馬路保潔車的設計【公路清掃車】,公路清掃車,馬路保潔車的設計【公路清掃車】,馬路,保潔,設計,公路,清掃,打掃 （學號）： 長春理工大學光電信息學院 畢 業(yè) 設 計（論 文）譯文 連桿混合驅動機構設計 姓 名 學 院 機電工程分院 專 業(yè) 機械設計制造及其自動化 班 級 指導教師 2010 年 月 日 機械裝備的發(fā)展 一．機械裝備的應用 近十幾年來，隨著計算機技術和現代控制理論等相關科技的迅速發(fā)展，以數控加工為代表的柔性加工日趨完善，基本上實現了自由曲面形狀加工階段的自動化，但其精加工主要還依靠熟練工人的手工操作。由于手工操作生產效益低下，加工質量不穩(wěn)定，難以適應自由曲面低成本、短周期、高質量的要求，研究一種高效自動化的研拋設備勢在必行，本研究針對自由曲面研拋加工所開發(fā)的虛擬軸混聯機床就是為了適應這種需求。 二．狀態(tài)分析 本處所開發(fā)的是并聯、串聯有層次聯結在一起的混聯機床。通過大量文獻閱讀，建立了各種并聯機構模型，運用 Adams 軟件對各種并聯機構模型進行分析，證明了3PTT運動副可以實現動平臺三維空間運動。 用 Adams 軟件建立的該機床并聯機構模型，并進行自由度問題研究和動平臺的運動分析。仿真結果表明，該并聯機構具有三個自由度，動平臺是平動的運動狀態(tài)。 三、自由曲面研拋機床的位姿分析 根據該機車的運動特性，利用解析法建立并聯機構的正解方程，首先建立并聯機構的解析圖形，如圖2所示。 圖2 研拋機床并聯機構解析圖 兩端取模平方知： 利用齊次變換的方法建立了自由曲面研拋機床串聯機構的位置正解，并將串并聯機構通過動平臺為紐帶，得到機床的位置正解。運用歐拉角表達研拋工具的軸線姿勢，發(fā)現該軸線姿勢只與串聯機構有關，而與并聯機構無關。 四、自由曲面研拋機床的動力學分析及其仿真 機床的動力學研究，包括機構慣性力計算、受力分析、動力平衡、動力學模型建立、計算機動態(tài)仿真等。特別是在機器的運行速度不斷提高的情況下，動力學問題的重要性就顯得尤為突出，由于計算機的不斷發(fā)展，使動力學計算、分析、模擬的手段逐步實現了現代化。對機構動力學研究的深入，促進了機器的運轉速度進一步提高，對機器的控制提供較為精確的理論基礎。 五、自由曲面研拋機床結構的研究 機床的研制分為二大部分：一是確定其機械結構方案包括機床機架設計；動平臺設計；終端執(zhí)行器設計等。二是研制控制電路和控制軟件等。機床應有三個性能指標：對稱性、工作空間、各向同性的基礎上來設計混聯機床。自由曲面研拋機床的主、俯視圖如圖 3 所示。 圖3 自由曲面研拋機床的主、俯視圖 六、結論 （1）通過“3 并聯軸2 串聯軸”的五坐標聯動，用并聯機構控制研拋工具的位置，用串聯機構控制研拋工具的姿勢，有效地拓展了研拋加工作業(yè)空間。 （2）建立了 3PTT 并聯機構 ADAMS 機構學模型，進行了自由度問題的研究。仿真結果表明： 3PTT 并聯機構是平動的機構。 （3）應用解析法推導了機床的并聯機構的位置正解；利用齊次變換的方法建立了自由曲面研拋機床串聯機構的位置正解。運用歐拉角表達研拋工具的軸線姿勢，發(fā)現該軸線姿勢只與串聯機構有關，而與并聯機構無關。 （4）基于影響系數理論與拉格朗日方程，推導出了串、并聯機構動力學方程，并建立了 ADAMS 動力學仿真模型，仿真結果表明：該機床在 x、y、z 三個方向上的速度、加速度差異很大。如果在 z 方向需要大的速度和加速度，三個滑塊均需加同一方向的力，數值相差要足夠小，在 x、y 方向需要較大的速度和加速度時，在三個滑塊上力的數值要相差足夠大。 （5）在自由曲面虛擬軸混聯研拋機床的結構、運動學與動力學研究以及前人關于研拋理論的工作基礎上，開發(fā)了自由曲面虛擬軸混聯研拋機床的樣機。 串-并混聯研拋機床運動與控制研究 1994 年在芝加哥國際機床展覽會（IMTS94）上，美國的 Ingersoll 和 Giddings & Lewi公司分別首次展出了名為 Hexapod 和 Variax 的并聯機床，引起舉世關注。并聯機床以空間并聯構型為基礎，打破了近兩個世紀以來單一的以笛卡爾坐標直線位移為基礎的串聯機床 結構和運動學原理，被譽為“本世紀機床機構的最大變革與創(chuàng)新”、“21 世紀的機床”。其后，意大利、日本、俄羅斯、挪威、瑞士、瑞典、丹麥等國的制造商竟相研發(fā)并聯機床。1997 年底，清華大學和天津大學聯合研制出了我國第一臺并聯機床 VAMT1Y。 與傳統的串聯構型機床相比，純并聯構型的并聯機床在結構及運動特性上具有剛度重量比大，運動部件質量小、響應速度快，誤差累積小，可以很容易地實現 6 軸聯動，運動學逆解求解容易、便于實現實時控制，機床結構簡單，技術附加值高等優(yōu)點。但并聯機床同時也存在著工作空間小，運動學的正解求解困難，控制復雜，各軸間存在著深度的非線性運動耦合，運動學標定困難，機床的剛度和運動精度不高等缺點。為克服并聯機床的缺點，串-并混聯式機床應運而生。 混聯機床幾乎繼承了并聯機床的全部優(yōu)點，同時其工作空間增大，運動學正解的求解困難程度及控制復雜程度均明顯降低。盡管其剛度和運動學精度仍不如串聯機床高，但已顯示出強大的生命力。目前，商品化的并聯機床已投入使用。 課題組通過多年的研究發(fā)現，研拋屬于彈性加工，研拋過程中作用反力較小，因而對機床的剛度要求較低，同時，研拋機床需要在其終端執(zhí)行器上安裝位移-力柔順控制器，柔順控制器的安裝使研拋加工對機床運動精度的要求被弱化。研拋加工所具有的這些工藝特性，使得串-并混聯機床揚長避短，可以在研拋加工中得到較好的應用。 基于對吉林省科技發(fā)展重點規(guī)劃課題“精密自動研拋加工模具自由曲面的虛擬軸專用機床”的研究（機床照片見圖 1），本文就串-并混聯研拋機床的概念設計、運動學分析、插補控制、研拋實驗等問題展開研究。 對串聯構型、并聯構型、混聯構型機床的結構特性、運動特性、控制特性等內容進行了分析比較，選定在并聯 3 自由度平動平臺上串聯 2 回轉自由度的串-并混聯形式作為自由曲面研拋機床的構型。機床結構見圖 2。 對 3 自由度平動平臺的支鏈結構形式進行了分析。通過齊次坐標變換方法，從支鏈平臺結構位姿變換及其空間幾何關系分析入手，建立了三支鏈并聯平臺的封閉位置關系，得出了以虎克鉸為聯接關節(jié)條件下 3 自由度平動平臺的最簡單構型形式和平臺工作空間與平臺機構體積比值最大條件下的結構參數配置。 基于并聯平臺封閉位置關系，給出了機床的運動學正解，并對機床工作空間的形狀、構成進行了剖析。本文所述構型形式的研拋機床具有由三段圓弧面構成的柱形工作空間，工作空間的上頂和下底均為由四個球弧面構成的復合曲面。首次將工具靈活性的概念引入機床的工作空間分析，并按照研拋工具所具有的靈活程度，將機床工作空間劃分為完全靈活工作空間、大部分靈活工作空間、小部分靈活工作空間和不靈活工作空間四個子區(qū)。通過推理，得出了機床完全靈活工作空間的主要影響因素是研拋工具桿長度的結論。機床工作空間形式及構成見圖 3。 基于并聯平臺封閉位置關系和研拋工具的位置-姿態(tài)要求，對機床運動學逆解的構成及求解方法進行了研究。由于研拋姿態(tài)角δ1的存在，工具桿軸線可以形成一個以δ1為半角的姿態(tài)圓錐，致使機床的運動學逆解具有多值、不確定性。為使機床的運動學逆解合理、唯一，需添加工藝和運動限定條件。本文對研拋正壓力與研拋姿態(tài)角之間的關系、研拋線速度與研拋姿態(tài)角之間的關系進行了分析，提出了滿足研拋正壓力和研拋線速度雙重控制要求的δ1選擇工藝限定條件，并基于對加工效率、運動干涉等問題的考慮，提出了限定姿態(tài)圓錐使用范圍的運動條件。綜合考慮，提出了研拋工具姿態(tài)的選擇控制策略，同時給出了機床各種靈活程度工作空間內運動學逆解的求解方法。姿態(tài)圓錐及其可選用的范圍見圖4 和圖 5。 對離線插補和在線插補的工藝特性進行了分析比較，結合目前插補控制的發(fā)展趨勢，選擇在線的直接插補作為新開發(fā)數控系統的插補控制方式。并結合 NURBS 曲面的參變量定義域特性，給出了 NURBS 曲面研拋的路徑規(guī)劃方式。 對研拋軌線行間距與表面許用殘留高度誤差、研拋工具半徑、曲面曲率半徑之間的關系（圖 6），插補步長與表面加工誤差、研拋工具半徑、曲面曲率半徑之間的關系（圖 7）行了較為深入的分析，找出了兩類加工誤差的主要影響因素，并據此提出了針對粗研磨和精整拋光的研拋軌線行間距、插補步長確定方法。 五坐標虛擬軸研拋機床數控系統的研究 一、說明 我國于 2001 年正式加入 WTO 以來，經濟發(fā)展迅速。隨著汽車、航空航天以及一批高新技術產業(yè)的發(fā)展，含有自由曲面的零件所占的比例越來越大，對自由曲面的加工質量和效率要求也越來越高。但是目前對自由曲面的精加工主要還依靠熟練工人的手工操作。由于手工操作生產效益低下，加工質量不穩(wěn)定，難以適應自由曲面低成本、短周期、高質量的要求，研究一種高效自動化的研拋設備勢在必行。本文針對用于自由曲面研拋加工的 JDYP51 型五坐標虛擬軸研拋機床，研究出了一種基于 PMAC 的開放式數控系統。 二、虛擬軸機床機構設計的分析 本課題所研究的是并聯、串聯組合在一起的混聯機床，該機床為 3+2 式虛擬軸機床，即 3 個并聯軸實現 X、Y、Z 向 3 個坐標運動，并聯機構帶動動平臺實現平動，在動平臺上安裝 2 自由度串聯機器手，串聯機構下加裝主軸裝置。用此機床進行模具自由曲面的研拋加工。機床照片如圖 1 所示， 虛擬軸機床的總體結構如圖 2 所示，它的并聯機構由靜平臺、動平臺和三個導軌立柱—滑塊—支鏈相結合的機構組成 ，支鏈采用定長桿，各桿件一端與滑塊，另一端與動平臺用虎克鉸連接，滑塊由伺服電機和滾珠絲杠螺母副驅動，沿導軌作上下移動。機床的串聯機構連接在動平臺上，由兩個轉動關節(jié)構成，分別繞軸轉動來調整研拋工具的位姿。 以上所述即為并聯機構的位置關系，同時可以利用齊次變換的方法建立機床串聯機構的位置方程，并將串并聯機構通過動平臺為紐帶，得到機床整體的位置關系。 三、開放式數控系統的硬件設計與實現 我們通過對 JDYP51 型虛擬軸研拋機床的研究，設計使用了一種基于PMAC 的開放式數控系統。根據此數控系統所設計的數控裝置目前已經完成，如圖 4 所示，控制裝置區(qū)域劃分由上至下為：實時顯示區(qū)，飼服控制區(qū)，控制電路區(qū)，核心控制區(qū)和主軸控制區(qū)。 制機、PMAC 運動控制器、雙端口 RAM（DPRAM）、伺服單元及交流伺服電機等組成。圖中的虛線將上位機和下位機的功能模塊分開，實線框以外部分為系統的外部設備。由框圖可以看出，PMAC 控制器與主機（IPC）之間的通訊采用了兩種方式。一種是總線通訊方式，另一種是利用 DPRAM 進行數據通信，主機與 PMAC 運動控制器主要通過 ISA 總線通訊，至于控制器和電機的狀態(tài)、所處的位置、速度、跟隨誤差等數據則通過 DPRAM 交換信息。 圖4 JDYP51 NC 裝置 四、開放式數控系統的軟件研究 虛擬軸機床數控系統實現正常工作，需要三個部分的系統軟件來執(zhí)行：IPC的用戶界面應用程序；IPC 與 PMAC 上下位機間的通訊程序；PMAC 中對各種輸入、輸出量進行監(jiān)控的 PLC 程序。其中通訊程序的開發(fā)工作量最大、最困難、也最具有技巧性，Delta Tau 公司提供的 Pcomm32 已經對通訊程序進行了充分的開發(fā)，我們可以通過 Pmac.dll 進一步利用。人機界面應用程序采用Visual C++6.0 語言進行開發(fā)。PLC 程序采用 Delta Tau 公司提供的語言進行設計開發(fā)。系統軟件工作機理如圖 6 所示， 五、結論 本課題對 JDYP51 型五坐標虛擬軸研拋機床的數控系統進行了研究和設計，建立了一種基于 PMAC 和 IPC 的雙 CPU 開放式數控系統，完成了機床的數控裝置，并通過此數控裝置對機床進行了初步的調試和試運行，實現了基本的運行要求。本論文主要的研究工作及研究成果如下： 1．對虛擬軸機床機構整體設計和工作原理進行了分析研究，通過分別對機床并聯機構、串聯機構和主軸研頭的位置解析，得到機床輸入與輸出的位置正逆解關系式，為數控系統對機床的軌跡運動控制提供了基礎。 2．對可編程多軸運動控制器(PMAC)進行了深入系統的研究，針對本虛擬軸機床設計開發(fā)了一種基于 PMAC 和 IPC 的雙 CPU 開放式數控系統硬件結構，根據硬件設計要求選擇了相應的硬件設施和電子器件，組建完成了數控系統的控制裝置。 3．對 CNC 系統軟件結構與功能做了深入的研究，建立了數控系統軟件結構框架。根據數控系統硬件的結構設計，提出了系統軟件工作機理，同時參與了人機控制界面的開發(fā)并對系統軟件設計做了進一步的研究。此控制界面軟件實現了部分的硬件軟件化，將部分控制按鈕和指示燈等硬設施轉化為軟件控制，同時可以根據需要添加多個 I/O 通道，具有良好的開放性和實時性。 4．通過數控系統的控制裝置對 JDYP51 型五坐標虛擬軸研拋機床進行了調試，并在調試過程中完成了數控系統的參數設置與調整，初步完成了機床的合理運行。通過對飼服系統的 PID 調節(jié)及位置速度反饋的分析結果，實現了較為理想的運動狀態(tài)。 Polishing Machine Development Yudy and development on hybrid virtual axis machine tool forpolishing free-form surfaces 1 Introduction With the development of automobile industry,electric industry and some new high-techindustries ,the larger is the proportion of NC machining parts with free-form surface in all, thehigher and higher requirements are made for quality and efficiency of machining on free-formsurfaces. After the roughing method is used, precision machining, such as polishing and polishing,is necessary to obtain required workpiece surfaces. Near for over ten years, With the developmentat a high speed in relevant science and technology, such as the technology of the computer andmodern control theory, etc., flexibility machining become more perfect. The automatic machiningof free-form surfaces come to true basically. However, these subsequent processes of precisionmachining still depend mainly on the handwork of skilled mechanists. Productivity effect ofhandwork is very low and its quality is unstable. As to the machining of free-form surfaces, lowcost and short period and high quality were its main aim. As a result of that, the research of a kindof increasingly automated polishing equipment is imperative. Series-parallel virtual axis machine tools for polishing free-form surfaces meets the requirement . 2 Work principle and degree of freedom study on hybrid virtual axis machine tools for polishing The sliding block that was drived by servo electromotor and rolling screw thread-nut move up and down along with rail. The inseries mechanism of the machine tool was linked with move platform. It was made up of two rotation joints. The pose of polishing tools was adjusted around axis. The structure principle of the machine tool is shown as Figure.1. 3.Position and pose analysis of series-parallet virtual axis machine tool for polishing free-form surface. Fig2 Model of parallel mechanism was established by ADAMS software, It is analyzed out that the parallel mechanism has three DOF and the motion status of move platform is linear motion. it is shown As Fig2 Positive position solution of inseries mechanism of machine tools for polishing free-form surfaces was established through homogeneous transformation of the coordinate frames. Inseries and parallel mechanism were regarded moving the platform as the tie, so positive position solution of machine tools was got. Axes position of polishing tools is related to inseries mechanism but not parallel mechanism. It was proved by Euler angles. 4 kinetics analysis and simulation of series-parallel virtual axis machine tools for polishing free-form surfaces Kinetics analysis of machine tools included inertia force calculate, force analysis, balance of motive force, establishment of kinetics model, dynamic simulation with computer,etc. In the case of increasing velocity of machine tools, the importance of kinetics questions become particularly outstanding. Because of the uninterrupted development of computer, the methods of kinetics calculate and analysis and simulation become modernization. With the deep study of kinetics, the velocity of machine tools was further improved. It offers theory basis for control of the machine tools.The move platform can only realize linear motion in 3D space. There is not rotation kinetic nergy. Then the kinetic energy of move platform is design of machine tools shelfand . 5.Stand on structure of series-parallet virtual axis machine tool for polishing free-form surface. The front view and bottommove platform and end effector,view of the polishing machineetc. Second, there are study andtool for free-form surfaces manufacture of control circuitand so on. There are three perfor-mance indexes :symmetry.worksp-ace.isotropy. On the basisof these, series-parallel machine tools were designed. Overall appearance of machine tools must be aesthetic. There are another requirements with good igidity and stability and enough operation space. Front view and bottom view of machine tools for polishing free-form surfaces are shown as Figure.3. 6 conclusion 1. Five coordinates axes move together throng three parallel axes and two inseries axes. The position of polishing tools was controlled by parallel mechanism and the pose was controlled by parallel mechanism. Thus, the work space for polishing was increased effectually. 2.3PTT parallel mechanism structure model of Adams was established. The problem of degree of freedom was studied. The simulation shows: 3PTT parallel mechanism move linearly. 3.Analytics methods were applied to deduct the positive position solution of machine tool’sparallel. Positive position solution was obtained by making use of homogeneous transformation of the coordinate frames. Axes pose of polishing tools was expressed by Euler angle. It is shown that the axes pose is related to inseries mechanism,but not parallel mechanism. 4.On the basis of influence coefficient theory and Lagrangian equation, it was deducted that the kinetic equation of inseries and parallel mechanism. Kinetic simulation model was established by Adams. The simulation shows: there are much difference of velocity and acceleration in X,Y, Z direction of the machine tool.. If it is required that high velocity and acceleration in Z direction, the same direction forces were added to the three siding blocks. The difference of value should be small enough. The difference of force value on the three sliding blocks should be big enough, if requiring high velocity and acceleration in X, Y direction. 5.Through studying the structure and kinematics and kinetic of the inseries-parallel virtual axis machine tool for polishing free-form surfaces and on the working foundation of polishing theory of forefathers, it was developed that the sample of inseries-parallel virtual axis machine tool for polishing free-form surfaces. Keywords: parallel mechanism helix theory degree of freedom influence coefficient free-form surfaces polishing virtual axis machine tool Study on the Kinematics and Interpolation Control of the Series-Parallel Hybrid Polishing Machine Tool In 1994 on the Chicago international exhibition of machine tool (IMTS’94), the parallel machine tools of Hexapod and Variax are displayed by the Ingersoll and Giddings & Lewis company of America for the first time, and it is paid close attention by the whole world. Based on the three dimensional parallel mechanism, the parallel machine tool founds a new principle of the construction and the kinematics for the machine tool, and is known as " the biggest transformation and innovation of the mechanism for machine tool in this century ", " the machine tool of the 21 century ". In after years, the manufacturers of Italy, Japan, Russia, Norway, Switzerland, Sweden and Danish etc. develop parallel machine tool competitively. In the end of 1997, the first parallel machine tool VAMT1Y of our country was developed by the Tsinghua University and Tianjin University jointly. Compared with the traditional series machine tool, the parallel machine tool has many merits on the aspect of the structure and the kinematics characteristic such as higher proportion of the rigidity and weight, less quality of the moving parts, rapider respond speed, less error accumulation, easier realization for 6 axles uniting to move, easier calculation for inverse kinematics result that is expedient for real time control, simpler structure of machine tool, higher technical additional value and so on. However, the parallel machine tool has also the disadvantages such as smaller work space, more difficult calculation for forward kinematics result, deeper nonlinear coupling among each axis and more complex control for interpolation, more difficult kinematics marking, weakIt is against the shortcomings of the parallel machine tool that the hybrid machine tool with series-parallel conformation has been developed. The series-parallel hybrid machine tool has inherited all advantages of the parallel virtual axis machine tool nearly, and its workspace to be increased, the difficulty to calculate the forward kinematics result and to control the machine tool to be reduced. For these reasons, theer rigidity and movement precision of the machine tool. series-parallel hybrid machine tool has shown powerful vitality though its rigidity and movement precision is still lower than the series machine tool. Observing the conformation of the machine tools to be made recently, mostly of them are series-parallel one. Studying the polishing for many years, the group knows that the polishing machining belongs to flexible machining. In the polishing process, the requirements for the rigidity and the movement precision of the machine tool are both lower because the active force of the polishing process is smaller and the displacement-force obedience controller is installed in the bearing rod of the polishing tool. For these reasons, the series-parallel hybrid machine tool can be used as a better polishing machine tool. Based on the polishing machine tool made by the group, these questions such as the conception design, the kinematics analysis, the interpolation control and the polishing experiment of the series-parallel hybrid polishing machine tool have been discussed deeply in the paper. Fig. 1 is the photo of the machine tool. After analyzing the structure characteristic, the kinematics characteristic and the control characteristic among the series conformation, the parallel conformation and the series-parallel conformation, select the conformation connected 2 series rotation mechanisms on the 3 DOFS translation moving platform as the conformation of the polishing machine tool. Fig. 2 is the mechanisms of the machine tool. The chain structure of 3 DOFS translation platform is analyzed. Through the method ofhomogeneous transformation and the analysis of dimensional geometry connection about the position-posture of the parallel platform, the closed position connection of the parallel platform is given out, and based on it, the conclusion is revealed that the most simple mechanism of the 3 DOFS translation platform is 3 single-link chains mechanism which is symmetrical in space and jointed by Hook joints. The structure parameters are discussed under the condition of the biggest ratio between the workspace and the structure space of the platform. Based on the closed position connection of the parallel platform, the forward kinematics result of the machine tool is given out, and the workspace of the machine tool is discussed in form and shape. The workspace of the series-parallel hybrid virtual axis polishing machine tool is a column space that is made up of 3 circular-arc surfaces, and its top and bottom are both the complex curved surface consists of 4 ball-arc surfaces. The concept of tool flexibility was introduced firstly in the analysis of machine tool workspace, and according to it, the workspace of the machine tool is divided into four kinds of flexible workspace, the full flexible-workspace, the most flexible-workspace, the fraction flexible-workspace and unhandy workspace. The main influence factor on the full flexible-workspace of the machine tool is the bearing rod length of the polishing tool. The workspace of the machine tool is shown as Fig. 3. Based on the closed position connection of the parallel platform and the requirement of position-posture on polishing tool, the inverse kinematics result of the machine tool is analyzed in form and calculating method. Being the polishing posture angle δ1, the axes of the polishing tool bearing rod can form a cone with half-angle δ1(shown as Fig. 4). That makes the inverse kinematics result of the machine tool have the characteristic of more values and uncertainty. In order to make the inverse kinematics result uniquely, the technical restricting conditions and the motion restricting conditions should be appended. The relations among the active force, the polishing velocity and the polishing posture angle δ1 are analyzed, and the technical restricting conditions, the motion restricting conditions are put forward. The method of calculating the polishing posture in four kinds of flexible workspace is introduced. After that, the inverse kinematics result of the machine tool is given out. Fig. 5 is the semi-cone that the axes of the polishing tool bearing rod should be located on. According to the property of the variable definition region of the NURBS curved surface, the polishing path has been planned. For the reason of its excellent property, online direct interpolation control is chosen as the interpolation control method of the new developing system. Based on the analysis about the row space of the polishing trace and its influence factor, the interpolation step size and its influence factor, the methods how to determine the row space of the polishing trace and the interpolation step size are given out. The relation between row space and radius of the curved surface is shown in Fig. 6, and the relation between interpolation step size and radius of the curved surface is shown in Fig. 7. Research on CNC System of five-coordinate Virtual Axis polishing Machine Tool 1．Introduction Since our country was affiliated to WTO in due form in 2001, the economic development is speedier. With the development of automobile industry, aeronautics and astronautics industry and some new high-tech industries, the larger is the proportion of NC machining parts with free-form surface in all, the higher and higher requirements are made for quality and efficiency of machining on free-form surfaces. However, these subsequent processes of precision machining still depend mainly on the handwork of skilled mechanists presently. Productivity effect of handwork is very low and its quality is unstable. As to the machining of free-form surfaces, low cost and short period and high quality were its main aim. As a result of that, the research of a kind of increasingly automated polishing equipment is imperative. This paper regards the JDYP51 model five-coordinate virtual axis polishing machine tool for polishing free-form surfaces. We have researched a kind of open architecture CNC system which is based on PMAC. 2．Mechanism design analysis of virtual axis machine tool The series-parallel machine tool, which is well arranged by in series and parallel, is researched in this dissertation.It is a “3+2” model virtual axi