3自由度并联机床的运动学和动力学研究(翻译)

3自由度并联机床的运动学和动力学研究

摘要：中国东北大学已经研制出一种用于钢坯研磨的新型3自由度并联机床。它具有结构简单，刚度大的优点，更高的力量重量比，较大的工作空间，简单的运动学方程，没有运动的奇异位姿。在使用相应刀具情况下该机器人可用于磨削，研磨，抛光等加工过程。在本文中，介绍了简单的机器人的结构和自由度，运动学和工作空间，精度分析，静态和动态的分析及其相关参数。

关键词：并联机床；运动学；动力学；3自由度

1.前言

与传统机床相比，并联机床具有更高的精度，高刚度的优点，和更高的刚度质量比，所以近些年它得到了行业和机构大量的研究和评估。由美国Giddings & Lewis公司研制的“六足虫”并联机床被认为是21世纪机床领域中的革命性理念。然而这个Stewart平台存在运动耦合的缺点，并且具有复杂的运动学和构件要求十分严格。这类少于六自由度并联机床在行业和机构也因此受到越来越多的关注。意大利Comau研制出了一种命名为Tricept的四条腿的的三自由度并联机床。东北大学已经开发出了一种新型三自由度的三腿平行磨削机床（图1）。与“六足虫”并联机床相比，此三腿平行磨削并联机床具有以下优点：（1）结构简单且具有更大工作空间；（2）动力学方程简单便于控制操作；（3）在工作空间没有运动耦合状态。

图1

2.并联机床

2.1 3自由度系统的布局

该三自由度并联机构由一个移动平台，基础平台，一个平行的联动和三条腿的连接两个平台。中间腿支链控制的移动平台的三个自由，如图2所示。移动平台的转换是由平行连杆机构控制。

图2

2.2 运动学和工作空间

移动平台平行于基础平台，一个坐标系统（O- X，Y，Z）选择如图2所示，这种机制的逆向运动学正解方程可以表示为：

123l l l ===其中w=a-b

，2m = ，n=w/2 ，a 和分别表示基础平台的两侧的长度和等边三角形状的移动平台的长度。该机构的位置正解方程可表示为：

2222

222132X l l w Y w Z =

-+=

从公式1和2可知系统在整个工作空间无奇异位姿和运动耦合。其工作空间的形状如图3所示：它是一个三角曲面的金字塔。其最大断面和深度均大于正常工作情况的数值。这对于如磨削、抛光、焊接等加工形式都是非常适合的。

图3

3.控制系统

研磨操作应进行连续路径控制，

控制连续路径符合雅可比矩阵之间的

关系。p V （动平台的速度）和l V （腿的延伸率）可以表示为p l V JV = 其中：312

],[]T

p dl dl dl dX dY dZ V V dt

dt dt

== 该雅克比矩阵计算如下：

222222222222[

]l l J w

如果P ?和 θ?分别代表每分钟位置的变化和动平台的旋转角度，并且K 描述角度对三条腿的线位移，如下方程可以确立：

1kJ P θ?=?

根据上述所提到的，连续的路径控制单元的设计已经完成。三条腿的控制是用C 语言编制的软件程序来实现的。它具有良好的适应性和可移植性。机器人示意图如图4所示。

图

4. 静力学和动力学分析 4.1 静力学

假设三脚并联机床载荷（如磨削载荷）矩阵是F ，驱动臂力矩阵是1F （图5），则有：

[]X

Z F F F F =和11

3[]F F F F =

且根据虚位移理论，正解矩阵为：1T F J F =-，静力学逆解为11()T F J F -=-从上面的静力学分析也可以看出转矩是由平动机构承担的。此外切削力是由三个环节的拉力承担。这个机制在力学结构上是合理的。

图5

4.2.动力学

根据朗格朗日方程，每条腿的轴驱动力i F 为：

(),1,2,3i i i i

d K K P

F i dt q q q ???=

-+=??? 其中K 是动能，P 的潜在能量，i q 是关节的广义坐标。用于驱动腿如图6所示，忽略关节摩擦力和平移运动机理，可以得出以下的动力学

方程：

1111

()(2())()(()sin cos )i i P P P ci ci i ci i

ci ci ci i i ci i i i i m m m m F M X Y Z m l l l l m m l Mg mg l m m θθθθθ===--=+++++--+++∑∑∑

其中ci l 是固定端到质心的距离，m 是连杆i 的质量，m 是较低的联络线振荡环节i 的质量，M 是动平台质量，1θ是连杆i 和底平台夹角。

图6

5.结论

这种新型并联机床是非常方便实用。由于机构的独特运动转换方式，其运动学是简单的，且无奇异位形和运动。因此，该机构易于进行实时控制。如果有其他的刀具，这个机器人还可以改装发展其他机床和机器人进行应用。

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毕业设计(论文)外文资料翻译系部：专业：姓名：学号：外文出处：English For Electromechanical (用外文写) Engineering 附件：1.外文资料翻译译文；2.外文原文。指导教师评语：此翻译文章简单介绍了各机床的加工原理，并详细介绍了各机床的构造，并对方各机床的加工方法法进行了详细的描述，翻译用词比较准确，文笔也较为通顺，为在以后工作中接触英文资料打下了基础。签名：年月日注：请将该封面与附件装订成册。

附件1：外文资料翻译译文机床机床是用于切削金属的机器。工业上使用的机床要数车床、钻床和铣床最为重要。其它类型的金属切削机床在金属切削加工方面不及这三种机床应用广泛。车床通常被称为所有类型机床的始祖。为了进行车削，当工件旋转经过刀具时，车床用一把单刃刀具切除金属。用车削可以加工各种圆柱型的工件，如：轴、齿轮坯、皮带轮和丝杠轴。镗削加工可以用来扩大和精加工定位精度很高的孔。钻削是由旋转的钻头完成的。大多数金属的钻削由麻花钻来完成。用来进行钻削加工的机床称为钻床。铰孔和攻螺纹也归类为钻削过程。铰孔是从已经钻好的孔上再切除少量的金属。攻螺纹是在内孔上加工出螺纹，以使螺钉或螺栓旋进孔内。铣削由旋转的、多切削刃的铣刀来完成。铣刀有多种类型和尺寸。有些铣刀只有两个切削刃，而有些则有多达三十或更多的切削刃。铣刀根据使用的刀具不同能加工平面、斜面、沟槽、齿轮轮齿和其它外形轮廓。牛头刨床和龙门刨床用单刃刀具来加工平面。用牛头刨床进行加工时，刀具在机床上往复运动，而工件朝向刀具自动进给。在用龙门刨床进行加工时，工件安装在工作台上，工作台往复经过刀具而切除金属。工作台每完成一个行程刀具自动向工件进给一个小的进给量。磨削利用磨粒来完成切削工作。根据加工要求，磨削可分为精密磨削和非精密磨削。精密磨削用于公差小和非常光洁的表面，非精密磨削用于在精度要求不高的地方切除多余的金属。车床车床是用来从圆形工件表面切除金属的机床，工件安装在车床的两个顶尖之间，并绕顶尖轴线旋转。车削工件时，车刀沿着工件的旋转轴线平行移动或与工件的旋转轴线成一斜角移动，将工件表面的金属切除。车刀的这种位移称为进给。车

六自由度摇摆平台

大黄蜂机器人六自由度摇摆台大黄蜂机器人有限公司的六自由度平台系统由采用Stewart机构的六自由度运动平台、计算机控制系统、驱动系统等组成。六自由度运动平台（如下图）的下平台安装在地面上，上平台为运动平台，它由六只电动缸支承，运动平台与电动缸采用六个虎克铰连接，电动缸与固定基座采用六个虎克铰连接，六只电动缸采用伺服电机驱动的电动缸。计算机控制系统通过协调控制电动缸的行程，实现运动平台的六个自由度的运动，即笛卡尔坐标系内的三个平移运动和绕三个坐标轴的转动。

各主要部分简述如下：本设备主要由以下部分组成：运动上平台、下平台（基座）、电动缸及伺服电机、驱动器系统、综合控制及监测系统。各自功能如下：上平台：是有效载荷的安装基面，提供六自由度的摇摆运动。下平台：是六自由度摇摆台的安装基面，需要承受足够大的冲击力。电动缸及伺服电机：通过控制电动缸活塞杆的行程，实现运动平台台体的六自由度运动，共6套。驱动器系统：接收用户控制指令，通过控制伺服电机的输入，对伺服电机的输出转速和转角进行控制，达到控制电动缸活塞杆出速度和行程的目的，共6套。综合控制监测系统：硬件为用户计算机，软件为研制方配合开发；同时，它还对平台的运动过程进行监测，预防和处理系统的异常情况。

平台总体运动能力指标如上表，具体表述如下： a.平台定位精度及重复定位精度为0.5mm及0.1mm； b.平台转动精度及重复转动精度为0.1°及0.05°； c.行程回差小于0.2mm； d.平台X方向运动速度可从0mm/s到250mm/s连续变化；YZ方向运动速度可从0mm/s到250mm/s连续变化； e.单支杆可承受轴向力不小于700N； f.单支杆的运动速度可从0m/s到250mm/s连续变化； g.平台中位位置固有频率：不小于40Hz； h.机械组件需具有开放性，可拆卸组装； i.机械设计安全系数不小于 2.0，驱动裕度不小于 3.0； j.额定载荷下，全行程往复工作寿命不小于1×104次，存储寿命不小于48月；

组合机床外文文献

Int J Adv Manuf Technol (2006) 29: 178–183 DOI 10.1007/s00170-004-2493-9
ORIGINAL ARTICLE
Ferda C. C ? etinkaya
Unit sized transfer batch scheduling in an automated two-machine ?ow-line cell with one transport agent
Received: 26 July 2004 / Accepted: 22 November 2004 / Published online: 16 November 2005 ? Springer-Verlag London Limited 2005 Abstract The process of splitting a job lot comprised of several identical units into transfer batches (some portion of the lot), and permitting the transfer of processed transfer batches to downstream machines, allows the operations of a job lot to be overlapped. The essence of this idea is to increase the movement of work in the manufacturing environment. In this paper, the scheduling of multiple job lots with unit sized transfer batches is studied for a two-machine ?ow-line cell in which a single transport agent picks a completed unit from the ?rst machine, delivers it to the second machine, and returns to the ?rst machine. A completed unit on the ?rst machine blocks the machine if the transport agent is in transit. We examine this problem for both unit dependent and independent setups on each machine, and propose an optimal solution procedure similar to Johnson’s rule for solving the basic two-machine ?owshop scheduling problem. Keywords Automated guided vehicle · Lot streaming · Scheduling · Sequencing · Transfer batches entire lot to ?nish its processing on the current machine, while downstream machines may be idle. It should be obvious that processing the entire lot as a single object can lead to large workin-process inventories between the machines, and to an increase in the maximum completion time (makespan), which is the total elapsed time to complete the processing of all job lots. However, the splitting of an entire lot into transfer batches to be moved to downstream machines permits the overlapping of different operations on the same product while work proceeds, to complete the lot on the upstream machine. There are many ways to split a lot: transfer batches may be equal or unequal, with the number of splits ranging from one to the number of units in the job lot. For instance, consider a job lot consisting of 100 identical items to be processed in a three-stage manufacturing environment in which the ?ow of its operations is unidirectional from stage 1 through stage 3. Assume that the unit processing time at stages 1, 2, and 3 are 1, 3, 2 min, respectively. If we do not allow transfer batches, the throughput time is (100)(1+3+2) = 600 min (see Fig. 1a). However, if we create two equal sized transfer batches through all stages, the throughput time decreases to 450 min, a reduction of 25% (see Fig. 1b). It is clear that the throughput time decreases as the number of transfer batches increases. Flowshop problems have been studied extensively and reported in the literature without explicitly considering transfer batches. Johnson [1], in his pioneering work, proposed a polynomial time algorithm for determining the optimal makespan when several jobs are processed on a two-machine (two-stage) ?owshop with unlimited buffer. With three or more machines, the problem has been proven to be NP-hard (Garey et al. [2]). Besides the extension of this problem to the m -stage ?owshop problem, optimal solutions to some variations of the basic two-stage problem have been suggested. Mitten [3] considered arbitrary time lags, and optimal scheduling with setup times separated from processing was developed by Yoshida and Hitomi [4]. Separation of the setup, processing and removal times for each job on each machine was considered by Sule and Huang [5]. On the other hand, ?owshop scheduling problems with transfer batches have been examined by various researchers. Vickson
1 Introduction
Most classical shop scheduling models disregard the fact that products are often produced in lots, each lot (process batch) consisting of identical parts (items) to be produced. The size of a job lot (i.e., the number of items it consists of) typically ranges from a few items to several hundred. In any case, job lots are assumed to be indivisible single entities, although an entire job lot consists of many identical items. That is, partial transfer of completed items in a lot between machines on the processing routing of the job lot is impossible. But it is quite unreasonable to wait for the
F.C. ?etinkaya (u) Department of Industrial Engineering, Eastern Mediterranean University, Gazimagusa-T.R.N.C., Mersin Turkey E-mail: ferda.cetinkaya@https://www.360docs.net/doc/5210312938.html,.tr Tel.: +90-392-6301052 Fax: +90-392-3654029

机床加工外文翻译参考文献

机床加工外文翻译参考文献(文档含中英文对照即英文原文和中文翻译) 基本加工工序和切削技术基本加工的操作机床是从早期的埃及人的脚踏动力车和约翰·威尔金森的镗床发展而来的。它们为工件和刀具提供刚性支撑并可以精确控制它们的相对位置和相对速度。基本上讲，金属切削是指一个磨尖的锲形工具从有韧性的工件表面上去除一条很窄的金属。切屑是被废弃的产品，与其它工件相比切屑较短，但对于未切削部分的厚度有一定的增加。工件表面的几何形状取决于刀具的形状以及加工操作过程中刀具的路径。大多数加工工序产生不同几何形状的零件。如果一个粗糙的工件在中心轴上转动并且刀具平行于旋转中心切入工件表面，一个旋转表面就产生了，这种操作称为车削。如果一个空心的管子以同样的方式在内表面加工，这种操作称为镗孔。当均匀地改变直径时便产生了一个圆锥形的外表面，这称为锥度车削。如果刀具接触点以改变半径的方式运动，那么一个外轮廓像球的工件便产生了；或者如果工件足够的短并且支撑是十分刚硬的，那么成型刀具相对于旋转轴正常进给的一个外表面便可产生，短锥形或圆柱形的表面也可形成。

平坦的表面是经常需要的，它们可以由刀具接触点相对于旋转轴的径向车削产生。在刨削时对于较大的工件更容易将刀具固定并将工件置于刀具下面。刀具可以往复地进给。成形面可以通过成型刀具加工产生。多刃刀具也能使用。使用双刃槽钻钻深度是钻孔直径5-10倍的孔。不管是钻头旋转还是工件旋转，切削刃与工件之间的相对运动是一个重要因数。在铣削时一个带有许多切削刃的旋转刀具与工件接触，工件相对刀具慢慢运动。平的或成形面根据刀具的几何形状和进给方式可能产生。可以产生横向或纵向轴旋转并且可以在任何三个坐标方向上进给。基本机床机床通过从塑性材料上去除屑片来产生出具有特别几何形状和精确尺寸的零件。后者是废弃物，是由塑性材料如钢的长而不断的带状物变化而来，从处理的角度来看，那是没有用处的。很容易处理不好由铸铁产生的破裂的屑片。机床执行五种基本的去除金属的过程：车削，刨削，钻孔，铣削。所有其他的去除金属的过程都是由这五个基本程序修改而来的，举例来说，镗孔是内部车削；铰孔，攻丝和扩孔是进一步加工钻过的孔；齿轮加工是基于铣削操作的。抛光和打磨是磨削和去除磨料工序的变形。因此，只有四种基本类型的机床，使用特别可控制几何形状的切削工具1.车床，2.钻床，3.铣床，4.磨床。磨削过程形成了屑片，但磨粒的几何形状是不可控制的。通过各种加工工序去除材料的数量和速度是巨大的，正如在大型车削加工，或者是极小的如研磨和超精密加工中只有面的高点被除掉。一台机床履行三大职能：1.它支撑工件或夹具和刀具2.它为工件和刀具提供相对运动3.在每一种情况下提供一系列的进给量和一般可达4-32种的速度选择。加工速度和进给速度，进给量和切削深度是经济加工的三大变量。其他的量数是攻丝和刀具材料，冷却剂和刀具的几何形状，去除金属的速度和所需要的功率依赖于这些变量。切削深度，进给量和切削速度是任何一个金属加工工序中必须建立的机械参量。它们都影响去除金属的力，功率和速度。切削速度可以定义为在旋转一周时