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学士学位论文原创性声明本人声明，所呈交的论文是本人在导师的指导下独立完成的研究成果。除了文中特别加以标注引用的内容外，本论文不包含法律意义上已属于他人的任何形式的研究成果,也不包含本人已用于其他学位申请的论文或成果。对本文的研究作出重要贡献的个人和集体，均已在文中以明确方式表明。本人完全意识到本声明的法律后果由本人承担。作者签名： 日期： 学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅。本人授权南昌航空大学可以将本论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文。 作者签名： 日期：导师签名： 日期：毕业设计（论文）外文翻译题目五轴磨床加工工具运动链的设计和分析专 业 名 称 机械设计制造及其自动化班 级 学 号 068105337学 生 姓 名 郑帅栋指 导 教 师 罗海泉填 表 日 期 2010 年 5 月 18 日五轴磨床加工工具运动链的设计和分析E.L.J. Bohez，设计与制造工程部门，亚洲技术研究所摘要：五轴CNC加工中心现在应用得非常广泛。大多数机器的运动学原理都是以直角笛卡儿坐标系统为基础的。这篇文章对有可能的概念上的设计和基于理论上有可能的自由度的结合并且真实存在的器械进行了分类。本文还定义了一些有用的定量参数，例如：工作空间利用因素、机器加工工具的空间利用率、方位空间的指标和方位角。同时还分析了不同概念的优缺点，给出了选择的标准和机器结构的设计。最近在工业中提出的一些基于斯图尔特平台的概念也将在这篇文章中进行简要的论述。关键词：五轴；机器加工工具；运动链；工作空间；CNC；旋转轴1.介绍机器加工工具的主要设计规范应该满足以下法则：1） 运动件在工具和零件的定位和安置上应该 有足够的弹性。2） 以可能的最快的速度进行定位和安置。 3） 以可能的最高的精确度进行定位和安置。 4） 加工工具和工件的快速切换。5） 保护环境。6） 可能的高速材料移动率。 一台机器的加工工具的轴的个数通常是由机器自由度数或者是在机器滑动过程中独立可控的运动数来决定的。随着加工工具轴对应Z坐标轴的产生，ISO轴命名法推荐使用右手坐标法则。一个三轴磨床有三个方向的线性滑动：X、Y和Z，这使得机器能放置在相应轴向滑动范围内的任何一个位置。加工工具轴的方向在加工的时候保持不变。这就限制了与工件连接的加工工具的弹性，并最终导致很多不同的结构。为了增加在可能的加工工具、工件定位中的弹性而不用重新设计结构，我们将要在增加更多的机器的自由度。对于一个传统的三线性轴机器，能通过提供旋转滑动来实现。图1就展示了一个五轴磨床的例子。2.运动链接图制作一个机器的运动链接图对于分析机器是很有用的。从运动链接图中我们可以很快区别两组轴：图2展示了在图1中五轴磨床的运动链接图。从图中我们可以看到，工件由四根轴运载，而加工工具只由一根轴运载。 五轴机器就像两个相互协作的机器人，一个机器人运载工件，另一个机器人则运载加工工具。为了得到工件和工具定位上最大的弹性，机器至少需要5个自由度，这意味着工具和工件能在任何角度下连接起来。从一个刚性的物体运动连接点的观点来说，我们也可以理解对轴的个数的最低要求。为了定位两个在空间上相互连接的刚体，每个刚体（工具和工件）需要6个自由度或者12个自由度。然而，任何不改变两者之间定位的共同的平移和旋转的存在将会使自由度数目减少6个。两个刚体之间的距离是由工具的加工路径来决定的，这个距离也将会允许减少一个多余自由度，这样就使得最小的自由度数为5。3.文化背景（略）4.五轴机器运动结构的分类按照机器的旋转和平移轴分类，我们可以把机器运动结构分为四大类：（1）三个平移轴和两个旋转轴；（2）两个平移轴和三个旋转轴；（3）一个平移轴和四个旋转轴；（4）五个旋转轴。近乎所有存在的五轴机器设备都属于（1）类。很多的定位焊接机器人、圈丝机器和激光加工中心也属于这一类。只有有限的一些用来加工轮船推进器的五轴机器属于（2）类。（3）和（4）类只有在设计需要增加更多自由度的机器人的时候才会用到。五根轴可以分布在工具和工件之间的结合处。第一种分类是根据运载轴的工具和工件的数量和在运动链中各个轴的次序来划分的。另一种分类是根据旋转轴放置的位置（是在工具那边还是在工件那边）来划分的。基于笛卡儿坐标的机器中的五个自由度是：三个平移运动X、Y、Z（一般表示为TTT）和两个旋转运动AB、AC、BC（一般表示为RR）。三个旋转轴（RRR）和两个直线运动轴（TT）的结合是很少见的。如果一根轴承载着工件，习惯上是用一个附加的标记来注释它。图1中的机器能以XYABZ。XYAB轴运载着工件，Z轴运载着工具。图3中展示的是XYZAB，三根直线运动轴运载工具,两根旋转轴运载着工件。4.1基于工件和工具运载轴次序的分类理论上，如果认为在工具和工件运载轴的两个运动链上的轴的次序有不同的结构，可能的结构的数目会非常大。同时只有两根直线运动轴和三根旋转轴结合也包括在内。在一个五轴机器中能以以下方式将一根工具运载轴和四根工件运载轴结合：对于X，Y，Z，A，B，C中任意一个可能作为工具运载的轴，其他工件运载轴可以在剩下的五根轴中选取。所以，对于任意可能的工具运载轴选择（六选一或者有六种可能），在剩下的五根轴中选取四根进行不同结构的排列个数为5*4！=120。所以，理论上只有一根工具运载轴的五轴机器就有6*120=720种可能。其他的结合方式也可以用这种方法分析。假设t代表工具运载轴的数目，w表示工件运载轴的数目（w+t=5），那么全部可能的结合数如下所示：这个方程式的值恒等于6！或者当w+t=5时这个值等于720。在这些720的结合中，有一些只包含两根直线运动轴。如果只考虑有三根直线运动轴的五轴机器，只有3*5！=360的结合也是仍是有可能的。这些结合的预设值Gt主要是由t的预设值决定的。这个预设值和由w的预设值所决定的Gw 的预设值是一致的，其中w=5-t。运用以上的定义，我们可以把五轴机器分为以下小群：（1）G0/G5组；（2）G1/G4组；（3）G2/G3组；（4）G3/G2组；（5）G4/G1组；（6）G5/G0组。4.2基于旋转轴的位置的分类我们能根据旋转轴装配的位置对机器进行分类。只有那些有两根旋转轴和三根线性轴的机器我们才会进一步考虑。可能的结构如下：（a）旋转轴装配在工具杆上；（b）旋转轴装配在机器平台；（c）两者的结合。如果机器的轴的R或者T的类型一样，那么在工具或者工件运载运动链中轴的次序就不重要了。一般来说，如果在工件运载运动链中有根平移轴和根旋转轴，在工具运动链中有根平移轴和根旋转轴，那么结合的个数为11：其中每一组的结合的个数在下面中将会一个个给出。所有组的结合总数为60。从设计的观点来说，这是我们所考虑的选择的数量中较为容易处理的一个。5.五轴机器的工作空间在定义五轴机器设备的工作空间之前，要适当的定义加工工具的工作空间和工件的工作空间。加工工具的工作空间就是通过沿着工具运载轴路线描绘出工具扫过参考点（例如工具尖端）而得到的。工件运载轴的工作空间也是用同样方法定义的（把机器平台的中心选择作为参考点）。这些工作空间能由计算扫过过的体积决定6。基于以上的定义，我们能定义一些对于不同类型机器比较、选择和设计有用的定量参数。5.1.工作空间利用因素 这个因素可以定义为，工件空间和工具空间的交集与工具空间和工件空间的并集的比。公式为5.2.可加工的体积大小一旦工件相对于工件参考点是固定的，并且一个特殊的工具相对于工具参考点也是固定的，那么我们就有可能确定可加工的体积的大小。可加工的体积就是能够在工件上切除的全部体积。机器工具空间和工件的交集给出了可以切除的材料的总量，或者说是可加工的体积（这是对于特殊的工件和工具机构来说的）。5.3.机器工具空间效率机器工具空间效率的定义为：机器工具空间（省略了一部分）和包含着机器的最小凸起体积。5.4.五轴机器的定位空间指数一个我们用来估计定位的最大范围的方法是为了决定能在机器上用两根旋转轴加工的球的最大部分。空间定位指数定义为能够由用所有旋转轴加工的机器来加工的最大的球顶体积除以机器工具空间。如果这个指数趋近于1，这就意味着所有的旋转轴能够在整个机器工具空间中运用。如果这个指数比1小，这就意味着大概百分之的工作空间能运用所有的旋转轴。以上的定义都是理论上的定义。实际上的定位空间指数会因为避免零件和机器、工具和工件之间的碰撞而进一步受到限制。能够加工的球顶变小就说明了这一点。6.五轴机器的选择标准我们的目的不是对五轴机器对于某一项特定的运用的选择或者设计进行一个彻底的研究。我们只是论述能用来判断五轴机器的选择的主要的标准。6.1.五轴机器设备的应用 应用能在布置和造型上进行区分。图12和图13说明了五轴的布置和五轴造型上的区别。6.1.1.五轴布置 如图12所示，一个在不同角度有着很多孔和平面板的零件，仅仅用一台三轴磨床来加工这个零件是不可能的。如果我们在用一台五轴机器，那么工具能在任何方向和工件定位连接起来。一旦达到了正确的位置，在大多数轴固定的情况下，我们就可以对孔和平面板进行加工了。平面板中能包括独立结构的2D平面。如果我们仅仅是要钻孔，那么理论上一轴CNC同步控制就足够了，而加工2D平面时两轴同步控制就够了。然而，三轴同步现在也很普遍了。当我们把工件和工具放置在连接在一起的时候，这就增加了在开始切削前的快进的速度。6.1.2.五轴造型 图13所示为一个五轴造型的例子，为了加工这个形状复杂的表面，我们需要在切削时控制好与零件接触的刀具的位置。刀具工件的位置在每一步工序中都会改变。CNC控制器需要在材料切除过程中同步控制五轴。更多关于造型的细节能在参考文献13中找到。五轴的机器有如下的应用：（1）生产刀刃，如： 压缩机和涡轮的浆；（2）燃料泵的注射器；（3）头饰的外形；（4）医学器官例如人造心脏阀；（5）复杂表面的铸型。6.2.轴结构的选择在设计和选择一个结构时，零件的尺寸和重量是首要的标准。重型工件要求工件运动链短。同时，水平加工平面又是较好的一种设计，这种设计会使定位和处理工件变得很便利。把一个重型工件放在一个单独旋转轴运动链上将会很大程度上增加定位的弹性。从图4中我们可以看出，用一个单独水平旋转轴来运载工件会使得机器更加具有弹性。在很多情况下，我们应该把工具运动链保持得尽量短，因为我们还必须运载工具轴驱动装置。7.基于斯图尔特平台的新的机器概念（略）8.结论理论上，五轴机器有很多构成方式。近乎所有经典的笛卡儿坐标五轴机器都属于由三根线性轴和两根旋转轴，或者三根旋转轴和两根线性轴组成的系列。这个系列又可以细分为有着720种情况的六组。就算只考虑三根线性轴的情况，在每个系列中仍然有360种组合。这些不同的组合是根据在工具和工件运载运动链中轴的次序来区分的。如果在对由三根线性轴和两根旋转轴组成的五轴机械进行分组时，只考虑在工具和工件运动链中旋转轴的位置，那么我们能五轴机器分为三组。在第一组中，两根旋转轴安置在工件运动链。在第二组中，两根旋转轴安置在工具运动链。在第三组中，每个运动链都安置一根旋转轴。每一组仍然有20种可能的情况。对于一个特定的应用领域，要从这些组合中选出一组最好的是一项很复杂的工作。为了使这项工作变得容易些，我们定义了一些用于比较的指数，例如：机器刀具空间、空间利用因素、定位空间指数、定位角度指数和机器刀具空间效率。列出了用来计算机器刀具空间和在机器上能加工的最大球顶的直径的算法。详细论述了两个运用这些指数的例子。第一个例子论述的是加工珠宝的五轴机器的设计。第二个例子则阐明了一台机器在线性轴中有着相同范围，在这种情况下，旋转轴选项的选择（略）。运用得最广泛的五轴机器的两根旋转轴安置在运动链末端处的工件一侧。这种结构给出了一种对于机器刀具结构的模块设计。然而，从应用的观点来说，这种模块设计并不总是最理想的。因为理论上存在很多可能的结构，很明显的是，对于一个特殊的工件装置需要一个合适的特定的五轴机器。模块设计应该以在所有的五轴结合中的模块性为基础。当前在设计中的模块性是以三线性轴机器为基础的。五轴磨床使得机器结构的数量变小。这对增加精确度和减小大部分尺寸是有帮助的。然而，它也有一些缺点：（1）五轴机器的高价；（2）增加的旋转轴的同时也增加了定位误差；（3）在同等的进给下，在机器轴上的切削速度更高。在购买五轴机器之前必须要对需要加工的产品的范围进行深入的研究。那些零件也应该分为五轴定位或者是五轴造型，或者两者都是。例如，有着旋转平台的机器对于生产诸如压缩机的旋转工件是很好的。一根旋转轴在刀具侧，一根旋转轴在工件侧，这样的布置将会提供更大的工作空间利用因素。最近所介绍的虚拟轴机器有着一个主要的优点：潜在的更高的动力响应和更高的硬度。然而，它的工作空间利用因素比经典的五轴机器要低。这些机器的更高强度使得他们非常适于高速磨所需要的高速杆19的设计。9International Journal of Machine Tools & Manufacture 42 (2002) 505520Five-axis milling machine tool kinematic chain design and analysisE.L.J. Bohez*Department of Design and Manufacturing Engineering, Asian Institute of Technology, P.O. Box 4, Klong Luang, 12120 Pathumthani, ThailandReceived 23 May 2000; received in revised form 12 September 2001; accepted 13 September 2001AbstractFive-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on arectangular Cartesian coordinate system. This paper classifies the possible conceptual designs and actual existing implementationsbased on the theoretically possible combinations of the degrees of freedom. Some useful quantitative parameters, such as theworkspace utilization factor, machine tool space efficiency, orientation space index and orientation angle index are defined. Theadvantages and disadvantages of each concept are analyzed. Criteria for selection and design of a machine configuration are given.New concepts based on the Stewart platform have been introduced recently in industry and are also briefly discussed. 2002Elsevier Science Ltd. All rights reserved.Keywords: Five-axis; Machine tool; Kinematic chain; Workspace; CNC; Rotary axis1. IntroductionThe main design specifications of a machine tool canbe deduced from the following principles:? The kinematics should provide sufficient flexibility inorientation and position of tool and part.? Orientation and positioning with the highest poss-ible speed.? Orientation and positioning with the highest poss-ible accuracy.? Fast change of tool and workpiece.? Save for the environment.? Highest possible material removal rate.The number of axes of a machine tool normally refersto the number of degrees of freedom or the number ofindependent controllable motions on the machine slides.The ISO axes nomenclature recommends the use of aright-handed coordinate system, with the tool axis corre-sponding to the Z-axis. A three-axis milling machine hasthree linear slides X, Y and Z which can be positionedeverywhere within the travel limit of each slide. The toolaxis direction stays fixed during machining. This limits* Tel.: +66-2-524-5687; fax: +66-2-524-5697.E-mail address: bohezait.ac.th (E.L.J. Bohez).0890-6955/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0890-6955(01)00134-1the flexibility of the tool orientation relative to the work-piece and results in a number of different set ups. Toincrease the flexibility in possible tool workpiece orien-tations, without need of re-setup, more degrees of free-dom must be added. For a conventional three linear axesmachine this can be achieved by providing rotationalslides. Fig. 1 gives an example of a five-axis millingmachine.Fig. 1.Five-axis machine tool.506E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 5055202. Kinematic chain diagramTo analyze the machine it is very useful to make akinematic diagram of the machine. From this kinematic(chain) diagram two groups of axes can immediately bedistinguished: the workpiece carrying axes and the toolcarrying axes. Fig. 2 gives the kinematic diagram of thefive-axis machine in Fig. 1. As can be seen the work-piece is carried by four axes and the tool only by oneaxis.The five-axis machine is similar to two cooperatingrobots, one robot carrying the workpiece and one robotcarrying the tool.Five degrees of freedom are the minimum required toobtain maximum flexibility in tool workpiece orien-tation, this means that the tool and workpiece can beoriented relative to each other under any angle. Theminimum required number of axes can also be under-stood from a rigid body kinematics point of view. Toorient two rigid bodies in space relative to each other 6degrees of freedom are needed for each body (tool andworkpiece) or 12 degrees. However any common trans-lation and rotation which does not change the relativeorientation is permitted reducing the number of degreesby 6. The distance between the bodies is prescribed bythe toolpath and allows elimination of an additionaldegree of freedom, resulting in a minimum requirementof 5 degrees.3. Literature reviewOne of the earliest (1970) and still very useful intro-ductions to five-axis milling was given by Baughman 1clearly stating the applications. The APT language wasthen the only tool to program five-axis contouring appli-cations. The problems in postprocessing were alsoFig. 2.Kinematic chain diagram.clearly stated by Sim 2 in those earlier days of numeri-cal control and most issues are still valid. Boyd in Ref.3 was also one of the early introductions. Beziers book4 is also still a very useful introduction. Held 5 givesa very brief but enlightening definition of multi-axismachining in his book on pocket milling. A recent paperapplicable to the problem of five-axis machine work-space computation is the multiple sweeping using theDenawit-Hartenberg representation method developedby Abdel-Malek and Othman 6.Many types and design concepts of machine toolswhich can be applied to five-axis machines are discussedin Ref. 7 but not specifically for the five-axis machine.The number of setups and the optimal orientation ofthe part on the machine table is discussed in Ref. 8. Areview about the state of the art and new requirementsfor tool path generation is given by B.K. Choi et al. 9.Graphic simulation of the interaction of the tool andworkpiece is also a very active area of research and agood introduction can be found in Ref. 10.4. Classification of five-axis machines kinematicstructureStarting from Rotary (R) and Translatory (T) axes fourmain groups can be distinguished: (i) three T axes andtwo R axes; (ii) two T axes and three R axes; (iii) oneT axis and four R axes and (iv) five R axes. Nearly allexisting five-axis machine tools are in group (i). Also anumber of welding robots, filament winding machinesand laser machining centers fall in this group. Only lim-ited instances of five-axis machine tools in group (ii)exist for the machining of ship propellers. Groups (iii)and (iv) are used in the design of robots usually withmore degrees of freedom added.The five axes can be distributed between the work-piece or tool in several combinations. A first classi-fication can be made based on the number of workpieceand tool carrying axes and the sequence of each axis inthe kinematic chain. Another classification can be basedon where the rotary axes are located, on the workpieceside or tool side. The five degrees of freedom in a Car-tesian coordinates based machine are: three translatorymovements X,Y,Z (in general represented as TTT) andtwo rotational movements AB, AC or BC (in general rep-resented as RR).Combinations of three rotary axes (RRR)and two linear axes (TT) are rare. If an axis is bearingthe workpiece it is the habit of noting it with anadditional accent. The five-axis machine in Fig. 1 canbe characterized by X?Y?A?B?Z. The XYAB axes carry theworkpiece and the Z-axis carries the tool. Fig. 3 showsa machine of the type XYZA?B?, the three linear axescarry the tool and the two rotary axes carry the work-piece.507E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 3.XYZA?B? machinery.4.1. Classification based on the sequence of workpieceand tool carrying axesTheoretically the number of possible configurations isquite large if the order of the axes in the two kinematicchains of the tool and workpiece carrying axes is countedas a different configuration. Also the combinations withonly two linear axes and three rotary axes are included.One tool carrying axis and four workpiece carryingaxes can be combined in a five-axis machine as follows:for each possible tool carrying axis X,Y,Z,A,B,C the otherfour workpiece carrying axes can be selected from thefive remaining axes. So the number of combinations offour axes out of five with considering different permu-tation as another configuration is 54!=120 for eachpossible tool axis selection (1 out of 6 or 6 possibilities).So theoretically there are 6120=720 possible five-axismachines with one tool carrying axis. The same analysiscan be done for all other combinations. With t the num-ber of tool carrying axes and w the number of workpiececarrying axes (w+t=5) the total number of combinationsis as follows.Ncomb=?6t?t!?6tw?w! t?3, t+w=5(1)Ncomb=?6w?w!?6wt?t! t?3, t+w=5(2)The value of this equation is always equal to 6! or720 when w+t=5. Some of these 720 combinations willbe containing only two linear axis. If only five-axismachines with three linear axes are considered, only35!=360 combinations are still possible.The set Gt of combinations is characterized by a fixedvalue of t. This set is identical to the set G?w charac-terized by a fixed value of w, w=5?t. Using above defi-nitions following subgroups of five-axis machines exist:(i) Group G0/G?5; (ii) Group G1/G?4; (iii) GroupG2/G?3; (iv) Group G3/G?2; (v) Group G4/G?1; (vi)Group G5/G?. G5/G0? machineAll axes carry the tool and the workpiece is fixed ona fixed table. Fig. 4 shows a machine with all the fiveaxes carrying the tool. The kinematic chain is XBYAZ(TRTRT). This machine was one of the earliest modelsof five-axis machines to handle very heavy workpieces.As there are many links in the tool carrying kinematicchain, there can be a considerable error due to elasticdeformations and backlash in the slides.4.1.2. G0/G5? machineAll axes carry the workpiece and the tool is fixed inspace. This construction is best used for very smallworkpieces (see Section 6.3).Fig. 4.XBYAZ machine.508E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 5055204.1.3. G4/G1? machineFour axes carry the tool and one axis carries the work-piece. There are basically two possibilities, the work-piece carrying axis can be R? or T?.4.1.4. G1/G4? machineOne axis carries the tool and the other four axes carrythe workpiece. There are basically two possibilities, thesingle axis kinematic chain can be R or T. Fig. 1 is anexample of such a machine, with the single tool carryingaxis T.4.1.5. G3/G2? machineThree axes carry the tool and two axes carry the work-piece. There are basically three possibilities, the work-piece carrying axes can be both linear (T?T?) bothrotational (R?R?) or mixed (T?R?). Fig. 5 gives anexample of a machine with the tool carried by two rotaryaxes and one linear axis. This machine allows processingof large workpieces but the construction of the toolsideis complicated. The most common configuration is theworkpiece carried by the two rotary axes such as the onegiven in Figs. 3, 6 and . G2/G3? machineTwo axes carry the tool and three axes carry the work-piece. There are basically three possibilities, the tool car-rying axis can be both linear (TT) both rotational (RR)or mixed (TR). Fig. 7 shows the mixed construction. Fig.8 shows two linear axes carrying the tool.4.2. Classification based on the location of rotaryaxesThe machines can be classified depending on the placewhere the rotation axes are implemented.Fig. 5.X?Z?CAY machine.Fig. 6.B?C?ZYX machine.Fig. 7.Z?X?C?BY machine.509E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 8.Z?A?B?YX machine.Only machines with two rotary axes and three linearaxes will be considered further. The possible configur-ations are:(a) rotation axes are implemented on tool spindle;(b) rotation axes are implemented on machine table;(c) combination of both.The sequence of the axes in the tool or workpiececarrying kinematic chain is not important if the axes areof the same type R or T. In general, if there are N?Ttrans-latory axes and N?Rrotary axes in the workpiece carryingkinematic chain and NTtranslatory axes and NRrotaryaxes in the tool kinematic chain, then the numbers ofcombinations is 11:Ncomb?(N?T?N?R)!N?T!N?R!(NT?NR)!NT!NR(3)with N?T?NT?3, N?R?NR?2The number of combinations of each group will be givenbelow case by case. The total number of combinationsover all groups is 60. From the design point of view thisis a more tractable number of alternatives to be con-sidered.4.2.1. R?R? machineThe two rotary axes carry the workpiece. The tool axiscan be fixed or carried by one (T), two (TT) or three(TTT) linear axes.The number of possible designs is the sum of the fol-lowing combinations:(i) For the group G0/G5? the tool is fixed in space allthe five axes will carry the workpiece. The numberof different designs is 10 (NT?=3 and NR? =2), (Figs.15 and 16).(ii) For the group G1/G4?, NT+NR=1, so NT=1 and NR=0,is the only possible choice for the tool kinematicchain. Equation (3) gives NCOMB=6. The combi-nationsare:R?R?T?T?T;T?T?R?R?T;R?T?R?T?T;T?R?T?R?T; R?T?T?R?T; T?R?R?T?T. Fig. 9 showsthese six designs.(iii)For the group G2/G3? the tool axes are TT so NT?=1,NR?=2, NT=2, NR=0 and Equation (2) gives NCOMB=3.The three design combinationsare: R?R?T?TT;R?T?R?TT and T?R?R?TT. The group G2/G3? containsthree instances of the R?R? machine. These instancesare represented in Fig. 10.(vi) If the tool axes are TTT the workpiece carrying axescan only be R?R?. So only one design combinationis possible.From the above-mentioned findings it can also be con-cluded that the total number of R?R? five-axis machineconfigurations is 20.Machines with two axes on the clamping table can beseen in Figs. 1, 3, 6 and 8. The advantages are:Fig. 9.Members of group G1/G4?.510E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 10.R?R? machines in group G2/G3?.? In case the spindle is horizontal, optimal chip removalis obtained through the gravitational effect of thechips just dropping.? The tool axis during machining is always parallel tothe Z axis of the machine. So the drilling cycles canbe executed along the Z-axis of the machine. Circlesunder a certain orientation of the workpiece arealways executed in the XY plane of the machine. Theabove-mentioned functions can be executed in thesimple three-axis numerical control mode.? The compensation of the tool length happens all thetime in the NC control of the machine, as with three-axis machines.Disadvantages:? Machines with a rotating table are only for work-pieces with limited dimensions.? The useful workspace is usually much smaller thanthe product of the travel in X,Y and Z axis.? The transformation of the Cartesian CAD/CAM coor-dinate (XYZIJK) of the tool position to the machineaxes positions (XYZAB or C) is dependent on the pos-ition of the workpiece on the machine table. Thismeans that in case the position of the workpiece onthe table is changed this cannot be modified by atranslation of the axes system in the NC program.They must be recalculated. In case the control of theNC machine cannot transform Cartesian coordinatesto machine coordinates, then a new CNC programmust be generated with the postprocessor of theCAD/CAM system every time the position of theworkpiece changes.Important applications for this type:? Five-sided cutting of electrodes for EDM and otherworkpiece.? Machining of precision workpieces.? Turbines and tire profiles with a certain workpiecegeometry rotated over a certain angle. The same NCprogram can be repeated after the zero of the rotationaxis has been inclined over a certain angle.4.2.2. RR-machineThenumberofpossibledesigncombinations(NCOMP=20) is the same as in the case of the R?R?machine because of the symmetry. Five-axis machineswith the rotation axes implemented on the tool axisspindle can be seen in Figs. 4 and 5.Advantages:? These machines can machine very large workpieces.? The machine axis values of the NC program XYZ,depend on the tool length only. A new clamping pos-ition of the workpiece is corrected with a simpletranslation. This happens with a zero translation in theCNC control of the machine.Disadvantages:? The drive of the main spindle is very complex. Simpledesign and construction is only obtained when thewhole spindle with the motor itself is rotating.? There is a lower stiffness because the rotation axis ofthe spindle is limiting the force transmission. At highrevolutions per minute (higher than 5000 rpm) thereis also a counter acting moment because of the gyro-scopic effect which could be a disadvantage in casethe tool spindle is turning very fast.? Circular interpolation in a random plane and drillingcyclesunderrandomorientationareoftennotimplemented.? A change in the tool length cannot be adjusted by azero translation in the control unit, often a completerecalculation of the program (or postprocessing) isrequired.Important applications of this type of machine tool are:? All types of very large workpieces such as air planewings.4.2.3. R?R machineOne rotary axis is implemented in the workpiece kine-matic chain and the other rotary axes in the tool kinem-atic chain (e.g. Fig. 7).The groups G4/G1?, G4?/G1, G3?/G2, G3/G2? coverthis design. Nowadays there are many machines on themarket with one rotation axis on the tool spindle and511E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520one rotation axis on the table. They are, however, com-bining most of the disadvantages of both previous typesof machines and are often used for the production ofsmaller workpieces. The application range of thismachine is about the same as with machines with tworotation axes implemented on the table.In all possible designs of this machine the NR?=NR=1and NT?+NT=3. The total number of possible designs is:NCOMBNT?0,N?T?3?NCOMBNT?1,N?T?2?NCOMBNT?2,N?T?1?NCOMBNT?3, NT?0or 4+6+6+4=20 possible designs.(i) ForNT?=0andNT=3thefourcombinationsare:R?RTTT; R?TRTT; R?TTRT; R?TTTR.(ii) ForNT?=1andNT=2thesixcombinationsare:T?R?RTT;T?R?TRT;T?R?TTR;R?T?RTT;R?T?TRT; R?T?TTR.(iii)For NT?=2 and NT=1 the six combinations are (seeFig.11):R?T?T?TR;T?R?T?TR;T?T?R?TR;R?T?T?RT; T?R?T?RT; T?T?R?RT.(iv)ForNT?=3andNT=0thefourcombinationsare:R?T?T?T?R; T?R?T?T?R; T?T?R?T?R; T?T?T?R?R.5. Workspace of a five-axis machineBeforedefiningtheworkspaceofthefive-axismachine tool, it is appropriate to define the workspaceof the tool and the workspace of the workpiece. TheFig. 11.R?R machines in the group G2/G3?.workspace of the tool is the space obtained by sweepingthe tool reference point (e.g. tool tip) along the path ofthe tool carrying axes. The workspace of the workpiececarrying axes is defined in the same way (the center ofthe machine table can be chosen as reference point).These workspaces can be determined by computing theswept volume 6.Based on the above-definitions some quantitativeparameters can be defined which are useful for compari-son, selection and design of different types of machines.5.1. Workspace utilization factor WRA possible definition for this is the ratio of theBoolean intersection of the workpiece workspace andtool workspace and the union of the tool workspace andworkpiece workspace.WR?WSTOOL?WSWORKPIECEWSTOOL?WSWORKPIECE(4)A large value for WRmeans that the workspace of thetool and the workspace of the workpiece are about equalin size and overlap almost completely. A small value ofWRmeans that the overlap of tool workspace and work-piece workspace is small and that a large part of theworkpiece workspace cannot be reached by the tool. Theanalogy with two cooperating robots can be clearly seen.It is only in the intersection of the two workspaces ofeach robot that they can shake hands. For the five-axismachine tool this corresponds to the volume in whichthe tool and workpiece reference point can meet.However, in the case where all the five axes carry theworkpiece and the tool is fixed in space the above defi-nition would give a zero value for the workspace utiliz-ation. In the case of cooperating robots it would meanthat there is only one point were they can shake hands.In the case of a five-axis machine, the workpiece canstill be moved in front of the tool and remove metal.The reason is that many points from the workpiece canserve as reference point on the workpiece. All pointswhich can cut on the toolsurface can be used as toolreference point. It is therefore necessary to modify theabove definition for the case of a five-axis machine. Allpoints of the largest possible workpiece which can bebrought into contact with all the tool reference pointsshould be considered as the intersection of the tool work-space and workpiece workspace in the case of five-axismachines. The set of workpiece reference points whichcan be brought in contact with the set of tool referencepoints is defined as the machine tool workspace.WSMT?(WSTOOL?WSWORK),Toolref,WorkrefSo the above formula should be modified as follows.WR?(WSTOOL?WSWORKPIECE)Toolref,WorkrefWSTOOL?WSWORKPIECE(5)512E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520The union of all possible intersections of the toolworkspace and workpiece workspace for all possible toolreference point and workpiece reference points shouldbe used for the numerator.For the denominator the tool workspace and work-piece workspace are taken for a fixed single referencepoint. For the tool reference point the center of thespindle nose reference surface is taken. For the work-piece workspace the center of the machine table surfaceis taken as the reference point.To each possible meeting point corresponds an orien-tation of the toolvector and the vector perpendicular tothe machine table. In fact for each possible meeting pointof the tool and workpiece reference point there can bemore then one possible orientation of the tool andmachine table.5.2. Machinable volumeOnce the workpiece has been fixed relative to theworkpiece reference point, and a specific tool relative tothe tool reference point, it is possible to determine themachinable volume. The machinable volume is the totalvolume which can be removed from the workpiece fora particular instance of the tool and workpiece, and setup of tool and workpiece. The intersection of themachine tool workspace (Section 5.1) and the workpiecegive the amount of material which can be removed orthe machinable volume, for a particular workpiece andtool setup.5.3. Machine tool space efficiency MTSThe machine tool space efficiency is defined as theratio of the Machine Tool workspace (clipped) and thesmallest convex volume which envelopes the machine.MTS(6)?(WSTOOL?WSWORKPIECE)?Toolref,?WorkrefVolume5.4. Orientation space index of a five axis machineOSIA way to asses the maximum range of orientation isto determine the largest part of a sphere which can beproduced on the machine by using the two rotary axes.The orientation index is defined as the ratio of thevolume of the largest spherical dome which can bemachined with the machine using the full range of therotary axes. Divided by the machine tool workspace.OS1?VOLDOME(R1,R2)?(WSTOOL?WSWORKPIECE)?Toolref,?Workref(7)If this index is close to unity it means that the fullrange of the rotary axes can be used in the wholemachine tool workspace. If this index is much smallerthan unity it means that about OSIpercent of the work-space can use the full range of the rotary axes.The above definition is a theoretical definition. Thereal orientation workspace index will be further limitedby the need to avoid collision between parts of themachine, tool and workpiece. This will be reflected in asmaller spherical dome which can be machined.5.5. Outline of algorithm to compute the machine toolworkspaceThe output of the CAM module is an ordered set ofpoints and vectors: x,y,z,i,j,k. The points are the x,y,zcoordinates of the Cutter Location point (or tool refer-ence point) on the tool and the vector components of thetool vector i,j,k. These vectors are given in the work-piece coordinate systems fixed rigidly to the workpiece.The transformation from workpiece to machine coor-dinates is called the geometry transform 2 or inversekinematics. In the case of the five-axis milling machineit is necessary to transform this x,y,z,i,j,k data to themachine slide position coordinates (further called T1, T2,T3, R1and R2) which control the motions of the machine.In nearly all cases the required motions are obtained bya combined movement of the workpiece and the tool onthe specific machine tool. The geometry transformationwill transform from the workpiece coordinate system toapresetmachinecoordinate systemfixed tothemachine frame.The workpiece coordinates x,y,z,i,j,k can be expressedin function of the machine coordinatesT1?FT1x,y,z,i,j,k; T2?FT2x,y,z,i,j,k; T3(8)?FT3x,y,z,i,j,k; R1?FR1i,j,k; R2?FR2i,j,kThe inverse of this transformations gives:x?FXT1,T2,T3,R1,R2; y?FYT1,T2,T3,R1,R2; z?FZT1,T2,T3,R1,R2; i?FiR1,R2; j?FjR1,R2; k(9)?FkR1,R2The range of the machine axes is limited by themaximum travel of T1, T2, T3, R1and R2. The limits arethe corner points of a five-dimensional hypercube or par-allelotope with Nrr-dimensionalNr?2nr?nR?(10)hyper faces, faces, edges and points 12. To find anapproximation of the machine tool workspace a regularfive-dimensional pointgrid of equally spaced points can513E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520be transformed by putting the coordinates of each pointin Eq. (9). The number of points to be transformed is L5with L the linear density per axis (e.g. L=10 requires100,000 transformations). If only the points on the two-dimensional faces of the hypercube are transformed, thenonly L2N2points need to be transformed (L=10 gives8000 points to be transformed). The volume of this pointset is the machine tool workspace. If this machine toolworkspace is now put on the machine table, then thepart which interferes with the machine frame must besubtracted (clipped).5.6. Outline of algorithm to compute the orientationspace indexThe equation of a sphere surface is given in sphericalcoordinates as: x=r sin cos ; y=r sin sin ; z=r cos; the range of is from 0 to 2 and from 0 to canbe matched to the range of the machine rotary axes R1and R2. At tool path to mill the largest possible part ofa sphere can now be determined. The first step in thedetermination is the selection of the orientation of thetool axis relative to the sphere. At each point x,y,z ofthe sphere there are three possible orientations along theunit vectors iriand i. If the tool axis is oriented alongirthe tool axis will be perpendicular to the sphere sur-face. If the tool axis is oriented along ior i, the toolaxis will be parallel to the isoparametric lines on thesphere = constant or = constant. The tool path canbe generated with the following equations:x?r sin(y/2n) cos y; y?r sin(y/2n) sin y; z?r cos(y/n)for r=constant, n=number of turns and ?2n.The CL point will follow a spiral motion with n thenumber of full turns.The orientations of the tool vector for each CL pointshould be selected from the three possible orientation-s:Perpendicular to sphere:i?sin(y/2n) cos y, j?sin(y/2n) sin y, k?cos(y/2n)Parallel to the isoparameric line = constant:i?sin(y/2n) cos y, j?sin(y/2n) sin y, k?sin(y2/n)Parallel to isoparameric line = constant, which isalways parallel to the xy plane:i?sin y, j?cos y, k?0.Normally it will be clear which toolorientation vectorwill give the largest r. The number of turns is notimportant as this toolpath will probably never be cut onthe machine so a value, e.g. 10 can be taken. The angle can be related to maximum range of R1and R2throughthe geometry transform of the machine. The maximumradius of the sphere can be determined by starting withan initial guess r0and check if this is within the rangeof the machine. The problem can be somewhat be morecomplicated due to the many possible locations of thesphere on the machine table, here also a good initialguess starts the iteration process. A point x,y,z locatedon the sphere surface will have a radius r2=(x?x0)2+(y?y0)2+(z?z0)2. With x0, y0, z0the center of thesphere. The equation to be checked is:r2?FXT1,T2,T3,R1,R22?FYT1,T2,T3,R1,R22?FZT1,T2,T3,R1,R22This relation must hold for all corner points of the five-dimensional parallelotope which defines the machinerange. Using equation (10) gives N1=80 corner points.5.7. Orientation angle index of a five-axis machineOAIIf a large range of orientation is required it should bepossible to make a complete sphere. To make a completesphere two RR axis are needed. One axis with a rangeof 360 and another perpendicular axis with a range of180 are the minimum requirement. The Orientationangle index is defined as the ratio of the product of themax range of the two rotary axes divided by 360180multiplied by 12/90. With 12the angle in degreesbetween the two rotary axes (e.g. in Fig. 6, 12=45).OAI?R1?R2360180a1290(11)If this index is 1 it is possible to mill a full sphere.Often there is only a subspace of the workspace availablein which this full range of the two rotary axes orien-tations can be used. To be able to asses the size of thepart OAIindex should be used in combination with OSI6. Selection criteria of a five-axis machineIt is not the objective to make a complete study onhow to select or design a five-axis machine for a certainapplication. Only the main criteria which can be used tojustify the selection of a five-axis machine are discussed.6.1. Applications of five-axis machine toolsThe applications can be classified in positioning andcontouring. Figs. 12 and 13 explain the differencebetween five-axis positioning and five-axis contouring.6.1.1. Five-axis positioningFig. 12 shows a part with a lot of holes and flat planesunder different angles, to make this part with a three-axis milling machine it is not possible to process the partin one set up. If a five-axis machine is used the tool can514E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 12.Five-axis positioning.Fig. 13.Five-axis contouring.be oriented relative to the workpiece in any direction.Once the correct position is reached, the holes or the flatplanes can be machined while keeping most of the axispositions fixed. The flat planes can also include 2D pock-ets with islands. If only holes need to be drilled it is intheory sufficient to have a one axis simultaneous CNCcontrol, with 2D pockets a 2 axis simultaneous CNCcontrol is sufficient. However, simultaneous control ofthree axes is now common. This increases the speed inthe rapid traverse mode when the tool and workpieceare positioned relative to each other before any cuttingtakes place.6.1.2. Five-axis contouringFig. 13 shows an example of five-axis contouring, tomachine the complex shape of the surface we need tocontrol the orientation of the tool relative to the part dur-ing cutting. The tool workpiece orientation changes ineach step. The CNC controller needs to control all thefive-axes simultaneously during the material removalprocess. More details on countouring can be found inRef. 13. Applications of five-axis contouring are: (i)production of blades, such as compressor and turbineblades; (ii) injectors of fuel pumps; (iii) profiles of tires;(iv) medical prosthesis such as artificial heart valves; (v)molds made of complex surfaces.6.2. Axes configuration selectionThe size and weight of the part is very important asa first criterion to design or select a configuration. Veryheavy workpieces require short workpiece kinematicchains. Also there is a preference for horizontal machinetables which makes it more convenient to fix and handlethe workpiece. Putting a heavy workpiece on a singlerotary axis kinematic chain will increase the orientationflexibility very much. It can be observed from Fig. 4that providing a single horizontal rotary axis to carry theworkpiece will make the machine more flexible.In most cases the tool carrying kinematic chains willbe kept as short as possible because the toolspindle drivemust also be carried.6.3. Example 1 five-axes machining of jewelryA typical workpiece could be a flower shaped part asin Fig. 14. This application is clearly contouring. Thepart will be relatively small compared to the toolassembly. Also small diameter tools will require a highspeed spindle. A horizontal rotary table would be a verygood option as the operator will have a good view ofthe part (with range 360). All axes as workpiece carry-ing axes would be a good choice because the toolspindlecould be fixed and made very rigid. There are 20 waysin which the axes can be combined in the workpiecekinematic chain (Section 4.2.1). Here only two kinematicchains will be considered. Case one will be a T?T?T?R?R?kinematic chain shown in Fig. 15. Case two will be aR?R?T?T?T? kinematic chain shown in Fig. 16.For model I a machine with a range of X=300 mm,Fig. 14.Jewel application515E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 15.T?T?T?R?R? five-axis machine.Fig. 16.R?R?T?T?T? five-axis machine.Y=250 mm, Z=200 mm, C=n 360 and A=360, and amachine tool table of 100 mm diameter will be con-sidered. For this kinematic chain the tool workspace isa single point. The set of tool reference points which canbe selected is also small. With the above machine travelranges the workpiece workspace will be the space sweptby the center of the machine table. If the centerline ofthe two rotary axes intersect in the reference point, aprismatic workpiece workspace will be obtained with assize XYZ or 300250200 mm3. If the centerlines of thetwo rotary axes do not intersect in the workpiece refer-ence point then the workpiece workspace will be larger.It will be a prismatic shape with rounded edges. Theradius of this rounded edge is the excentricity of theworkpiece reference point relative to each centerline.Model II in Fig. 15 has the rotary axes at the begin-ning of the kinematic chain (R?R?T?T?T?). Here also twodifferent values of the rotary axes excentricity will beconsidered. The same range of the axes as in model Iis considered.The parameters defined in Section 5 are computed foreach model and excentricity and summarized in Table1. It can be seen that with the rotary axes at the end ofthe kinematic chain (model I), a much smaller machinetool workspace is obtained. There are two main reasonsfor this. The swept volume of the tool and workpieceWSTOOL?WSWORKis much smaller for model I. Thesecond reason is due to the fact that a large part of themachine tool workspace cannot be used in the case ofmodel I, because of interference with the linear axes.The workspace utilization factor however is larger forthe model I with no excentricity because the union of thetool workspace and workpiece workspace is relativelysmallercomparedwithmodelIwithexcentricitye=50 mm. The orientation space index is the same forboth cases if the table diameter is kept the same. ModelII can handle much larger workpieces for the same rangeof linear axes as in model I. The rotary axes are here inthe beginning of the kinematic chain, resulting in a muchlarger machine tool workspace then for model I. Alsothere is much less interference of the machine tool work-space with the slides. The other 18 possible kinematic516E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Table 1Workspace comparison of two five-axis machinesT?T?T?R?R?Model IR?R?T?T?T?Model IIExcentricitye=0 mme=50 mme=0 mme=150 mmWSMT25.13 dm325.13 dm348.0 dm332.4 dm3WSMTclipped14.57 dm314.57 dm348.0 dm332.4 dm3WSTOOL? WSWORK15 dm330.85 dm3107.7 dm339.8 dm3WR0.970.470.440.814Largest sphere100 mm100 mm300 mm250 mmOSI0.0360.0360.290.25OAI2222Space32 dm345 dm3100.53 dm356.55 dm3MTS0.470.570.480.57chain selections will give index values somewhat inbetween the above cases.6.4. Example 2 rotary table selectionTwo machines with the same kinematic diagram(T?T?R?R?T) and the same range of travel in the linearaxes will be compared (Fig. 17).There are two options for the rotary axes: two-axistable with vertical table (model I), two-axis table withhorizontal table (model II). Tables 2 and 3 give the com-parison of the important features.It can be observed that reducing the range of the rotaryaxes increases the machine tool workspace. So model Iwill be more suited for smaller workpieces with oper-ations which require a large orientation range, typicallycontouring applications. Model II will be suited forlarger workpieces with less variation in tool orientationor will require two setups. This extra setup requirementcould be of less importance then the larger size. Thehorizontal table can use pallets which transform theinternal setup to external setup.The larger angle range in the B-axes ?105 to +105,Fig. 17.Model I and model II T?T?R?R?T pared to ?45 to +20, makes model I more suitedfor complex sculptured surfaces, also because the muchhigher angular speed range of the vertical angular table.The option with the highest spindle speed should beselected and it will permit the use of smaller cutter diam-eters resulting in less undercut and smaller cuttingforces. The high spindle speed will make the cutting ofcopper electrodes for die sinking EDM machines easier.The vertical table is also better for the chip removal. Thelarge range of angular orientation, however, reduces themaximum size of the workpiece to about 300 mm and100 kg. Model II with the same linear axes range asmodel I, but much smaller range in the rotation, can eas-ily handle a workpiece of double size and weight. ModelII will be good for positioning applications. Model I can-not be provided with automatic workpiece exchange,making it less suitable for mass production. Model II hasautomatic workpiece exchange and is suitable for massproduction of position applications.Model I could, however, be selected for positioningapplications for parts such as hydraulic valve housingswhich are small and would require a large angular range.517E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Table 2Specifications of five-axis machine tools in Fig. 17Machine typeModel IModel IIRange of B-axis?105 to +105?45 to +20Range of A-axisn360n360Angular speed /s8500/14,0003000/3000Type of tableVerticalHorizontalDiameter table320 mm520 mmMax. table load100 kg200 kgX Y Z range600450500 mm600450500 mmToolnose holdingISO 40ISO 40Weight4500 kg5500 kgPallet exchangeNoYesTable 3Workspace comparison of five-axis machine tools in Fig. 17Model IModel IIWSMT212.0 dm3145.6 dm3WSMTclipped84.0 dm3145.6 dm3WSTOOL?WSWORK334.5 dm3180.5 dm3WR0.250.81Largest sphere300 mm930 mmOSI0.170.05OAI1.170.36Space9000 dm39000 dm3MTS0.0370.076.5. Selection of machine options6.5.1. Automatic tool change (ATC)An automatic tool change on a CNC machine is a veryuseful option for mass production. The most importantfeature to look for when selecting this option is the toolexchange time. Today machines with a tool exchangetime below 1 s are available. An ATC should, however,not be a high priority option for a mold and die makingshop. It can however be very useful if unattended mach-ining is required. An ATC on a machine tool increasesthe downtime of the machine. Frequent breakdown isdue to two reasons 14:? Breakdown of the hydraulic or pneumatic system.? When power fails and the tool exchange arm is half-way the toolexchange operation, it can happen thatthe arm has to be withdrawn by manually actuatingthe control valves in the correct sequence.6.5.2. Automatic pallet change (APC)This option is again very useful for small to large ser-ies production. A requirement for APC is that themachine table which holds the workpiece is horizontal.Many machines equipped with APC have two or moretables in carrousel which allows the set up (still a diffi-cult job to automate) of the part while the machine isworking on another part on the machine.The configuration of Fig. 1 provides the machine tooldesigner with an easy design for the tool exchanger, theprovision of an automatic workpiece exchange is, how-ever, much more difficult and normally not provided,because of the vertical table. The configuration of Fig.3 allows both Automatic Tool Exchange (ATC) andAutomatic Workpiece Exchange (AWC).6.5.3. Horizontal or vertical spindle machining centerThe most popular machining center for series pro-duction is the horizontal machining center (tool spindlehorizontal Fig. 18). The main reasons for this are15:? Chips drop out of the way during machining, provid-ing an uncluttered view of the cut and preventingrecutting of chips.? The table indexing capability enables multiple sidesof a workpiece to be machined in one setup.? Easy to provide APC.The disadvantages of the horizontal machining centerare:? Heavy tools deflect.518E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520Fig. 18.Horizontal spindle machine.? Trust of cutting tool must be absorbed by fixtures.? Generally more expensive than the vertical spindlemachine.The most popular machine for a job shop and moldmakeris the vertical spindle machine (Fig. 19). The mainreasons are:Fig. 19.Vertical spindle machine.? Trust of the cutting tool is directly absorbed into themachine table.? Ideal for large, flat plate work and single surface3D contouring.? Heavy tools can be used without concern aboutdeflection.? Generally less costly.The main disadvantage is the extensive chip buildupwhich obstructs the view and recuts chips7. New machine concepts based on the StewartplatformConventional machine tool structures are based onCarthesian coordinates. Many surface contouring appli-cations can be machined in optimal conditions only withfive-axis machines. This five-axis machine structurerequires two additional rotary axes. To make accuratemachines, with the required stiffness, able to carry largeworkpieces, very heavy and large machines are required.As can be seen from the kinematic chain diagram of theclassical five-axis machine design the first axis in thechain carries all the subsequent axes. So the dynamicresponce will be limited by the combined inertia. Amechanism which can move the workpiece without hav-ing to carry the other axes would be the ideal. A newdesign concept is the use of a HEXAPOD. Stewart 16described the hexapod principle in 1965. It was first con-structed by Gough and Whitehall 20 in 1954 andserved as tire tester. Many possible uses were proposedbut it was only applied to flight simulator platforms. Thereason was the complexity of the control of the six actu-ators. Recently with the amazing increase of speed andreduction in cost of computing, the Stewart platform isused by two American Companies in the design of newmachine tools. The first machine is the VARIAXmachine from the company Giddings and Lewis, USA.The second machine is the HEXAPOD from the Inger-soll company, USA. The systematic design of Hexapodsand other similar systems is discussed in Ref. 17.The problem of defining and determining the work-space of virtual axis machine tools is discussed in Ref.18. It can be observed from the design of the machinethat once the position of the tool carrying plane isdetermined uniquely by the CL date (point + vector), itis still possible to rotate the tool carrying platformaround the tool axis. This results in a large number ofpossible length combinations of the telescopic actuatorsfor the same CL data.7.1. Variax machineThis machine approaches the Stewart platform veryclosely. One upper and lower platform is connected by519E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520six crossed telescopic linear axes (Fig. 20). These tele-scopic axes can expand and retract by means of revolv-ing ballscrew spindles and a servomotor per axis. Thebottom platform caries the workpiece pallet and the topplatform the toolpallet. The top platform carries themachining spindle and drive. The lightweight triangularframework provides high stiffness. The telescopic actu-ators are supported at the two endpoints. This results inonly compressive or tension load resulting in high stiff-ness. Further variations on the same structure are:? The machine is made with a vertical platform for car-rying the workpiece, getting the benefits of a horizon-tal spindle machine.? The duplicating tool platform on both sides of theworkpiece platform would increase the productivityby reducing the number of setups and two tools cut-ting simultaneously.7.2. Hexapod machineThe HEXAPOD (Fig. 21) machine does not resemblethe Stewart platform as closely as the VARIAXmachine. To avoid the large space taken by the six tele-scopic axes in the VARIAX machine, the six axes areconnected to the (fixed) top platform instead of the bot-tom. To be able to realize this construction it was neces-sary to have a machine mainframe to support this upperfixed platform. This frame is also made from a triangularbeam mesh. The movable platform is now much smallerand carries the spindle and its drive. This machine hasa much larger useful workspace than the VARIAXmachine. The telescopic axes are larger. The tool carry-ing platform is much smaller and the mass to be movedis smaller.Fig. 20.Variax machine.Fig. 21.Hexapod machine.Advantages:? Stiff construction.? The telescopic legs are only loaded in compressionand tension.? Simple assembly.? All leg drives are the same (repetitive construction).? Small moving masses.? No special fabrication or assembly features arerequired for the machine elements.Disadvantages:? A six axis CNC control is required.? The build in coordinate transform is a heavy load forthe CNC control.? The tilting angle is limited to 15 degrees. So if fullfive-axis capability is required, a tilting and rotarytable will be necessary. So that the machine is notreally a six-axis machine.? Large thermal expansions.? Unfavorable workspace to machine volume ratio.8. ConclusionTheoretically there are large number of ways in whicha five-axis machine can be built. Nearly all classical Car-tesian five-axis machines belong to the group with threelinear and two rotational axes or three rotational axesand two linear axes. This group can be subdivided in sixsubgroups each with 720 instances. If only the instanceswith three linear axes are considered there are still 360instances in each group. The instances are differentiatedbased on the order of the axes in both tool and workpiececarrying kinematic chain.520E.L.J. Bohez / International Journal of Machine Tools & Manufacture 42 (2002) 505520If only the location of the rotary axes in the tool andworkpiece kinematic chain is considered for groupingfive-axis machin