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示教型雕铣机设计【机+电】【9张图纸】【优秀】

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示教型雕铣机设计

33页 11000字数+说明书+外文翻译+9张CAD图纸【详情如下】

A0装配图.dwg

主轴.dwg

外文翻译--三轴并联铣床的功能仿真器 中文版.doc

外文翻译--三轴并联铣床的功能仿真器 英文版.pdf

导轨.dwg

支撑底座.dwg

支撑架.dwg

支架.dwg

滚珠丝杠副.dwg

电路图.dwg

示教型雕铣机设计说明书.doc

论文.doc

轴套.dwg

目录

摘要I

AbstractII

1绪论2

1.1示教型雕铣机课题介绍2

1.2小型示教型雕铣机的特点及现状2

1.2.1 国内数控雕铣机的发展和现状2

1.2.2 典型数控雕铣机的介绍3

1.3示教型雕铣机的主要技术参数5

2示教型雕铣机总体布局设计方案6

2.1机床总体布局设计6

2.2  设计方案分析6

3各轴系统的设计方案8

3.1 Z向主传动系统的方案设计8

3.2  进给系统方案设计8

3.2.1 滚珠丝杠副的选择8

3.2.2  滚珠丝杠的支承结构9

3.2.3  支承轴承的选择10

3.2.4  滚珠丝杠的制动装置10

3.2.5 步进电机与进给丝杠的联结结构10

3.2.6  导轨11

4主轴系统零部件的计算与校核12

4.1 主轴系统的重力计算12

4.2  主轴铣削力计算12

4.3 滚珠丝杠副的选择计算13

4.4  进给伺服电机功率的计算及选择20

5电气部分设计25

5.1 硬件部分电路设计25

5.2 80C51外部电路扩展25

5.3控制系统总体设计26

结论28

致谢29

参考文献30

1绪论

1.1示教型雕铣机课题介绍

随着微电子技术的突飞猛进，直接推动微型计算机的急剧发展。微电子技术和微型计算机技术带动整个高科技群体飞速发展，从而使雕铣机的发展有了质的飞跃。使其完成了从二维到三维加工技术的变革。随着生活水平的不断提高， 人们对产品的性价比也越来越高，这就对雕铣机的研制提出了更苛刻的要求。因此，功能完善，性能稳定，造型美观并且价格合理的产品是我们不懈的追求。

雕铣机引入教学领域，使教与学更生动、有趣，学生更容易接受那些抽象的东西， 便于提高数控技术课程的教学效果。因此，本课题拟设计一款价格低廉，功能完善的雕铣机用于教学演示。

1.2小型示教型雕铣机的特点及现状

示教技术是随着数控技术发展起来的，目前，对示教系统的性能及精度等方面都提出了较高要求。现在市面上的雕铣机主要有以下几特点：

1.应用PC机的强大计算功能，将刀补、译码、插补、加减速控制等放在PC上解决。最后PC上形成的是各种步进电机的控制脉冲。

2.应用PC机的并口直接输出各向步进电机的控制脉冲，以控制工作台的移动。

3.步进电机的驱动采用集成的驱动芯片。

4.通过限位开关以及各运动方向的开关来保证雕铣机的安全工作。

示教型雕铣机是一款模拟经济实用的高精密数控雕铣设备，该款设备主要模拟雕铣机的运动，实现简单的示教雕铣功能。

1.2.1 国内数控雕铣机的发展和现状

随着家具制造业、广告招牌业、模具业的发展，尤其是模具业对表面加工要求的提高，以及传统电火花加工的不足，最近的一两年综合铣削与高速雕刻优点的CNC雕铣机在国内有了较大的发展。

2007年我国的雕铣机产业产能已经超过11000台/年,产值超过15亿RMB。目前雕铣机的生产主要以广东、北京、浙江三大板块主导。国内几家著名的数控机床厂在这个领域里面都有较好的成绩。比如北京精雕、广东佳铁、南京四开、上海洛克等都是国内著名的数控雕铣机厂家。在雕刻CAD/CAM技术、CNC数控技术、精密雕刻机设计技术工艺等领域取得了重大的突破，并真正实现了先进技术向产业化的转化。

1.2.2 典型数控雕铣机的介绍

北京精雕-睿雕系列Carver600G_U

北京精雕生产的睿雕Carver600G_U机械性能参数指标见表1-1。模型见图1-1。

  表1-1 Carver600G_U机械性能参数指标

主要性能指标项标准值

工作台尺寸700×650mm

X、Y、Z轴工作行程600×500×300mm

快速移动速度10m/min

主轴转速2100-24000rpm

最高切削进给速度6m/min

X/Y/Z轴运动定位精度0.008/300mm

X/Y/Z轴重复定位精度0.005mm

机床外形尺寸2042×1890×2144mm

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徐州工程学院外文翻译三轴并联铣床的功能仿真器米洛斯Glavonjic和德拉甘米卢蒂诺维奇和莎莎Zivanovic收稿日期：2007年7月12日 接稿日期：2008年6月27日 发表时间：2008年7月24日 施普林格出版社有限公司2008年伦敦摘要：尽管许多实验室，许多人以并联机床的运动机为研究和发展的主题，不幸的是，至今还是没有个人有一定的成就。因此,利用低成本的但是功能强大的模拟器模拟三轴联动铣床来获取基本经验。这个想法是基于这样的模拟器可以由传统的三轴数控机床的控制驱动基础上进行的。本文描述了一个包括相应的并联机构，运动学建模和编程算法的选择模拟器的发展过程。功能模拟器的想法已经被充分验证在标准化操作条件下，使得一些软材料试件加工成功。关键词：并联机床； 功能仿真器；模拟和测试1简介在当今世界上，教育和培训具有战略上的重要性，特别是在技术和科学学科。这也适用于并行结构机研究和开发这个世界性的话题。对并联机床的基本知识的已经出版很多书，许多不同的并行机制，3至6个自由度，包括三自由度并联机构平移正交，也有使用。今天，不幸的是，研究机构，大学实验室，和企业绝大多数没有并联机床。究其原因，很明显，是教育和培训的新技术，如个人知识管理，成本高。为了有助于实现在造型，设计，控制，编程实践经验的收购，以及个人知识管理，降低成本，可以使用新提出的三轴并联铣床功能仿真器来实现。这个想法是基于这样的模拟器可以由传统的3轴数控机床的控制驱动基础上进行的。作为传统的三轴数控机床的轴是相互正交，不同的三自由度正交平移关节空间并联机构，可用于生成模拟器。本文描述了模拟器发展，包括相应的并联机构，运动学建模和编程算法的选择程序。功能模拟器应经被验证了在行业标准化操作条件下成功加工一些软质材料。2模拟器的概念根据现在的知识,以系列运动机器和可用的资源为其程序,模拟器看作一种混合的三轴驱动传统数控铣床空间并联机构。其中的一种功能仿真器的概念，如图1所示。完全平行的三自由度不断支撑关节的长度和线性驱动机制，由传统的三轴数控机床的控制。这个机制是基于线性三角，但与正交的线性驱动关节，促进其用XM，YM和水平或垂直轴系列运动机ZM连接。通用平台，始终保持与基地的同时，使主轴在三个不同的正交XP中。在图一中,始终如一的平行与地平行,使主轴的位置在三个不同的正交XP,YP,ZP方向。在论文中。一些可能的配置的机制、其中的一个平台被选中,因为它使便于安装并联机构的机器在XM轴上。其中的2个自由度被用来减少来自XM和YM轴的震动,除了选择和调整引擎的机理与所选择的串行机,下面的过程，模型，算法，以及软件必须定义和发展:-对并联机构运动造型,即直接运动学、矩阵, 运动学和奇异性分析模型-模拟工作空间分析和适当的设计参数的选择-模拟器的设计制造3模拟器的机制作用同时作为垂直和水平三轴数控机床的串行正交和驱动仿真器的轴，是最好的，如果三个自由度空间并联，模拟器的机制以及正交平移的关节。与串行数控机床的轴耦合，这将是必不可少的，在一般情况下，至少有一个两个自由度被动的去耦串联机构。数控机床模拟器与移动刀架和工作台的是最方便的。在这样的概念下两三个轴的耦合，使其中一个自由度串联他们的去耦和被动的模拟器驱动机制就足够了。如果没有横向和纵向的3轴数控机床运动结构的划分，有三自由度正交平移关节，考虑和模拟器使用空间并联机构的一些例子，如图2，他们的工作区的形状也显示在图中。该机制类似于上面的例子，在图所示，基本运动学的概念差异问题是可以解决的。自由度被动串行，用于分离驾驶一系列数控机床轴运动机制的例子如图所3示。在一些系列数控机床的概念中，其轴线可直接用作模拟的并行机制平移关节。在这种情况下，模拟器的一般概念的基础上，如图所示机制就可能被简化了。图4显示了没有自己的关节并联机构简化模拟器的例子。数控机床的驱动是一个卧式加工中心。相应的机械接口连接与分离轴加工中心联合组成一个平行四边形。两自由度串联机构加工中心分离出来Y和Z轴。图5显示了一个简化的立式数控铣床与两个耦合轴模拟器的设计。模拟器的机制有一个自己的移动式，联合两自由度串联机构也是垂直轴数控铣床脱钩使用方法。4模拟器造型的例子图一中对模拟器详细的运动学分析是以图六中的几何模型为基础的，由于机械本身特有的性质，平台和底座是平行的，因此，图一中的每个空间平行四边形由支柱表示。连接底座和平台的坐标构架P和B是平行的，同时平行于参考系列机器协调框架 M ，这使得整个模拟器造型归于普通化。这意味着分离并联机构的造型本身是可行的，并且不考虑其安装在水平还是垂直的系列机器上，也不考虑其在平台上的轴的位置。构架B和P中的向量V分别用Bv 和 Pv.表示。模拟器参数定义的向量：移动平台上的连接中心之间的中心点Ci的位置向量在构架P被定义为PPCi;（i=1，2，3）工具末端的位置向量在构架P中被定义为PPT ; xTP yTP zTPt , where zTP=-h.模拟器的驱动轴参考点Ri的位置向量被定义为BPRi; （i=1，2，3 ）连接坐标向量L=l1 l2 l3T, ,l1,l2, 和l3是系列CNC机器在lmin li lmax范围内提供动力和控制的标量变数，而Bai是单位向量，,和领域坐标向量：代表工具末端已编制好的位置向量，而代表平台的位置，即连接在上面的坐标构架P的原操作。由于坐标构架B和P总是平行的，所以这两个向量之间的关系是很明显的，即 (1)其它向量和参数的定义如图六所示，其中Bwi和Bqi是单位向量，而C是相互连接的平行四边形的固定长度。模拟器连接坐标向量和 系列机器连接坐标之间的关系如图六所示，是根据图六中几何关系，得出下列等式：等式4中等号两边加以平方得出：在等式3中应用运动学造型便被简化。为了满足这个要求，人们已经找到了具体的方法，即设置参考点Ri， 通过替代等式5中的机械参数，得到三个等式的方程组：由这个方程组又得出：相反的运动学等式如和直接运动学等式如由以上等式得出：如上所提，通过调整模拟器的机械参数，等式6，相反和直接运动学的解大大被简化了。为了满足等式6中的条件，采用了六根指示长度的校准支柱，如图七，应用通过校正支柱长度而得出的相反和正运动学解，定义了sliders（不知道啥意思） Si, (i=1, 2, 3)的参照点位置，并通过校准plain环固定，如图七。4.1 分析运动学的正解和逆解分析逆运动学方差解，等式8，在给定平台位置的情况下，不同的平行机械构造有：基本构造，图2a，在等式8中，在平方根之前的所有符号都是负号可供选择的构造之一，图2b，在等式8中，在平方根之前所有符号都是正的其它可能的机械构造，在等式8中，在平方根之前的符号是正负号用相同的方法，通过对运动学正解分析，等式9，在驱动轴位置给定的情况下，建立不同的平行机械构造：基本构造，图2a，和实际情况一致，在等式9中，在平方根之前是正号供选择的构造，图2c和d，在等式9中，在平方根之前是负号，根据驱动系列机器的结构可通过不同的方法实现图2所示的基本的和供选择的构造。4.2 雅可比矩阵和异常分析鉴于PKM异常关系重大，这个问题已被细致分析，如图2a中显示的机械变型，这种机械变型可用来发展水平机器中心的模拟器，如图1。考虑时间的情况下区分等式8，得到的雅可比矩阵为： 由于方程组7中的等式有连接和领域坐标的功能，根据它们的区别也可以得出雅可比矩阵：其中是正逆运动学的雅可比矩阵，用这种方法，可以识别出三种不同形式的异常，比如，正逆运动学异常和联合异常。仔细分析雅可比矩阵的决定因素，正逆运动学异常和联合异常是显而易见的。通过适当的描述和等式，图8中显示了可能的模拟器异常构造，从图8中可以看出，所有的异常都处在理论上可获得工作空间的临界上，所以，通过足够的设计解答和或机械限制可以轻松地避免这些异常，这就意味着可获得的模拟器工作空间要比理论上的工作空间要小，理论上工作空间的界线是在半径C的汽缸上，而半径C的轴是从逆运动学等式8中得出的XB, YB, ZB，同时半径C的范围是以图8中的OB为中心的。5 模拟器的实例大家都知道，除了要选择合适的运动学布局，选择正确的几何维度也是非常重要的，因为要考虑已定的用途，这是个困难的工作，开发PKM的设计工具仍然需要研究，调整图1、4和5中的模拟器设计参数是为了在可用CNC机器运作效果的基础上获得更多的模型和工作空间维度，其中制造的模拟器就是配给CNC机器的，这个程序必须要进行重复，因为在选择基础设计参数时，要考虑机构因素可能的干扰和det(J) 与 det(J1)决定因素的重要性（等式14、15和16中涉及）。在图6中模拟器变型的几何模型中，可以看到工作空间维度主要受到平行四边形长度C的影响，同时要达到图8中D3, D3I2, 和 D3I1异常得出的机械距离。对于配备模拟器的可用CNC机器，要用重复的程序对平行四边形长度C和坐标（l1,2,3min l1,2,3max）的重要结合进行分析，在每次重复过程中，要注意潜在的设计限制、干扰以及det(J) 与 det(J1)的重要性，即异常产生的距离。用这种方法得到的参数在图9中模拟器原型的详细设计中得到轻微的纠正，长度C=850 mm、l1,2,3min=200 mm和l1,2,3max=550 mm的平行四边形的形状、体积和可获得工作空间的位置如图2a所示。在采用这种构想和设计参数的基础上，构造了头两个模拟器，如图9、10所示。6 模拟器编程和测试在PC平台上以CADCAM environment标准开发模拟器编程系统（图11），几何工作空间模型可以和其它系统交换，并且可以模仿工具轨迹，线性插值工具轨迹是从CL文件标准。模拟器使用者可以选择其它方式也能画出工具轨迹，系统的基础部分是由developed and implemented postprocessor组成的，并且不用后处理器发电机，后处理器包括正逆运动学（inverse and direct kinematics）、模拟器设计参数和模拟器工具途径的运算法则（图12），模拟器工具途径线性化是必要的，因为CNC机器线性插值是被当做模拟器联合坐标插值使用的，这样的话，模拟器的工具轨迹仍在先定半径的偏差范围之内，先定半径是CL文件中点Tj1 和点 Tj之间，对于以这种方式获得数控机床长节目传送到数控机床，可以在空闲的模拟器运行验证。对轴的运动范围已经在处理器上检查了。该模拟器在这个阶段的测试包括：核查的程序和通信系统，切割加工各种试件测试（图13）。7结束语为了有助于实现在造型，设计，控制，编程实践经验的收购，以及降低个人知识管理的成本，提出了三轴并联铣床功能仿真。所开发的三维并联数控铣床功能仿真器作为混合系统，现有的技术设备（数控机床的CAD - CAM的硬件和软件）和并联机制，为全面和复杂的教学提供了设施。关于功能模拟器的想法，为验证一些软质材料在进行标准化测试操作条件下作出成功的决策。这个想法可能会进一步用于模拟器的决策。致谢由塞尔维亚科技部支持，并提出的尤里卡计划3239工作。8ORIGINAL ARTICLEFunctional simulator of 3-axis parallel kinematicmilling machineMilos Glavonjic&Dragan Milutinovic&Sasa ZivanovicReceived: 12 July 2007 /Accepted: 27 June 2008 /Published online: 24 July 2008#Springer-Verlag London Limited 2008Abstract Parallel kinematic machines (PKM) are research-and-development topic in many laboratories although manyof them, unfortunately, have no PKM at all. Therefore, theuse of low cost but functional simulator of a 3-Axis parallelkinematic milling machine is suggested as a help to acquirethe basic experiences in the PKM field. The idea is based onthe possibility that the simulator could be driven andcontrolled by a conventional 3-Axis Computer NumericalControl machine tool (CNC). The paper describes thedevelopment procedure of a simulator including the selec-tion of a corresponding parallel mechanism, kinematicmodelling, and the programming algorithm. The functionalsimulator idea has been verified by successful making ofsome standardized test pieces of soft material, under fulloperational conditions.Keywords Parallelkinematicmachines.Functionalsimulator.Modellingandtesting1 IntroductionThe strategic importance of education and training, espe-cially in technology and scientific subjects, is growingthroughout the world. This also applies to the parallelkinematic machines (PKMs) which are today research-and-development (R&D) and educational worldwide topic.Basic knowledge about diverse aspects of PKM has beenpublished 1. Many different topologies of parallelmechanisms with 3 to 6 dof, including a 3-dof translationalorthogonal parallel mechanism, have been used 15.Today, unfortunately, the great majority of research insti-tutes, university laboratories, and companies have no PKM.The reason, obviously, is the high cost of education andtraining for a new technology, such as PKM.In order to contribute towards the acquisition of practicalexperiences in modelling, design, control, programming,and the use of PKM, a low cost but functional simulator of3-Axis parallel kinematic milling machine is proposed 2.The idea is based on the possibility that the simulator couldbe driven and controlled by a conventional 3-Axis CNCmachine tool.As the axes of the conventional 3-Axis CNC machineare mutually orthogonal, different 3-dof spatial parallelmechanisms with orthogonal translatory joints may be usedto build the simulator 2, 7.The paper describes the procedure for simulator devel-opment including the selection of a corresponding parallelmechanism, kinematic modelling, and the programmingalgorithm. The idea about the functional simulator wasverified by successful making of some standardized testpieces out of soft materials, made under full operationalconditions.2 Simulators conceptIt would be possible, thanks to the previous knowledgeabout serial kinematic machines and available resourcesfor their programming, to make the simulator as a hybridstructure consisting of driving conventional 3-Axis CNCmilling machine and driven 3-dof spatial parallel mecha-nism. One of the possible concepts of a functional simulatorInt J Adv Manuf Technol (2009) 42:813821DOI 10.1007/s00170-008-1643-xM. Glavonjic (*):D. Milutinovic:S. ZivanovicMechanical Engineering Faculty, University of Belgrade,Kraljice Marije 16,11120 Belgrade, Serbiae-mail: mglavonjicmas.bg.ac.yufor 3D milling of softer materials, shown in Fig. 1, consistsof: Fully parallel 3-dof mechanism with constant strutlengths and linear joints actuated and controlled by theconventional 3-Axis CNC machine. The mechanism isbased on linear DELTA mechanism 6 but withorthogonal linear actuated joints to facilitate itsconnection with XM,YM, and ZMaxes of horizontal orvertical serial kinematic machines. The universalplatform, which always remains parallel with the base,enables the placement of the spindle in three differentorthogonal XP, YP, ZPdirections as shown in Fig. 1.Out of several possible configurations of the mecha-nism, the one with the platform inside the trihedron(XB, YB, ZB) has been selected since it enables easymounting of the parallel mechanism on the serialmachine XMaxis guideways. Serial 2-dof passive mechanism for decoupling serialmachines YMand ZMaxes.In addition to the selection and adjustment of thesimulators mechanism with the chosen serial machine,the following procedures, models, algorithms, and softwarehave to be defined and developed:kinematic modelling of parallel mechanism, i.e., in-verse and direct kinematics, Jacobian matrices, andsingularity analysis,workspace analysis and selection of simulator properdesign parameters,simulator design and manufacturing,Fig. 1 Functional simulator conceptFig. 2 The basic concepts of simulators parallel mechanism814Int J Adv Manuf Technol (2009) 42:813821the procedure and accessories for adjustment ofparallel mechanisms referent points to simplify theprogramming,algorithms and software for simulator programming,the procedure for testing of simulator under workingconditions by machining of various test pieces fromsofter materials.3 On simulator mechanismsAs the axes of the vertical and horizontal 3-Axis CNCserial machines are orthogonal and actuating simulatorsaxes at the same time, it would be the best if 3-dof spatialparallel simulators mechanism has orthogonal translatoryjoints as well. As in serial CNC machines the axes arecoupled, it would be essential, in a general case, to have atleast one 2-dof passive serial mechanism for their decou-pling. The most convenient CNC machine tools for thesimulator are those with movable tool holder and workingtable. In such concepts two out of three axes are coupled sothat one 2-dof serial passive mechanism suffices for theirdecoupling and the actuation of the simulator.Without classification of kinematic structures of hori-zontal and vertical 3-Axis CNC machines, some examplesof 3-dof spatial parallel mechanisms with orthogonaltranslatory joints, which have been considered and usedfor the simulator, are presented in Fig. 2. The shapes oftheir workspaces are shown as well in the figure.The above and similar examples of the mechanism arethe result of the solution variances of the inverse and directkinematic problem of the basic concept illustrated in Fig. 1.The examples of 2-dof passive serial mechanisms usedto decouple the motion of the axes of driving serial CNCmachine are shown in Fig. 3.In some serial CNC machine concepts, their axes may bedirectly used as simulators parallel mechanism translatoryjoints. In such cases, the general concept of the simulatorbased on mechanisms shown in Fig. 2 may be simplified.Figure 4 shows an example of the simplified simulatorwith parallel mechanism without its own joints. The drivingserial CNC machine is a horizontal machining center. Thecorresponding mechanical interfaces connect joint paralle-lograms with decoupled axes of the machining centre. 2-dofserial mechanism decouples machining centers Y and Zaxes.Figure 5 shows the design of a simplified simulator for avertical CNC milling machine with two coupled axes.Simulators mechanism has one own translatory joint while2-dof serial mechanism is also used for decoupling of thevertical CNC milling machine axes.4 Simulator modelling exampleDetailed kinematic analysis of the simulator from Fig. 1, isbased on its geometric model, Fig. 6. As the platform, bymechanisms nature, remains parallel with the base, eachspatial parallelogram, Fig. 1, is represented by one strut.The fact that the coordinate frames, B and P,connected to the base and the platform are parallel and thatthey are, at the same time, parallel with the referent serialmachine coordinate frame M enables generalization ofthe modelling of the entire simulator. This means that it isfeasible to separate the modelling of the parallel mechanismitself, regardless of its mounting on the horizontal orvertical serial machine and the position of the spindle onFig. 3 The examples of serial mechanisms for decoupling of drivingmachines axesFig. 4 The example of the simulator without own translatory jointsInt J Adv Manuf Technol (2009) 42:813821815its platform. Vectors v referenced in frames B and Pare denoted byBv andPv.Vectors defined by simulator parameters:The position vectors of the midpoints Cibetween jointcenters at mobile platform are defined in the frame Pas,PPCi; i 1; 2; 3.The position vector of the tool tip is defined in theframe P asPPT; xTPyTPzTP?T, where zTP ?h.The position vectors of simulators driving axesreference points Riare defined as,BPRi; i 1; 2; 3.Joint coordinates vector:l l1l2l3?T, l1,l2, and l3are scalar variables poweredand controlled by serial CNC machine within the rangeof lmin? li? lmax, whileBaiare unit vectors,Ba11 0 0?T;Ba2 0 1 0?TandBa3 0 0 ? 1?T.World coordinates vector:BPT xTyTzT?Trepresents the programmed positionvector of the tool tip, while x BPOP xpypzp?Trepresents the location of the platform, i.e., the origin Opof the coordinate frame P attached to it. The relationshipbetween these two vectors is obvious since coordinateframes B and P are always parallel, i.e.,BPTBPOPPPT1Other vectors and parameters are defined as shown inFig. 6, whereBwiandBqiare unit vectors while c is fixedlength of joint parallelograms.The relationships between the simulators joint coordi-nates vector l l1l2l3?Tand the serial machine jointcoordinates m x0MyMzM?T, as shown in Fig. 6, are:x0M l3;yM l2;zM ?112On the basis of geometric relations shown in the Fig. 6,the following equations are derived:kBiwiBPOPPBPCi?BPRi3kBiwi lBiai cBqi4By taking the square of both sides in Eq. 4 the followingrelation is derived:c2 k2i l2i? 2liBaikBiwi?5By adoptingPBPCi?BPRi 06in Eq. 3, kinematic modelling is very simplified. In order tofulfill this requirement, specific calibration method, i. e.,setting of reference points Rihas been developed. ByFig. 6 Geometric model of the simulatorFig. 5 Example of a simulator on the vertical CNC milling machine816Int J Adv Manuf Technol (2009) 42:813821substituting other mechanisms parameters in Eq. 5, thesystem of the following three equations is obtainedx2p y2p z2p l21? 2l1xp? c2 0x2p y2p z2p l22? 2l2yp? c2 0x2p y2p z2p l23 2l3zp? c2 08:7from which are derived:inverse kinematic equations asl1 xp?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2? y2p? z2pql2 yp?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2? x2p? z2pql3 ?zp?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2? x2p? y2pq8:8as well asdirect kinematic equations asyp?s6?ffiffiffiffiffiffiffiffiffiffiffiffiffis26?4s5s7p2s5xp s1 s2ypzp s3 s4yp8:9where ares1l21? l222l1;s2l2l1;s3l22? l232l3;s4 ?l2l3;s5 1 s22 s24; s6 2 s1s2 s3s4? l1s2;s7 s21 s23? 2l1s1? c2 l21; lmin? li? lmax;i 1;2;3As it was mentioned, by adjustment of simulatorsmechanism parameters, Eq. 6, the solution of inverse anddirect kinematics is greatly simplified. To satisfy theconditions from Eq. 6 six calibration struts of selectedreferent length were used, Fig. 7. With the use of inverseand direct kinematics solutions with the calibrated strutlengths, the positions of reference points Riof sliders Si, (i=1, 2, 3) are defined and fixed by calibration plain rings,Fig. 7.4.1 The analysis of inverse and direct kinematics solutionsWith the analysis of inverse kinematics variance solutions,Eq. 8, different configurations of parallel mechanism for agiven platform position may be noted:the basic configuration, Fig. 2a, when in the Eq. 8, allsigns before the square root are negative,one of alternative configurations, Fig. 2b, when inEq. 8, all signs before square root are positive,other possible mechanism configurations, when in theEq. 8, signs before the square root are combined.In a similar way, through the analysis of direct kinematicsolution, Eq. 9, different configurations of parallel mecha-nism for given positions of driving axes may be established:the basic configuration, Fig. 2a, corresponding to thecase, when in Eq. 9, there is a positive sign beforesquare root,alternative configurations, Figs. 2c and d, when inEq. 9, there is a negative sign before square root.The basic and alternative configurations shown in Fig. 2may be realized in different ways subject to the structure ofthe driving serial machine.4.2 Jacobian matrices and singularity analysisIn view of the significance of PKM singularity, thisproblem has been analyzed in detail for the mechanismvariant shown in Fig. 2a, used for the development of theFig. 7 Setting of simulators reference pointsInt J Adv Manuf Technol (2009) 42:813821817simulator on horizontal machining center, Fig. 1. Differen-tiating Eq. 8 with respect to the time, Jacobian matrix isobtained asJ 1ypxp?l1zpxp?l1xpyp?l21zpyp?l2?xpzpl3?ypzpl3?126437510As the equations in Eq. 7 are implicit functions of jointand world coordinates, Jacobian matrix may be alsoobtained by their differentiation asJ J?1l? Jx11whereJ?1l121xp?l1001yp?l200?1zpl326437512Jx 2xp? l1ypzpxpyp? l2zpxpypzp l3243513are Jacobian matrices of inverse and direct kinematics.In this way, three different types of singularities can beidentified, e.g., singularities of inverse and direct kinemat-ics as well as combined singularities.With careful analysis of Jacobian matrices determinantsdet J xpl2l3 ypl1l3? zpl1l2? l1l2l3xp? l1?yp? l2?zp l3?14det Jx ?8 xpl2l3 ypl1l3? zpl1l2? l1l2l3?15det Jl ?8 xp? l1?yp? l2?zp l3?16the singularities of inverse and direct kinematics as well ascombined singularity may be noticed.Figure 8 shows these possible simulators singularityconfigurations with corresponding descriptions and equa-tions. As it can be seen from Fig. 8, all singularities are onthe borders of theoretically achievable workspace so that itwould be possible to avoid them easily with adequatedesign solutions and/or mechanical constrains. This meansthat the achievable simulators workspace is smaller thantheoretical workspace. The boundaries of theoretical work-space are on cylinders of radius c whose axes are XB, YB,ZBderived from inverse kinematic Eq. 8 and sphere ofradius c centered in OB, Fig. 8.5 The examples of simulatorsAs it is known in addition to selecting appropriatekinematic topology, the selection of the right geometricdimensions is very important since the performance ishighly influenced by PKM geometric dimensions 1, 8.To select the right dimensions with respect to a givenapplication is a difficult task, and the development ofdesign tools for PKM is still open research 1.The design parameters of simulators shown in Figs. 1, 4,and 5 were adjusted in order to get more adequate shapesand workspace dimensions on the basis of performances ofavailable CNC machines for which simulators wereplanned. The procedure is essentially iterative because indetermination of the basic design parameters the attention ispaid to the possible interferences of structural elements andthe values of det(J) and det(J1) determinants, Eqs. 14, 15,and 16.Fig. 8 Singularity types818Int J Adv Manuf Technol (2009) 42:813821In the geometric model of simulator variant from Fig. 6,it can be seen that workspace dimensions are primarilyaffected by parallelograms length c, as well as to theadequacy of the distance of the mechanism from D3, D3I2,and D3I1 singularities shown in Fig. 8.For available CNC machine for which the simulator wasplanned, parallelograms length c and values joint ofcoordinates l1,2,3minand l1,2,3maxwere analyzed in iterativeprocedure. In each iteration, attention was paid to thepotential design limitations, interferences, as well as to thevalues of det(J) and det(J1), i.e., to the distances fromsingularities.The parameters determined in this way have beenslightly corrected in detailed design of the simulatorprototype shown in Fig. 9. Shape, volume, and position ofachievable workspace for parallelograms length c=850 mmand l1,2,3min=200 mm and l1,2,3max=550 mm are shown inFig. 2a.On the basis of the adopted concepts and designparameters, the first two simulators have been built (Figs. 9and 10).6 Simulator programming and testingThe simulator programming system has been developed ina standard CADCAM environment on PC platform(Fig. 11). It is possible to exchange geometric workpiecemodels with other systems and simulate the tool path.Linear interpolated tool path is taken from the standard CLfile. The tool path may also be generated in some other wayselected by the simulator user. The basic part of the systemconsists of developed and implemented postprocessor,without the use of postprocessor generator. The postpro-cessor contains inverse and direct kinematics, simulatordesign parameters, and algorithm for simulators tool pathlinearization (Fig. 12). Simulators tool path linearization isessential because CNC machines linear interpolation isused as simulators joint coordinates interpolation. In thisway, simulators tool path remains within the tolerance tubeof predefined radius between points Tj1and Tjtaken fromCL file. The long program for CNC machine obtained inFig. 9 Completed simulator from Fig. 1Fig. 10 Completed simulator from Fig. 4Fig. 11 Simulator programming systemInt J Adv Manuf Technol (2009) 42:813821819this way is transferred to CNC machine and can beverified during idle running of the simulator. The motionrange of driving axes has been already checked in thepostprocessor.The testing of the simulator in this phase included:&verification of the system for programming and com-munication, and&cutting tests by machining various test pieces (Fig. 13).7 ConclusionIn order to contribute towards the acquisition of practicalexperiences in modelling, design, control, programming,and the use of PKM, a low cost but functional simulator of3-Axis parallel kinematic milling machine is proposed. Thedeveloped functional simulator of
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