robots.Key words: parallel manipulator; parallel kinematic machine; degree of freedom; roboINTRODUCTIONMechanical systems that allow a rigid body to move with respect to a fixed base play a very important role in numerous applications. A rigid body can move in various translational or rotational directions which are called degrees of freedom (DoFs). The total number of degrees of freedom for a rigid body cannot exceed six, for example, three axes, A robot includes a system to control several degrees of freedom of an end effector.The last few years have witnessed important developments in the use of industrial robots, mainly due to their flexibility. However, the mechanical architecture of the most common robots is not well adapted to certain tasks. Other types of architectures have, therefore, recently been developed for industrial use, including parallel manipulators. A parallel manipulator, which is a closed-loop mechanism, typically consists of a moving platform that is connected to a fixed base by several limbs or legs. Typically, the number of limbs is equal to the number of degrees of freedom such that every limb is controlled by one actuator and all the actuators can be mounted at or near the fixed base. For this reason, parallel manipulators. Because the external load can be shared by the actuators, parallel manipulators tend to have a large load-carrying capacity. Parallel manipulators are always presented as having very good performance in terms of accuracy, rigidity and the ability to manipulate large loads. They have been used in a large number of applications ranging from astronomy to flight simulators, and are becoming increasingly popular in the machine-tool industry,The conceptual design of parallel manipulators can be dated back to 1947, when Gough established the basic principles of a mechanism with a closed-loop kinematic structure to control the position and orientation of a moving platform to test tire wear and damage. He built a prototype in 1955 (Fig, 1a) where the moving element was a hexagonal platform whose vertices were all connected to links by ball-and-socket joints. The other end of the link was attached to the base by a universal joint. Six linear actuators modified the total link length. Stewart designed a platform manipulator as an aircraft simulator in 1965 (Fig, 1b), in which the moving element was a triangular platform whose vertices were all connected by ball-and-socket joints to support mechanisms each constituting of two jacks, also placed in a triangle. In 1978, Hunt made a systematic study of kinematic structure of parallel manipulators, with the planar three-RPS parallel manipulator as typical example. Since then, parallel manipulators have been studied extensively by numerous researchers.Most of the six-DoFs parallel manipulators studied to date have included six extendible limbs.These parallel manipulators possess the advantages of high stiffness, low inertia, and large payload capacity. However, they suffer the problems of relatively small useful workspace and design difficulties. Furthermore, their direct kinematics is very difficult to analyze. Therefore, parallel manipulators with less than six-DoFs have increasingly attracted attention for industry applications.This paper introduces parallel manipulators and the classification of parallel manipulators. Three typesof new parallel manipulators are introduced:a spatial three-DoFs parallel manipulator,a two-DoFsparallelmanipulator,and a planar three-DoFs serial-parallel manipulator.1DEFINITION OF PARALLEL MANIPULATORA parallel manipulator is made of an end-effector with n degrees of freedom with a fixed base linked together by at least two independent kinematic linkages. Actuation takes place through n-simple actuators.These mechanisms have the following characteristics. At least two linkages support the end-,effector. Each of those linkages contains at least one simple actuator. The number of actuators is the same as the number of degrees of freedom of the end-effecto.The mobility of the manipulator is zero when the actuators are locked.Parallel mechanisms are of interest for the following reasons:The load can be distributed on the multiple linkages.Few actuators are needed.When the actuators are locked, the manipulator remains in position, which is an important safety concern for certain applications.Parallel manipulators for which the number of linkages is strictly equal to the number of degrees of freedom of the end-effector are called fully parallel manipulators.2 DEGREES OF FREEDOM OF MECHANISMThe degrees of freedom of a mechanism are the number of independent parameters or inputs needed to completely specify the configuration of the mechanism. However, a general mobility criterion cannot be easily defined for closed-loop kinematic linkages,as Hunt and Lerbet already noted. Classical mobility formulae can indeed neglect some degrees of freedom. Grublers formulae is nevertheless generally used, which may be written asM=d(n-g-1)+(1)where M is system mobility (degrees of freedom);d is screw system order(d=3for planar and spherical motion, d=6for spatial motion); n is numberof links including the frame; g is number of joints; andare degrees of freedom associated with the i-th joint.3 CLASSIFICATION OF PARALLEL MANIPULATORSThe total number of degrees of freedom of a rigid body cannot exceed 6; therefore,the number of DoFs of a parallel manipulator will be between 2 and 6. Since the first parallel mechanism design, many mechanical designs have been proposed for parallel manipulators with 2 to 6 DoFs. A survey of 87 actuators proposed in the literature showed that 40% has six DoFs, 3.5% five DoFs,6% four DoFs,40%three DoFs,and the remaining two DoFs.3.1 Two-DoFs parallel manipulatorsMostexisting two-DoFs parallel manipulators are planar manipulators with two-translational DoFs. Such designs use only prismatic and revolute joints. McCloy showed that there are 20 different combinations. This number is reduced to 6 as shown in Fig. 2 if the actuators are assumed to be attached to the ground. There is no passive prismatic joint and no actuator is supporting the weight of another actuator.3.2 Three-DoFs parallel manipulatorsThere are many three-I?oFs parallel manipulators,so only the classical designs will be presented here.One example is the planar three-RRR (R stands for revolving joint) parallel manipulator as shown in Fig.3a.The moving platform has three planar DoFs,which are two translations along the x and yaxes and one rotation around the axis perpendicular to the O-xy plane. Another example is the spherical three-RRR parallel manipulator as shown in Fig. 3b,in which all the joint axes intersect at a common vertex. The motion of any point in the mechanism is rotation about the vertex. The moving platform has only rotational DoFs with respect to the base. Hunt presented the three-RPS parallel manipulator shown in Fig. 3c, which has complex DoFs,which cannot be strictly defined. The most famous robot with three translations is the DELTA (Fig.3d),proposed by Clavel and marketed by the Demaurex Company and ABB under the name IRB 340 FpexPicker. DELTA has been widely used in industry.Another type of three-DoFs parallel manipulator has the moving platform connected to the base through four legs,where the fourth leg is passive and is also the leading leg,which means that the leg determines the motion of the moving platform, for example,in the spherical coordinate parallel manipulator shown in Fig.3e.This parallel manipulator is used for the machine tool design by IFW of the University of Hannover. 3.3 Four-DoFs parallel manipulators.A four-DoFs fully parallel manipulator has d-=6,n=10,g=I2, and M=4.Substituting these coefficients into Eq.(1) gets F=22/4 which is the degrees of freedom for each leg.Therefore, there axe,actually,no four-DoFs fully parallel manipulators.The early mechanisms with four-DoFs were not fully parallel manipulators,i,e.manipulatorswith two actuators per linkage or with passive constraints.3.4 Five-DoFs parallel manipulatorsFive-DoFs fully parallel manipulators must have F=29/5,so there are no five-DoFs fully parallel manipulators. A five-DoFs parallel manipulator proposed by Austad consists of two parallel manipulators.3.5 Six-DoFs parallel manipulatorsSix-DoFsparallel manipulators are the most popular manipulators so they have been studied extensively.The architecture shown in Fig.4a is a classical six-DoFs parallel manipulator.Most six-DoFs parallel manipulators have six extendiblelimbs.These parallel manipulators possess the advantages of high stiffness, low inertia,and large payload capacity. However,they suffer the problems of relatively small useful workspace and design difficulties. Furthermore,analysis of their direct kinematics is very difficult. There are also.Some exotic chain manipulators in which the manipulatoris actuated by a planar mechanism, such as a four-bar mechanism, or a five-bar mechanism, or which have two actuators per leg and which usually have three legs.4 EVOLUTION OF PARALLEL MANIPULATORSAfter Gough established the basic principles of mechanisms with closed-loop kinematic structures in 1947,as shown in Fig. 1a, many other parallel manipulators with a specified number and type of degrees of freedom have also been proposed. The architecture designed by Stewart in 1965 is shown in Fig, 1b. As shown in Fig. 4a, theoretically speaking, the six legs can be arranged at will to design various six-DoFs parallel manipulators, such as the manipulator shown in Fig. 46, where the legs are arranged in a 3-2-1 style which is a very compact structure that can be used in microsystem. The arrangement of the six legs shown in Fig. 4c makes the manipulator move freely along a specified direction,which is very useful for the industrial applications.A six-DoFs parallel manipulator similar to that proposed by Pierrot has each pair of legs in the manipulator shown in Fig. 4a parallel to each other. The number of DoFs of the manipulator will be different if the inputs to the two legs in each pair are the same. The equivalent manipulator architecture is shown in Fig.5. The manipulator output will be three translations,which is probably the origin of the DELTA robot. The actuated links can be arranged as the well-known, fast robot DELTA shown in Fig. 3d. DELTA has been made in several versions,such as the Pollard mechanism Tsars manipulator, Fig.3f, is also among three translational parallel manipulators. Although Tsars manipulator has translations identical with that of DELTA,it is not exactly a version of DELTA. Their design concepts are different and Tsars manipulator is the first design to deal with the problem of a UPU chain. Another three-translational DoFs parallel manipulator, Star, was design by Herve based on the group theory.Although these design concepts provide ideas to design a new manipulator, additional work is needed to design a robot combining translational and rotational DoFs with less than six DoFs. For example, there are few spatial three-DoFs parallel manipulators combining two spatial translations and one rotation, as will be presented in the following section.5 NEW SPATAIAL THREE-DOFS 1 MANIPULATOR5.1 Manipulator structureThe spatial three-DoFs parallel manipulator shown in Fig.6a consists of a base plate,a movable platform,and three legs that connect the two plates. Each connecting leg has four degrees of freedom. Two of the three legs have identical chains with a two-DoFs joint (or two 1-DoF joints) and two 1-DoF joints.The third leg consists of a planar four-bar parallelogram and three 1-DoF joints. One 1-DoF joint in each leg is actuated.The moving platform is an isosceles triangle. The vertices of the platform are connected to a fixed-base plate through legs (1),(8) and (12).Legs (1) and (12) have identical chains with a constant link connected to a universal joint (or two revol
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