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随着信息技术的进步和全球化制造技术的进步，企业为了提高自身的竞争力，要求配置效率更高成本更低的加工设备，而传统机床在未来的加工业中会遇到难以克服的困难，例如在高速加工中（轨迹速度达到50m/min）和高效空间曲面加工及机床的通用性方面将无法满足现代加工技术的要求。因此探索和研究一种现代化机床具有十分重要的意义。

虚拟轴机床与传统的串联式数控机床相比具有很多优越性。传统数控机床各自由度是串联相接的，呈悬臂结构，且层叠嵌套致使传动链长，传动系统复杂，累计误差大，而精度低，成本昂贵，至今多数机床只是4轴联动，极少5轴。而虚拟轴机床的并联式加工中心结构特别简单，传动链极短，刚度大、质量轻、切削效率高、响应快，特别是很容易实现六轴联动，因而，能加工更复杂的三维曲面，且其加工精度和加工粗糙度都直接由控制程序来保证，因此，硬件成本低，而软件附加值高，是一种技术附加值极高的机电一体化产品。

此研究课题针对现今的机加工趋向，制定了设计一部并联机床实验台的任务，作者与合作人共同设计。其中的并联部分分配给了合作者，作者主要负责并联机床实验台的总体框架结构设计。

平台大致由并联机构——三根并联丝杠（驱动电机）、铸铁机架、装卡平台和电主轴以及弹簧铣夹头组成。

关键词：并联机构、虚轴加工、雅可比矩阵、正解算法

Abstract

With the progress of the information technology and the development of the global manufacturing techniques, enterprises require more efficient and lower cost machines by reason of enhancing their competitive ability. But conventional machine tools will encounter many difficulties which are hard to overcome in the future, for instance of high-speed machining ( path speed exceeding 50m/min)and high efficient space curved surfacing machining as well as flexibility of machines. Thus, it is very important to explore and study kind of modern machines.

Be compared to the normal numerical control machine tool, it has larger rigidity, stronger carrying capacity, smaller error, higher precision, smaller ratio of self-weight and load, better dynamical capacity, less investment of hardware, but stronger function of software. All of these show its high additional technical valve.

This research topic for the current trend of the processing machine, developed a design of a parallel machine test-bed task, which the Author co-design and a partner. Some of them parallel to the allocation of the partner, the author mainly responsible for the PMT test-bed framework of the overall structural design.

Platform from roughly parallel bodies - three parallel screw (motor driven), cast iron rack, with card platform and Spindle and milling chucks of spring.

Key words: parallel instruction, virtual axis processing, Jacobian Matrix, positive solution algorithm

第1章绪论1

1.1课题背景与意义1

1.2 并联机床发展历史及现状2

1.3本文主要研究内容5

第2章重要零部件选型6

2.1依照主轴功率确定电主轴型号6

2.2 选择主轴下部刀具夹头7

2.3选择工件的装卡方式8

第3章实验台支承部分及其连接的方案11

3.1机架的设计方案11

3.2铸造机架的材料及热处理14

3.3机架的截面形状、壁厚及周边筋的布置14

3.4立柱与底座的连接方式16

3.5底座的造型16

第4章实验台驱动电路17

4.1 电路布线方案17

4.2 电路控制要求17

4.3电路控制连线原理图17

第5章实验结果及三维建模18

5.1 设计并联实验台结果18

5.2 实验台solidworks建模18

第6章总结与展望19

参考文献20

致谢20

第1章绪论

1.1课题背景与意义

为了提高对生产环境的适应性，满足快速多变的市场需求，近年来全球机床制造业都在积极探索和研制新型多功能的制造装备与系统，其中在机床结构技术上的突破性进展当属90年代中期问世的并联机床(ParallelMachineTool)，又称虚(拟)轴机床(VirtualAxisMachineTool)或并联运动学机器(ParallelKinematicsMachine)。并联机床实质上是机器人技术与机床结构技术结合的产物，其原型是并联机器人操作机。与实现等同功能的传统五坐标数控机床相比，并联机床具有如下优点：

刚度重量比大：因采用并联闭环静定或非静定杆系结构，且在准静态情况下，传动构件理论上为仅受拉压载荷的二力杆，故传动机构的单位重量具有很高的承载能力。

响应速度快：运动部件惯性的大幅度降低有效地改善了伺服控制器的动态品质，允许动平台获得很高的进给速度和加速度，因而特别适于各种高速数控作业。

环境适应性强：便于可重组和模块化设计，且可构成形式多样的布局和自由度组合。在动平台上安装刀具可进行多坐标铣、钻、磨、抛光，以及异型刀具刃磨等加工。装备机械手腕、高能束源或CCD摄像机等末端执行器，还可完成精密装配、特种加工与测量等作业。

技术附加值高：并联机床具有“硬件”简单，“软件”复杂的特点，是一种技术附加值很高的机电一体化产品，因此可望获得高额的经济回报。

目前，国际学术界和工程界对研究与开发并联机床非常重视，并于90年代中期相继推出结构形式各异的产品化样机。1994年在芝加哥国际机床博览会上，美国Ingersoll铣床公司、Giddings&Lewis公司和Hexal公司首次展出了称为“六足虫”(Hexapod)和“变异型”(VARIAX)的数控机床与加工中心，引起轰动。此后，英国Geodetic公司，俄罗斯Lapik公司，挪威Multicraft公司，日本丰田、日立、三菱等公司,瑞士ETZH和IFW研究所，瑞典NeosRobotics公司，丹麦Braunschweig公司，德国亚琛工业大学、汉诺威大学和斯图加特大学等单位也研制出不同结构形式的数控铣床、激光加工和水射流机床、坐标测量机和加工中心。与之相呼应，由美国Sandia国家实验室和国家标准局倡议，已于1996年专门成立了Hexapod用户协会，并在国际互联网上设立站点。近年来，与并联机床和并联机器人操作机有关的学术会议层出不穷，例如第47～49届CIRP年会、1998～1999年CIRA大会、ASME第25届机构学双年会、第10届TMM世界大会均有大量文章涉及这一领域。由美国国家科学基金会动议，1998年在意大利米兰召开了第一届国际并联运动学机器专题研讨会，并决定第二届研讨会于2000年在美国密执安大学举行。1994～1999年期间，在历次大型国际机床博览会上均有这类新型机床参展，并认为可望成为21世纪高速轻型数控加工的主力装备。

我国已将并联机床的研究与开发列入国家“九五”攻关计划和863高技术发展计划，相关基础理论研究连续得到国家自然科学基金和国家攀登计划的资助。部分高校还将并联机床的研发纳入教育部211工程重点建设项目，并得到地方政府部门的支持且吸引了机床骨干企业的参与。在国家自然科学基金委员会的支持下，中国大陆地区从事这方面研究的骨干力量，于1999年6月在清华大学召开了我国第一届并联机器人与并联机床设计理论与关键技术研讨会，对并联机床的发展现状、未来趋势以及亟待解决的问题进行了研讨。

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内容简介：: nts nts nts机 0405 11 号马吟川指导老师：许宝杰 1 THE DESIGN OF PARALLEL KINEMATIC MACHINE TOOLS USING KINETOSTATIC PERFORMANCE CRITERIA /ftp/arxiv/papers/0705/0705.1038.pdf 1. INTRODUCTION Most industrial machine tools have a serial kinematic architecture, which means that each axis has to carry the following one, including its actuators and joints. High Speed Machining highlights some drawbacks of such architectures: heavy moving parts require from the machine structure high stiffness to limit bending problems that lower the machine accuracy, and limit the dynamic performances of the feed axes. That is why PKMs attract more and more researchers and companies, because they are claimed to offer several advantages over their serial counterparts, like high structural rigidity and high dynamic capacities. Indeed, the parallel kinematic arrangement of the links provides higher stiffness and lower moving masses that reduce inertia effects. Thus, PKMs have better dynamic performances. However, the design of a parallel kinematic machine tool (PKMT) is a hard task that requires further research studies before wide industrial use can be expected. Many criteria need to be taken into account in the design of a PKMT. We pay special attention to the description of kinetostatic criteria that rely on the conditioning of the Jacobian matrix of the mechanism. The organisation of this paper is as follows: next section introduces general remarks about PKMs, then is explained why PKMs can be interesting alternative machine tool designs. Then are presented existing PKMTs. An application to the design of a small-scale machine tool prototype developed at IRCCyN is presented at the end of this paper. 2. ABOUT PARALLEL KINEMATIC MACHINES 2.1. General Remarks The first industrial application of PKMs was the Gough platform (Figure 1), designed in 1957 to test tyres1. PKMs have then been used for many years in flight simulators and robotic applications2 because of their low moving mass and high dynamic performances. Since the development of high speed machining, PKMTs have become interesting alternative machine tool designs3, 4. nts机 0405 11 号马吟川指导老师：许宝杰 2 Figure 1. The Gough platform In a PKM, the tool is connected to the base through several kinematic chains or legs that are mounted in parallel. The legs are generally made of either telescopic struts with fixed node points (Figure 2a), or fixed length struts with gliding node points (Figure 2b). Along with high-speed cuttings unceasing development, the traditional tandem type organization constructs the platform the structure rigidity and the traveling carriage high speed becomes the technological development gradually the bottleneck, but the parallel platform then becomes the best candidate object, but was opposite in the tandem engine bed, the parallel working platform had the following characteristic and the merit: (1) structure is simple, the price is low The engine bed mechanical spare part number is series connected constructs the platform to reduce largely, mainly by the ball bearing guide screw, the Hooke articulation, the ball articulation, the servo electrical machinery and so on common module is composed, these common modules may by the special factory production, thus this engine beds manufacture and the inventory cost are much lower than the same functions traditional engine bed, easy to assemble and the transporting. (2) structure rigidity is high Because used closeness structure (closed-loop structure) to enable it to have high rigid and the high speed merit, its structural load streamline was short, but shouldered decomposes pulls, the pressure also to withstand by six connecting rods, by materials mechanics viewpoint, when the external force was certain, the bracket quantitys stress and the distortion were biggest, the both sides inserted the (build-in) next best, came is again both sides Jan supports (simply-supported), next was the bearing two strength structure, what the stress and the distortion were smallest was the tensity two strength structure, therefore it had the high rigidity. Its rigidity load ratio is higher than traditional the numerically-controlled machine tool. (3) processing speed is high, the inertia is low If the structure withstands the strength will change the direction, (will be situated between tensity and pressure), two strength components will be most save the material the structure, but it will move to the moving parts weight to reduce to lowly and simultaneously will actuate by six actuating units, therefore machine very easy high speed, and will have the low inertia. (4) working accuracy is high Because it for the multiple spindle parallel organization composition, six expandable pole poles long alone has an effect to cutting tools position and the posture, thus nts机 0405 11 号马吟川指导老师：许宝杰 3 does not have the traditional engine bed (i.e. connects engine bed) the geometrical error accumulation and the enlargement phenomenon, even also has the being uniform effect (averaging effect); It has the hot symmetrical structural design, therefore the thermal deformation is small; Therefore it has the high accuracy merit. (5) multi-purpose flexible Is convenient as a result of this engine bed organization simple control, easily according to processing object, but designs it the special purpose machine, simultaneously may also develop the general engine bed, with realizes the milling, boring, processings and so on grinding, but may also provide the essential measuring tool to compose it the measuring engine, realizes engine beds multi-purpose. This will bring the very big application and the market prospect, has the very broad application prospect in the national defense and the civil aspect. (6) service life is long Because the stress structure is reasonable, the moving part attrition is small, and does not have the guide rail, does not have the iron filings either the refrigerant enters the guide rail interior to cause it to scratch, the attrition or the corrosion phenomenon. (7) Stewart platform suits in the modular production Regarding the different machine scope, only need change the connecting rod length and the contact position, maintains also easily, does not need to carry on parts remaking and to adjust, only need the new organization parameter input. (8) transformation coordinate system is convenient Because does not have the entity coordinate system, the engine bed coordinate system and the work piece coordinate system transform depend on the software to complete completely, is convenient. When the Stewart platform applies in the engine bed and the robot, may reduce the static error (, because high rigidity), as well as dynamic error (because low inertia). But Stewart the platform inferiority lies in its working space to be small, and it has the singular point limit in the working space, but the serial operation platform, the controller meets time the singular point, accountant will figure out the actuation order which the drive is unable to achieve to create the ning error, but the Stewart platform will lose the support partial directions in the strange position the strength or moment of force ability, will be unable to complete the constant load object. Figure 2a. A bipod PKM nts机 0405 11 号马吟川指导老师：许宝杰 4 Figure 2b. A biglide PKM 2.2. Singularities The singular configurations (also called singularities) of a PKM may appear inside the workspace or at its boundaries. There are two types of singularities5. A configuration where a finite tool velocity requires infinite joint rates is called a serial singularity. A configuration where the tool cannot resist any effort and in turn, becomes uncontrollable, is called a parallel singularity. Parallel singularities are particularly undesirable because they induce the following problems: - a high increase in forces in joints and links, that may damage the structure, - a decrease of the mechanism stiffness that can lead to uncontrolled motions of the tool though actuated joints are locked. Figures 3a and 3b show the singularities for the biglide mechanism of Fig. 2b. In Fig. 3a, we have a serial singularity. The velocity amplification factor along the vertical direction is null and the force amplification factor is infinite. Figure 3b shows a parallel singularity. The velocity amplification factor is infinite along the vertical direction and the force amplification factor is close to zero. Note that a high velocity amplification factor is not necessarily desirable because the actuator encoder resolution is amplified and thus the accuracy is lower. Figure 3a. A serial singularity nts机 0405 11 号马吟川指导老师：许宝杰 5 Figure 3b. A parallel singularity 2.3. Working and Assembly Modes A serial (resp. parallel) singularity is associated with a change of working mode6 (resp. of assembly mode). For example, the biglide has four possible working modes for a given tool position (each leg node point can be to the left or to the right of the intermediate position corresponding to the serial singularity, Fig. 4a) and two assembly modes for a given actuator joint input (the tool is above or below the horizontal line corresponding to the parallel singularity, Fig. 4b). The choice of the assembly mode and of the working mode may influence significantly the behaviour of the mechanism5. Figure 4a. The four working modes Figure 4b. The two assembly modes nts机 0405 11 号马吟川指导老师：许宝杰 6 3. PKMs AS ALTERNATIVE MACHINE TOOL DESIGNS 3.1. Limitations of Serial Machine Tools Today, newly designed machine tools benefit from technological improvements of components such as spindles, linear actuators, bearings. Most machine tools are based on a serial architecture (Figure 5), whose advantage is that input/output relations are simple. Nevertheless, heavy masses to be carried and moved by each axis limit the dynamic performances, like feed rates or accelerations. That is why machine tools manufacturers have started being interested into PKMs since 1990. 3.2. PKMs Potentialities for Machine Tool Design The low moving mass of PKMs and their good stiffness allow high feed rates (up to 100 m/min) and accelerations (from 1 to 5g), which are the performances required by High Speed Machining. PKMs are said to be very accurate, which is not true in every case4, but another advantage is that the struts only work in traction or compression. However, there are many structural differences between serial and parallel machine tools, which makes it hard to strictly compare their performances. 3.3. Problems with PKMs a) The workspace of a PKM has not a simple geometric shape, and its functional volume is reduced, compared to the space occupied by the machine7, as we can see on Fig. 5 Figure 5. Workspace sections of Tricept 805 b) For a serial mechanism, the velocity and force transmission ratios are constant in the workspace. For a parallel mechanism, in contrast, these ratios may vary significantly in the workspace because the displacement of the tool is not linearly related to the nts机 0405 11 号马吟川指导老师：许宝杰 7 displacement of the actuators. In some parts of the workspace, the maximal velocities and forces measured at the tool may differ significantly from the maximal velocities and forces that the actuators can produce. This is particularly true in the vicinity of THE DESIGN OF PKMT USING KINETOSTATIC PERFORMANCE CRITERIA 5 singularities. At a singularity, the velocity, accuracy and force ratios reach extreme values. c) Calibration of PKMs is quite complicated because of kinematic models complexity8. 4. EXISTING PKMT DESIGNS In this section will be presented some existing PKMTs. 4.1. Fully Parallel Machine Tools What we call fully parallel machine tools are PKMs that have as many degrees of freedom as struts. On Fig. 7, we can see a 3-RPR fully parallel mechanism with three struts. Each strut is made of a revolute joint, a prismatic actuated joint and a revolute joint. Figure 6. 3-RPR fully parallel mechanism Fully PKMT with six variable length struts are called hexapods. Hexapods are inspired by the Gough Platform. The first PKMT was the hexapod “Variax” from Giddings and Lewis presented in 1994 at the IMTS in Chicago. Hexapods have six degrees of freedom. One more recent example is the CMW300, a hexapod head designed by the Compagnie Mcanique des Vosges (Figure 7) nts机 0405 11 号马吟川指导老师：许宝杰 8 . Figure 7. Hexapod CMW 300 (perso.wanadoo.fr/cmw.meca.6x/6AXES.htm) Fully parallel machine tools with fixed length struts can have three, four or six legs. The Urane SX (Figures8 and 13) from Renault Automation is a three leg machine, whose tool can only move along X, Y and Z axes, and its architecture is inspired from the Delta robot9, designed for pick and place applications. The Hexa M from Toyoda is a PKMT with six fixed length struts (Figure 9). Figure 8. Renault automation Urane SX (from “Renault Automation Magazine”, n 21, may 1999) nts机 0405 11 号马吟川指导老师：许宝杰 9 Figure 9. Toyoda Hexa M (www.toyodakouki. co.jp) 4.2. Other Kinds of PKMT The Tricept 805 is a widely used PKMT with three variable length struts (Figures 5 and 10). The Tricept 805 has a hybrid architecture: a two degrees of freedom wrist serially mounted on a tripod architecture. Another non fully parallel MT is the Eclipse (Figure 11) from Sena Technology10, 11. The Eclipse is an overactuated PKM for rapid machining, capable of simultaneous five faces milling, as well as turning, thanks to the second spindle. Figure 10. Tricept 805 from Neos robotics () nts机 0405 11 号马吟川指导老师：许宝杰 10 Figure 11. The Eclipse, from Sena Technology (macea.snu.ac.kr/eclipse/homepage.html) 5. DESIGNING A PKMT 5.1. A Global Task Given a set of needs, the most adequate machine will be designed through a set of design parameters like the machine morphology (serial, parallel or hybrid kinematic structure), the machine geometry (link dimensions, joint orientation and joint ranges), the type of actuators (linear or rotative motor), the type of joints (prismatic or revolute), the number and the type of degrees of freedom, the task for which the machine is designed. These parameters must be defined using relevant design criteria. 5.2. Kinetostatic Performance Criteria are Adequate for the Design of PKMTs The only way to cope with problems due to singularities is to integrate kinetostatic performance criteria in the design process of a PKMT. Kinetostatic performance criteria evaluate the ability of a mechanism to transmit forces or velocities from the actuators to the tool. These kinetostatic performance criteria must be able to guaranty minimum stiffness, accuracy and velocity performances along every direction throughout the workspace of the PKMT. To reach this goal, we use two complementary criteria: the conditioning of the Jacobian matrix J of the PKMT, called conditioning index, and the manipulability ellipsoid associated with J12. The Jacobian matrix J relates the joint rates to the tool velocities. It also relates the static tool efforts to the actuator efforts. The conditioning index is defined as the ratio between the highest and the smallest eigenvalue of J. The conditioning index varies from 1 to infinity. At a singularity, the index is infinity. It is 1 at another special configuration called isotropic configuration. At this configuration, the tool velocity and stiffness are equal in all directions. The conditioning index measures the uniformity of the distribution of the velocities and efforts around one given configuration but it does not inform about the magnitude of the velocity amplification or effort factors. The manipulability ellipsoid is defined from the matrix (J JT)-1. The principal axes of the ellipsoid are defined by the eigenvectors of (J JT)-1 and the lengths of the principal axes are the square roots of the eigenvalues of (J JT)-1. The eigenvalues are associated nts机 0405 11 号马吟川指导老师：许宝杰 11 with the velocity (or force) amplification factors along the principal axes of the manipulability ellipsoid. These criteria are used in Wenger13, to optimize the workspace shape and the performances uniformity of the Orthoglide, a three degree of freedom PKM dedicated to milling applications (Figur

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