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南京理工大学紫金学院毕业设计（论文）任务书系：机械工程系专 业：机械工程及其自动化学 生 姓 名：学 号：设计(论文)题目：换刀机器人设计水平移动系统设计起 迄 日 期:2010年 2 月24 日 6 月 5 日设计(论文)地点:南京理工大学紫金学院指 导 教 师:专业负责人:发任务书日期: 2010年 2 月 23 日任务书填写要求1毕业设计（论文）任务书由指导教师根据各课题的具体情况填写，经学生所在专业的负责人审查、系领导签字后生效。此任务书应在毕业设计（论文）开始前一周内填好并发给学生；2任务书内容必须用黑墨水笔工整书写或按教务处统一设计的电子文档标准格式（可从教务处网页上下载）打印，不得随便涂改或潦草书写，禁止打印在其它纸上后剪贴；3任务书内填写的内容，必须和学生毕业设计（论文）完成的情况相一致，若有变更，应当经过所在专业及系主管领导审批后方可重新填写；4任务书内有关“系”、“专业”等名称的填写，应写中文全称，不能写数字代码。学生的“学号”要写全号；5任务书内“主要参考文献”的填写，应按照国标GB 77142005文后参考文献著录规则的要求书写，不能有随意性；6有关年月日等日期的填写，应当按照国标GB/T 74082005数据元和交换格式、信息交换、日期和时间表示法规定的要求，一律用阿拉伯数字书写。如“2009年3月15日”或“2009-03-15”。毕 业 设 计（论 文）任 务 书1本毕业设计（论文）课题应达到的目的：通过毕业设计的锻炼,学会综合运用所学的知识和技能进行实际工程问题的分析、综合及设计。培养调查研究、中外文献检索与阅读的能力; 掌握定性与定量相结合的独立研究与论证的能力; 熟练掌握设计、计算及绘图的能力; 锻炼文字与口头表达能力; 掌握撰写设计说明书的能力。并且能设计出合乎实际要求的换刀机器人机械结构。2本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）：技术要求：结构型式： 组合式直角坐标加旋转;自由度数： 4; 负载重量： 10 kg (单爪)末端操作器： 双手爪 工作空间： 纵向 11m; 横向 0.6m; 升降 1m; 旋转 180;运行速度： 五档可调;最大运行速度： 纵向 33.6 m/min; 横向 16 m/min; 升降 8m/min; 旋转 16 rpm; 重复定位精度： 0.6 mm;记忆刀位数： 不小于 170 把,可扩展;总重量： 600 kg. 工作要求：（1）完成总体方案的论证设计； （2）完成水平移动系统设计；（3）绘制总装图、部件图和零件图；（4）撰写设计说明书。毕 业 设 计（论 文）任 务 书3对本毕业设计（论文）课题成果的要求包括毕业设计论文、图表、实物样品等：(1)开题报告(含文献综述) ：3,000 汉字以上; (2) 外文资料翻译 ： 3,000 汉字以上;(3)总体装配图： 1 张; (4) 部件装配图： 1张; (5)主要零件图： 若干张 (总图数约合3张0号图) ; (6)毕业设计说明书,字数不少于10,000字,并附有200300汉字的中文摘要及相应的英文摘要。4主要参考文献：1（日）渡边茂. 产业机器人的应用M. 北京：机械工业出版社，1986年5月.2 龚振邦 等. 机器人机械设计M. 北京：电子工业出版社，1995年6月.3 马香峰 等. 工业机器人的操作机设计M. 北京：冶金工业出版社，1996年9月.4 余达太 马香峰. 工业机器人应用工程M. 北京：冶金工业出版社，1999年4月.5 程光仁 等. 滚珠螺旋传动设计基础M. 北京：机械工业出版社，1987年8月.6 李中杰 等. 步进电动机应用技术M. 北京：机械工业出版社，1988年12月.7 Ernest L. Hall et l. Robotics: A User-Friendly IntroductionM. New York:CBS College Publishing,1985.8 Yoram Koren. Robotics for EngineersM. McGraw-Hill Book Company, 1985.9 宋德锋 等. 无源式换刀机械手爪的研制J,机械设计，2005（3），18-22.10 薛焕然 等FMS中换刀机器人若干技术问题的探讨A，中国第三届机电一体化学术会会议论文集C，1994：6-9.11 白井良明 著. 王棣棠 译. 机器人工程M. 北京：科学出版社， 2001年2月.12 郭洪红. 工业机器人技术M. 西安：西安电子科技大学出版社，2006年3月.13 刘文波 等. 工业机器人M. 沈阳：东北大学出版社，2007年12月.14 周伯英. 工业机器人设计M. 北京：机械工业出版社，1995年10月.15（日）日本机器人学会. 新版机器人技术手册M. 北京：科学出版社，2007年8月.毕 业 设 计（论 文）任 务 书5本毕业设计（论文）课题工作进度计划：起 迄 日 期工 作 内 容2010年2月24日3月18 日 3月19日3月25 日3月26日3月31 日4月 1 日4 月 7 日4月 8 日4 月20日4月21日4 月30日5月 1 日5 月10日5月11日5 月17日5月18日5 月25日5月26日5 月31日6月 1 日6 月 5 日完成文献综述、开题报告、外文资料翻译总体方案论证工作空间设计运动参数设计、计算动力参数计算、结构设计绘制总装配图绘制部件装配图绘制相关零件图撰写、提交设计说明书修改设计说明书，准备答辩毕业答辩所在专业审查意见：负责人： 年 月 日系意见：系领导： 年 月 日 南 京 理 工 大 学 紫 金 学 院毕业设计(论文)外文资料翻译系： 机械工程系 专 业： 机械工程及自动化 姓 名： 学 号： (用外文写)外文出处： Journal of Mechanical Design SEPTEMBER 1999, Vol. 121 / 359367 附 件： 1.外文资料翻译译文；2.外文原文。 指导教师评语：译文基本上翻译出原文的意思，层次分明，具有条理，语句基本通顺，翻译质量稍差。少数的中文表达欠妥，一些专业术语翻译不准。 签名： 年 月 日注：请将该封面与附件装订成册。附件1：外文资料翻译译文带自动换刀装置加工中心的配置综合方法本论文的目的是提出带自动换刀装置加工中心的配置综合的设计方法，以满足所需的拓扑结构和运动特性。根据坐标系的概念、图论、概括化、具体化和运动合成，提出了这种设计方法并计算机化，而且综合了带有多达8个连杆的自动换刀装置的加工中心。结果，对于有鼓型刀库的加工中心，具有6连杆、7连杆和8连杆的加工中心的配置数分别为2、13和20。同样，对于有线型刀库的加工中心，具有5连杆、6连杆、7连杆和8连杆的加工中心的配置数分别为1、5 、20和60。此外，这项工作还提供了一种系统方法用于综合带拓扑和运动要求的空间开链机构。 引言 加工中心运动学可以被看作是开链式机构，他们具有特定拓扑特征的特殊功能。有关平面机构问题的创意设计在过去的几年里一直是许多项研究课题 （约翰逊，1965；弗罗伊登施泰因和真希，1979，1983；厄尔德曼等。1980年，严和徐，1983；严和陈，1985；严，1992年）。但是，空间运动开链型机构的结构综合设计方法不可得到。 过去的几年里，只有少数几篇文章涉及加工中心配置的设计。杉村（1981年）等，使用分析调查方法设计机床。伊藤和信乃（1982年，1983年和1987年），通过使用定向图机床法产生结构配置。列舍托夫和波特曼（1988）提出了综合的具有相同成型机床的功能配置代码。该概念广泛使用在合成5轴机床上（石泽等，1991； 坂本和稻崎，1992年）。然而，自动换刀系统并没有在考虑范围。 在主轴与加工中心刀库之间自动执行换刀操作的系统称为自动换刀装置(ATC)。ATC为减少加工过程中机器闲置的时间发挥了重要作用，从而提高了生产率。 本论文的目的是提出带有自动换刀装置加工中心的所有可能的配置系统产生的设计方法，该加工中心是一种开链式空间机构的受拓扑结构和运动限制空间。 拓扑特征 1.空间开链式多自由度机构。2.有固定的连杆（支架）。3.有单连杆。4.有在主轴和工作台之间有4个接头的工作台。5.有刀库，该刀库为从位于支架的连杆到主轴头的单一连杆分支。6. 单一连杆可以是主轴，刀库或者工作台。此外，单一连杆不能超过3个。7. 主轴产生的接头必须是转动副。8. 主轴端和工作台之间的接头必须是棱柱副。9. 刀库和分支连杆的接头是转动副，棱柱副，或圆柱副。如果有回转副或圆柱副，则必须依附于刀库。设计过程 图2是提出的开链式机构配置的设计过程。该设计理念进程启动现有机构进行调查，并推定出其拓扑结构和运动特性。设计过程的第二个步是基于树形图表现出的观念，链接邻接矩阵，和机构分配矩阵描述现有拓扑结构。第三步是把这些机构根据进程具体化变成其相应的广义树图。第四步是获取给定数量边和基于列举图的顶点所有可能的树形图。第五步是分配一些连杆和链接给有效的树形图来经过专业化以满足拓扑结构。在设计过程的最后一步是获得机构图集指定运动机构。 以下，以自动换刀加工中心作为例子来详细说明这种设计方法。 现有机构 在设计过程的第一步是研究现有的机构并推定它们的拓扑结构和运动特性。加工中心是由4个基本部件组成的机床：轴，刀库，换刀机构，以及包括动力轴运动的机床结构。那个机床结构在很大程度上决定了加工表面精度，刚度和动力性能。主轴旋转该工具加工工件所需的表面。该工具库储存工具并在机械加工操作中移动它们到合适位置来使用。该换刀机构在工具库和主轴工具间执行刀具转换。最简单的ATC是没有换刀机构的设计，且在工具库和主轴间的相对运动中实现换刀。图3（a）和（b）分别显示两个 3轴鼓型和直线型工具库的卧式加工中心。 为了代表和分析加工中心的拓扑结构和运动特性，基于国际标准化组织中心（国际标准化组织，1974）定义了坐标系来描述加工中心的每个运动轴的配置。 本标准坐标系是右手矩形笛卡儿之一，相关的工件安装在与主要线性横向对齐的机器。对机器的组成部分运动产生有利趋势，这给工件带来更多的优势。卧式加工中心的结构图附加ISO标准图如图3所示。 通过分析提供现有3轴无换刀机构的卧式加工中心，我们可以总结出如下拓扑结构和运动特性（陈燕，1995年）。 图2 设计过程（a）（b）图3 三轴水平加工中心结论 总之，本文提出了受拓扑结构和运动的限制的带自动换刀装置加工中心配置设计。设计过程已计算机化，已综合所有多达8加工中心可能的配置。从找到的配置中，设计者可以根据设计要求，专利权，机床结构和空间限制选择有用的。这种设计方法可以综合加工中心的可能的不同类型的机床结构配置，如4轴、垂直轴、或不同分配运动轴。此外，这项工作的成果可以扩展和应用于开链式拓扑结构和运动要求结构配置的综合，如机器人、车床、磨床，.等 。F.-C. Chen Department of Mechanical Engineering Ctiang Gung University Tao-Yuan 333, Taiwan, R.O.C. H.-S. Yan Department of Meclianical Engineering National Ctieng Kung University Tainan 701, Taiwan, R.O.C. A Methodology for the Configuration Synthesis of Machining Centers with Automatic Tool Changer The purpose of this paper is to present a design methodology for the configuration synthesis of machining centers with automatic tool changer to meet the required topology and motion characteristics. According to the concept of coordinate system, graph theory, generalization, specialization, and motion synthesis, this design methodology is proposed and computerized, and the machining centers with automatic tool changer up to eight links are synthesized. As the result, for the machining centers with drum type tool magazine, the numbers of configurations of machining centers with 6, 7, and 8 links are 2, 13, and 20, respectively. Similarly, for the machining centers with linear type tool magazine, the numbers of configurations of machining centers with 5, 6, 7, and 8 links are , 5, 20, and 60, respectively. Furthermore, this work provides a systematic approach for synthesizing spatial open-type mechanisms with topology and motion requirements. Introduction Machining center kinematics may be considered as an open-type mechanism, and they have special functions with specific topology characteristics. The problems associated with the creative design of planar mechanisms have been the subject of a number of studies (Johnson, 1965; Freudenstein and Maki, 1979, 1983; Erdman, et al., 1980; Yan and Hsu, 1983; Yan and Chen, 1985; Yan, 1992) over the pa,st years. However, design methodologies for the structural synthe-sis of open-type mechanisms with spatial motions are not available. In the past years, just a few articles focused on the configuration design of machining centers. Sugimura et al. (1981) used analyt-ical approach to investigate the machine tool design. Ito and Shinno (1982, 1983, and 1987) generated the structural configu-ration of machine tools by using directed graphs. Reshetov and Portman (1988) proposed the configuration code for synthesizing the machine tool configurations with the same shaping function. The concept of configuration code was widely used on the con-figuration synthesis of 5-axis machine tools (Ishizawa, et al, 1991; Sakamoto and Inasaki, 1992). However, automatic tool changers were not considered. The system that automatically performs tool changes between the spindle and the tool magazine of a machining center is called automatic tool changer (ATC). ATC plays an important role in reducing the machine idle time and therefore increases productiv-ity in machining process. The propose of this paper is to present a design methodology for the systematic generation of all possible configurations of machin-ing centers with automatic tool changer, that are open-type spatial mechanisms subject to topology and motion constraints. Terminology and Notation For the terminology and notation presented in this paper, we follow the graph theoretic terminology and notation in references (Harry, 1969; Deo, 1974). Graph A graph consists of a set of objects V = V, V2, V3, . . .) called vertices, and another set = e, e2, e, . ., whose elements are called edges, such that each edge e* unordered pair (V, V) of vertices. is identified with an Incidence When vertex y, is an end vertex of edge Cj, V, and Cj are said to be incident with each other. In the graph shown in Fig. 1(a), vertex V| is incident with edge e 1 and vertex V2 is incident with edges e, 62, 5, and e. Adjacency Two nonparallel edges are said to be adjacent if they are incident with a common vertex. Similarly, two vertices are said to be adjacent if they are the end vertices of the same edge. In Fig. l(fl), vertices V, and V2 are adjacent, and so are edges e, and 2-Degree of vertex The number of edges incident with vertex V, is called the degree, d(V,), of vertex V;. In Fig. 1(a), the degree of vertex V, is four. Pendant Vertex A vertex of degree one is called a pendent vertex. In Fig. vertex V, is a pendent vertex. I(), Contributed by the Mechanisms Committee for publication in the JOURNAL OF MRCHANICAL DESIGN. Manuscript received Oct. 1996; revised Jun. 1999. Associate Technical Editor: K. Kazerounian. Tree Graph A tree graph is a connected graph with no loop. Figure 1 (b) shows a tree graph with five vertices and four edges. Branch Vertex A cut-point of a graph is where the removal increases the number of components. A branch vertex V,- of a tree graph is a cut point whose removal results maximal subtrees containing Vi as an end-point. In Fig. h), vertex V, is a branch vertex. Path A walk is defined as a finite alternating sequence of vertices and edges. An open walk in which no vertex appears more than once is called a path. In Fig. 1(a), V,eiV2e5V4e4V5 is a path. Edge Sequence Edge sequence, jfiy, in a tree graph is defined as the edges connecting vertices ( and 7. In Fig. lb), ,5 denotes the edge sequence e,e2e4. Journal of Mechanical Design Copyright 1999 by ASI/IE SEPTEMBER 1999, Vol. 121 / 359 Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfm64 02 (a) 01000 10111 01010 01101 .01010. V, Vi V; (b) 11233 12 122 213 11 32112 , 3 2 1 2 IJ 63 (c) (d) Fig. 1 Terminology and notation of graphs Length of path The number of edges in a path is called the length of path. In Fig. 1(a), the length of the path VeyeVeW is three. Rooted Tree A tree is connected graph with no loop, A tree in which one vertex (called the root) is distinguished from all the others is called a rooted tree. Figure 1 b) shows a rooted tree where vertex V2 is the root. Adjacent matrix Adjacent matrix of a graph with n vertices is an n X n symmetric matrix X = x, such that: 1. x,j = 1, if there is an edge between ith andjth vertices; and 2. X;j = 0, if there is no edge between them. Figure 1(c) shows the adjacent matrix of the graph shown in Fig. 1(a). Distance Matrix Distance matrix of a tree graph with n vertices is defined as an X n symmetric matrix D = rfy such that: 1. If i = j , dij represents the number of edges incident with vertex i; and 2. If ; t j , dij represents the length of path between vertices i and;. Figure 1(d) shows the distance matrix of the graph shown in Fig. Kb). Design Process Figure 2 shows the proposed design process for the configura-tion design of open-type mechanism. The idea of the design process starts by investigating existing mechanisms and concludes their topology and motion characteristics. The second step of the design process is to describe the topological structures of existing mechanisms based on the concept of tree-graph representation, link adjacent matrix, and mechanism allocation matrix. The third step of the design process is to transform these mechanisms into their corresponding generalized tree graphs according to the pro-cess of generalization. The fourth step of the design process is to obtain all possible tree graphs with the given numbers of edges and vertices based on graph enumeration. The fifth step of the design process is to assign certain type of links and joints into available tree graphs subject to required topology constraints through the process of specialization. The last step of the design process is to obtain the atlas of mechanisms subject to specified motion con-straints. 360 / Vol. 121, SEPTEMBER 1999 In the following, a machining center with automatic tool changer is taken as an example to illustrate this design methodol-ogy in detail. Existing Mechanisms The first step of the design process is to study existing mecha-nisms and conclude their topology and motion characteristics, A machining center is a machine tool consisting of four basic components: a spindle, a tool magazine, a tool change mechanism, and a machine tool structure including motion of power axes. The machine tool structure largely determines the accuracy of ma-chined surface, stiffness, and dynamic quality. The spindle rotates the tool to machine the workpiece to the desired surface. The tool magazine stores the tools and moves them to suitable positions for use in machining operations. The tool change mechanism executes tool changes between the tool magazine and the spindle. The simplest ATC is a design without a tool change mechanism, and the relative motions between the tool magazine and the spindle achieve tool change motions. Figures 3(a) and (b) show two 3-axis horizontal machining centers with drum type and linear type tool magazines, respectively. To represent and analyze the topological structures and motion characteristics of machining centers, a coordinate system is defined to describe the allocation of each motion axis of the machining centers based on International Organization for Standardization (ISO, 1974) nomenclature. This standard coordinate system is right-handed rectangular Cartesian one, related to a workpiece mounted in a machine and aligned with the principal linear sideways of that machine. The positive direction of movement of a component of a machine is that which causes an increasing positive dimension of the work-piece. The schematic drawings of horizontal machining centers appended to ISO standard are shown in Fig. 3. By analyzing available existing 3-axis horizontal machining centers without tool change mechanism, we conclude their topol-ogy and motion characteristics (Yan and Chen, 1995) as follows. Existing Mechanisms Coordinate Systems Topology Qiaracteristics Motion Characteristics Topological Structure Representations Generalization Generalized Tree Graphs Graph Enumeration Alias of Tree Graphs Specialization Topology Constraints Specialized Tree Graphs Motion Synthesis Motion Constraints Atlas of Mechanisms Fig. 2 Design process Transactions of the ASME Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmTool maga (a) Spindle head Tool magaz ng table (b) Fig. 3 Three-axis liorizontal macliining centers Topologv Characteristics 1. 2. 3. 4. 6. They are spatial open-type Mechanisms with multiple degrees of freedom. They have one fixed link (frame). They have a spindle which is a singular link. The J have a working table where the number of joints be-tween the spindle and the working table is four. They have a tool magazine which is a singular link branching from the link located from the frame to the spindle head. The singular links could be the spindle, the tool magazine, or the working table. And, the maximum number of singular links must be three. The joint incident with the spindle must be a revolute pair. The joints between the spindle head and the working table must be prismatic pairs. The joints between the tool magazine and the branching link are revolute, prismatic, or cylindrical pairs. And, if there is a revolute pair or a cylindrical pair, it must be incident with the tool magazine. Fig. 4 Tooi change motions Motion Characteristics 1. The spindle head has three relative motions in Y, Z, and X directions continuously with respect to the working table. 2. The ATC uses the relative motions between the tool magazine and the spindle to exchange tools. Figure 4 shows the tool change motions of the two machining centers shown in Fig. 3, where S and M represent the spindle and the tool magazine respectively, P and R represent the prismatic and revolute pairs respectively, X, Y, and Z represent the motion directions of kinematic pairs, and the circle with a number in it represent the motion sequence. 3. In order to achieve tool change motions, the relative degrees of freedom between the tool magazine and the spindle head must be at least three. Topological Structure Representations The second step of the design process is to describe existing mechanisms based on the concept of tree-graph representation, link adjacent matrix, and mechanism allocation matrix. The topological structure of a mechanism is characterized by its numbers and types of links and joints, and the incidence between them. Here, we use tree-graph representation, link adjacent matrix, and mechanism allocation matrix for the representations of the topological structures of machining centers. Tree-graph representation Based on the defined coordinate system, the mechanism can be described by representing its links and joints with vertices and edges, respectively, in which two vertices (edges) are adjacent whenever the corresponding links (joints) of the mechanism are adjacent. Table 1 Graph representations of links Link Symbol Frame Spindle Working table Tool magazine Connecting rod OFr S T M L, L, Journal of Mechanical Design SEPTEMBER 1999, Vol. 121 / 361 Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmTable 2 Joint Revolute joint Prismatic joint Cylindrical joint Graph representations of joints Degree of freedom 1 1 2 Symbol R, R, R,. P, P P,. C, Cy C, . According to this representation, the links of a machining center are represented by vertices with the link name as shown in Table 1, and the joints of a machining center are represented by edges with the name of the type of joints as shown in Table 2. The joint name has a subscript that denotes the allocation of motion axis of that joint. If the motion axis of a revolute joint is parallel to X axis, this joint is denoted as R; if the motion axis of a revolute joint is parallel to the Y axis, this joint is denoted as Ry, and so on. Figures 5(a) and b) show the corresponding tree-graph representations of the two machining centers shown in Fig. 3. Link Adjacent Matrix Link adjacent matrix (LAM) is defined to represent the topo-logical structure of a mechanism with N links and J simple joints. It is a symmetrical matrix of N hy N order. If represents the elements of LAM, then; 1. fly = L, if i = j ; 2. Oij = 0, if i = j and link i is not adjacent to link 7; 3. a = Jt, if i j and link ; is adjacent to link7. where subscripts i and j are the row and the column subscripts, respectively; L represents the name of links; Jt denotes the type of joint incident with links ; and j ; and DOF denotes the relative degree of freedom between links / and j . For the two machining centers shown in Fig. 3, their corresponding LAMs are shown in Figs. 5(c) and (d). M Cz I -7 P x PzPy M R f l Pv (a) (b) Mechanism Allocation Matrix In order to represent the structure of machining centers clearly, we present the concept of mechanism allocation matrix (MAM), by modifying the definition of LAM, as follows: 1. b,j = L, if; = j 2. by = 0, if i i= j and link ( is not adjacent to link; 3. by = Jt, if i j and link ; is adjacent to link7. where Ax represents the joint axis allocation in the coordinate system. For the two machining centers shown in Fig. 3, their corresponding MAMs are shown in Figs. 5(e) and (/). Generalized Tree Graphs The third step of the design process is generalization. The purpose of generalization is to transform the existing mechanisms, which involve various types of links and joints, into their corre-sponding generalized tree graphs. The process of generalization is based on a set of generalizing rules. These generalizing rules are derived according to defined generalizing principles. The general-izing principles and rules are described in detail in references (Yan and Chen, 1985; Yan and Hwang, 1988). For the tree graph of the machining center shown in Fig. 5(a), the generalization is carried out by the following steps: 1. The fixed link is released and generalized into a ternary link. 2. The links, such as the spindle, the tool magazine, or the working table, are all generalized into singular links. 3. The other links are generalized into binary links. 4. The prismatic pairs are generalized into revolute pairs. where singular, binary, and ternary links are the links incident with 1, 2, and 3 joints, respectively. Figure 6(a) shows its corresponding generalized tree graph. Similarly, the generalized tree graph of the machining center shown in Fig. 5(b) is shown in Fig. 6b). Atlas of Tree Graphs The fourth step of the design process is to generate all possible tree graphs with the given numbers of edges and vertices. The explicit numbers of tree graphs through A vertices can be obtained from the counting series, i.e., the generating function (Deo, 1974): Tix) = X + x + x + 2x + 3x + 6x+ Ix + 23 + 47: -I- lOex + 235A: + 551X + . . . (1) The atlas for the tree graphs counted in the first 10 terms of Eq. (1) may be found in reference (Harry, 1969). S R IL, 0 1 0 0 0 0 0 0 .0 0 0 0 0 0 P 0 0 0 Fr P 0 P 1 L, P 0 0 T O 1 0 OL3 0 0 0 2 0 0 0 0 0 c M. (c) S R L, I 0 0 0 0 0 0 0 0 0 P 0 T P 1 M (d) Specialized Tree Graphs The fifth step of the design process is specialization. The process of specialization is to assign specific types of links and joints into available atlas of tree graphs to generate all possible specialized tree graphs subject to topology constraints. Design requirements and constraints of links and joints of machining centers in their corresponding tree graphs are listed. Then, the assignment rules of links and joints are concluded. Finally, all possible topology struc-tures are obtained after specialization. S R zL| 0 y 0 0 0 0 0 0 0 0 0 p Fr z 0 x 0 0 0 0 0 0 0 P O P L, P 0 X T 0 0 OL, 0 0 z 0 0 0 0 0 c M S R zL, 0 y 0 0 0 0 0 0 0 P L, z 0 0 0 0 P L, X 0 0 0 0 0 0 0 P 0 T P xM (e) (f) Fig. 5 Topological structure representations 362 / Vol. 121, SEPTEMBER 1999 * (a) (b) Fig. 6 Generalized tree graphs Transactions of thie ASME Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmAdjacent matrix Distant matrix Findi, where 2*1/ . i-l,2,.orn. Findi, where di=4 , i=l,2,.orn, Set x = T k=0 Find i, where dsi=4-k &d =k, Set x = Fr Findi, where x = /, i=I,2,.orn, and x = 0, Set x = M i = i+1 k = k+l E=.R,P.P,P y SetEui=Jt,J3-i) wheredt +ra =4,b-I,2 or,n Topological constraints Link adjacent matrix Complete structure synthesis 4. There must be a vertex, which is a pendant vertex branching from the branch vertex located on the path from the frame to the spindle head, as the tool magazine. 5. The edge incident with the spindle must be assigned as a revolute pair. 6. The edges between the spindle head and the working table must be assigned as prismatic pairs. 7. The edges between the tool magazine and the branch vertex must be assigned as revolute, prismatic, or cylindrical pairs. And, if there is a revolute pair or a cylindrical pair, it must be incident with the tool magazine. Based on the topological requirements of existing mechanisms, the assignment rules of links and joints are concluded as follows. Link assignment rules 1. Select a pendant vertex as the spindle. 2. Select a vertex, where the length of path to the spindle is four, as the working table. If this vertex does not exist, delete this graph and go to step 6. 3. Select a vertex, which is located on the path from the spindle head to the working table, as the frame. 4. Select a vertex, which is the pendant vertex branching from the branch vertex located on the path from the spindle head to the frame, as the tool magazine. If this vertex does not exist, delete this graph and go to step 6. 5. The other unassigned vertices are assigned as links L. 6. Complete the link assignment. f Stop J Joint assignment rules Fig. 7 Specialization flowchart Topology Requirements Topology requirements are concluded according to the topology characteristics of existing mechanisms. For our example, the de-sign requirements of links and joints of the 3-axis horizontal machining centers in their corresponding tree graphs are: 1. There must be a pendant vertex as the spindle. 2. There must be a vertex, where the length of path to the spindle is four, as the working table. 3. There must be a root, which is located on the path from the spindle head to the working table, as the frame. 1. The edge incident with the spindle is assigned as a revolute pair. 2. The edges on the path from the spindle head to the working table are assigned as prismatic pairs. 3. Based on the length of path from the branch vertex to tool magazine, the edges can be assigned according to the joint permutations of R, P, and C. After specialization, we must identify these specialized tree graphs subject to topology constraints of the mechanisms of ma-chining centers we would like to create. For our example, the topology constraints are listed as follows: 1. The pendant vertices must be the spindle, the tool magazine, or the working table. 2. The vertex of tool magazine is located on the branch from the spindle head to the frame. 3. The revolute pair must be incident with the spindle or the tool magazine, and the cylindrical pair must be incident with the tool magazine. According to the link and joint assignment rules, we can spe-cialize the atlas of tree graphs to obtain the specialized tree graphs. The process of specialization can be computerized by inputting adjacent matrices of the tree graphs into the program and resulting with desired link adjacent matrices and the numbers of topological structures. Figure 7 shows the computer flowchart of specializa-tion, and the numbers of topological structures that satisfy the topological requirements and constraints are listed in Table 3. Atlas of Mechanisms The last step of the design process is to obtain the atias of mechanisms, based on the concept of axis allocation, subject to Table 3 No. of the topological structures of machining centers No. of links 7 No. of topological structures 30 30 30 Journal of Mechanical Design SEPTEMBER 1999, Vol. 121 / 363 Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmLink adjacent matrix I . = (z,y,.x) I Fmdb, whered +d, = 4&d=n-5 X h=l i,Set p = orOji *0&iJ,Sl Jl.-p = J&q &q S i , = / -P.q.0.k) r-i,Set p = i&q = J, oraj,*OAIl,Selp = J&q = l, J=U orn,J*S i i-(p.qAk) -!l 1 Pz Rz - Pz - Px and Px - Pz Pr -* Pz - Px for drum type and linear type tool magazines respectively, where x, y, and z axes are parallel to X, Y, and Z axes, respectively. According to the motion constraints, the first step of motion synthesis is to assign the directions of motion axes of the machine tool structure to speciaUzed tree graphs. And, the second step is to allocate the directions of tool change motion axes according to different types of tool change motion sequences. The last step is to check whether there is a redundant degree of freedom that is not assigned. Therefore, based on the motion constraints, the process of tool change motions is concluded as follows: 1. For the motion of grasping or leaving tool, there must he a linear degree of freedom in X direction between the spindle head and the tool magazine. 2. For the motion of extracting or inserting tool, there must be a linear degree of freedom in Z direction between the spindle head and the tool magazine. 3. For the motion of changing tools, there must be a rotary degree of freedom in Z direction or a linear degree of freedom in Y direction between the spindle head and the tool magazine. Therefore, by way of the graph theory approach, the procedures of tool change motion synthesis are proposed as follows: Step 1: If there is no degree of freedom between the branch vertex and the tool magazine that can be assigned as the tool change motion, go to step 4; otherwise continue. Step 2: If there is no degree of freedom between the spindle head and the branch vertex which can be assigned as the axis of tool change motion, assign the degree of freedom between the branch vertex and the tool magazine as the tool change motion, go to step 5; otherwise continue. Step 3: If there is a degree of freedom between the spindle head and the branch vertex which can he assigned as the axis of tool change motion, assign the degree of freedom between the branch vertex and the tool magazine or between the branch vertex and the spindle head as the tool change motion, and go to step 5. Step 4: If there is a degree of freedom between the branch vertex and the spindle head that can be assigned as the tool change motion, go to step 5; otherwise delete this spe-cialized tree graph. Table 4 No. of configurations of macliining centers No. of links 5 6 7 Drum type magazine 0 2 13 Linear type magazine 1 5 20 8 20 60 364 / Vol. 121, SEPTEMBER 1999 Transactions of the ASME Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmTR. S h S P S 1 R p y mv p R p, Rz-(a) (b) (c) R. S T R, R P v Rz (d) M R, R P y Rz s R, R P, R; (f) r* M Cz P x S T P x Pz P y Rz (g) p p *p *R f , ni fz fy z s (h) o a p R n * n * F r R P y R (i) M n p R F T R P y Rz (k) M RZR P y f Cz f S Fr PxPzTry R (m) R( s T P x PzPy R (n) P x P z P y f;Rz (o) Fig. 9 Tree-graph representations of machining centers Step 5: Continue to complete the tool change motion synthesis, go to step 1; otherwise stop. If there is a redundant degree of freedom between the branch vertex and the tool magazine that is not assigned as the tool change motions, delete this specialized tree graph. According to tool change motion sequences, we can assign acceptable speciaUzed tree graphs to their corresponding mecha-nisms step by step. And, some topological structures that can not satisfy the tool change motions should be removed. Figure 8 shows the computer flowchart of motion synthesis based on the graph theory approach. By inputting link adjacent matrices obtained in specialization, the corresponding mechanism allocation matrices are automatically synthesized. For the topolog-ical structures after specialization, the motion synthesis for differ-ent types of tool change motion sequences results the configura-tions of machining centers that can be represented by MAM in the computer program. And, Table 4 lists the number of configurations of machining centers up eight Unks for different types of tool magazines. As the result, for the machining centers with drum type tool magazine, the minimum number of links of the mechanism of machining centers is 6 and the numbers of configurations of machining centers with 6, 7, and 8 links are 2, 13, and 20, respectively. Similarly, for the machining centers with linear type tool magazine, the minimum number of links of the mechanism of machining centers is 5 and the numbers of configurations of machining centers with 5, 6, 7, and 8 links are 1, 5, 20, and 60, respectively. Figure 9 shows the tree-graph representations of machining centers with drum type tool magazine that are drawn automatically from the results of motion synthesis based on the concept of MAM. And, according to the tree-graph representa-tions, we can draw their corresponding schematic drawings of machining centers. Figures 10 and 11 are the schematic drawings of the configuration of machining centers with the drum type and linear type tool magazines, respectively. Figures 10(a)-() and 10(c)-(o) are 6 and 7 links, respectively. And, Fig. ll(fl), 11()-(/), and llg)-iz) are 5, 6, and 7 Unks, respectively. Conclusion In summary, a systematic design methodology is presented for the configuration design of machining centers with automatic tool changer subject to topology and motion constraints. The design process is computerized and all possible configurations of machin-ing centers up to eight links are synthesized. From the found (k) (1) (i) (n) Fig. 10 IVIachining centers with drum type magazine (o) Journal of Mechanical Design SEPTEMBER 1999, Vol. 121 / 365 Downloaded 26 Nov 2008 to 09. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfm(w) (x) (y) Fig. 11 Machining centers with linear type magazine M configurations, the designer can select the useful ones according to design requirements, patent rights, machine tool structural, and space constraints. This design methodology can synthesized all possible configurations of machining centers for different types of machine tool structures, such as 4