外文翻譯--對1ps+4tps型混合工作機(jī)床在插補(bǔ)原理和方法的研究

1、<p><b>　　南京理工大學(xué)</b></p><p>　　畢業(yè)設(shè)計(jì)(論文)外文資料翻譯</p><p>　　系　　部： 機(jī)械工程系 </p><p>　　專 業(yè)： 機(jī)械工程及自動化 </p><p>　　

2、姓 名： </p><p>　　學(xué) 號： </p><p>　　外文出處： Third International Conference On Natural Computation</p><p>　　0-7695-2875-9/07&

3、#169; 2007 IEEE </p><p>　　附 件： 1.外文資料翻譯譯文；2.外文原文。 </p><p>　　注：請將該封面與附件裝訂成冊。</p><p>　　附件1：外文資料翻譯譯文</p><p>　　對1PS+4TPS型混合工作機(jī)床在插補(bǔ)原理和方法的研究<

4、;/p><p>　　范守文，王小斌，師明全，黃鴻忠</p><p><b>　　中國電子科技大學(xué)</b></p><p>　　成都，四川，610054, 中華人民共和國</p><p><b>　　摘要</b></p><p>　　本文基于 4 dof 的1PS ，設(shè)計(jì)了新型的混

5、合工作機(jī)器 （HMT）＋4TPS 鍵入空間的混合機(jī)制和 a x－y 的工作臺。這一類型 HMT與它的傳統(tǒng)相比有一些優(yōu)勢： 大的工作空間、較好的靈活度等等?？梢詫?shí)現(xiàn)倒轉(zhuǎn)的換置模型和倒轉(zhuǎn)的運(yùn)動學(xué)模型的關(guān)閉。對應(yīng)HMTs運(yùn)動控制的CNC方案是運(yùn)動控制特性和基于傳統(tǒng)的數(shù)字控制機(jī)器的研究成果。即時(shí)的五軸插補(bǔ)器，它包括切削路徑計(jì)算，倒轉(zhuǎn)的換置分析模型，倒轉(zhuǎn)的運(yùn)動學(xué)的分析模型和 PVT插補(bǔ)模態(tài)，事實(shí)證明他們可以構(gòu)建。 通過切削路徑間隔計(jì)算和插補(bǔ)錯誤分

6、析來證明以上方法的可行性和高效性。</p><p>　　關(guān)鍵字： 混合的工作機(jī)床；計(jì)算機(jī)數(shù)字控制； 插補(bǔ)； 錯誤分析；切削</p><p><b>　　1. 介紹</b></p><p>　　PMT 機(jī)床是PM機(jī)床中一個有創(chuàng)造力的應(yīng)用實(shí)例，數(shù)字技術(shù)和計(jì)算機(jī)控制技術(shù)在這個領(lǐng)域內(nèi)也得到廣泛使用。作為一種新型的工作機(jī)床， PMT 有簡單結(jié)構(gòu)，低成本，

7、低的移動慣性、高速度、較好的靈活性、較高的技術(shù)要求的特點(diǎn)等。.PMT 使傳統(tǒng)的的數(shù)字機(jī)床更加完美，使它更適合對葉片，葉輪和螺旋槳等的表面的加工。</p><p>　　然而，現(xiàn)有的PMT，它只采用鉸鏈或者鏈約束的平行結(jié)構(gòu)，特別地被一些因素影響：比如連接器的位置和方向，移動的平臺對方向有限制能力。因此，它很難符合大多數(shù)數(shù)控機(jī)床對大的工作空間和加工困難而且復(fù)雜的表面的加工需求。為了要解決這一個問題，研究員在探索新結(jié)構(gòu)上

8、已經(jīng)做了很多努力。許多研究員開始關(guān)注（DOFs） PMTs 的少于 6 個自由度的結(jié)構(gòu)，特別是混合的工作機(jī)床（HMTs） [4]， PMT 的另一個重要的發(fā)展趨勢是 移動的 DOF 和旋轉(zhuǎn)的利用組合的機(jī)制個別地被實(shí)現(xiàn)的DOF 。這個結(jié)構(gòu)不僅釋放 移動 控制和旋轉(zhuǎn)的控制之間的聯(lián)結(jié)，而且也有大工作空間和較好的結(jié)構(gòu)能力的特點(diǎn)。特別地，它能解決向前的運(yùn)動學(xué)的位置和方位，因此它能很方便提供NC程序，控制和錯誤反饋。</p><

9、p>　　1PS＋4TPS 機(jī)制是新型的 4 DOFs 混合機(jī)制,在縮寫的 "1PS ＋ 4TPS" 之中，P 表示 prismical 關(guān)節(jié)，S 表示球的關(guān)節(jié)，T 表示連接關(guān)節(jié)，它能實(shí)現(xiàn)一次平移運(yùn)動和三次旋轉(zhuǎn)的運(yùn)動。新型的 HMT 的核心結(jié)構(gòu)是在 4個 DOFs 混合機(jī)制和 a x－y 的工作臺，如圖Fig.1所示 。新的機(jī)制給這個新型的混合工作機(jī)床的設(shè)計(jì)和運(yùn)動學(xué)的分析很好的進(jìn)行了描述，然后設(shè)計(jì) HMTs 的一

10、個 CNC 系統(tǒng)方案，給 HMTs 的路徑控制制定一個及時(shí)的五軸插補(bǔ)程序。而且也能討論切削路徑間隔計(jì)算和插補(bǔ)錯誤分析。</p><p>　　2. 新型HMT 結(jié)構(gòu)學(xué)的描述</p><p>　　一個 4 DOF 的混合機(jī)制圖顯示</p><p>　　圖1 新型混合機(jī)制結(jié)構(gòu)圖</p><p>　　這個混合的機(jī)制由五個運(yùn)動的次鏈組成，用同一個拓?fù)鋵W(xué)

11、和一段被動的行程，它包括四個可變長度推進(jìn)的行程，把固定的基礎(chǔ)結(jié)構(gòu)連結(jié)到一個移動的平臺上。在這個 4 DOF 的混合機(jī)制中，四個同樣的行程中，每一個都有一個固定的連接關(guān)節(jié)，一個操縱關(guān)節(jié)，一個移動連接和一個與移動平臺連接的附件。這第五鏈，把固定的基本中心連結(jié)到移動的平臺中心，是另外四個不同的結(jié)構(gòu)同一個鏈的一段被動的行程。.它包括與基本結(jié)構(gòu)連接的分析關(guān)節(jié)，一個移動的連接和一個連接平臺的全關(guān)節(jié)。上述的混合機(jī)制能和像 x－y 的平臺這樣的二軸系統(tǒng)

12、結(jié)合，形成五軸的機(jī)床。</p><p>　　3. 相反的換置分析模型</p><p>　　3.1.相反的換置分析模型</p><p>　　一個固定的叁考協(xié)調(diào)系統(tǒng)和和一個可移動的固定的叁考協(xié)調(diào)系統(tǒng)都被安裝在固定平臺和可移動平臺的中心。正如FIG2所示，固定平臺的四個連接關(guān)節(jié)都被安裝在能用來描述的固定框架上?？梢欢ㄆ脚_的四個球型關(guān)節(jié)都被安裝在能用來描述的可移動框架上，可

13、移動平臺的四個球形關(guān)節(jié)都各自固定在能用來描述的上，能用來描述的可移動框架的起始點(diǎn)。由三個角度決定它的可移動平臺的中心方向。</p><p>　　圖2 主要進(jìn)給方法圖解</p><p>　　可移動平臺上的球型關(guān)節(jié)的coordineate能用以下關(guān)系式表示：</p><p><b>　?。?）</b></p><p>　　相

14、反的變位分析方程序能被寫為：</p><p><b>　?。?）</b></p><p>　　是一個3×3旋轉(zhuǎn)變化的系統(tǒng)，它能通過三種角度獲得三種旋轉(zhuǎn)角度，，和，如下所示：（如FIG3所示）</p><p>　　3.2.倒轉(zhuǎn)運(yùn)動學(xué)的模型</p><p>　　運(yùn)動分析中的參數(shù)定義如下：驅(qū)動行程的長度，驅(qū)動行程的進(jìn)

15、給速度，移動平臺的角速度，移動平臺的中心點(diǎn)P的速度，驅(qū)動行程的角速度，驅(qū)動行程上部的最大中心速度，驅(qū)動行程下部的最大中心速度。最大中心上部離點(diǎn)的距離為，最大中心下部離點(diǎn)的距離為。如下定義：</p><p>　　，對于所有的給定數(shù)據(jù)，我們?nèi)。篿=1,2,3,4.</p><p>　　讓K=，由于可移動平臺的球型關(guān)節(jié)的速度與驅(qū)動臂上點(diǎn)的速度相同，所以我們有：</p><p&

16、gt;<b>　?。?）</b></p><p>　　公式兩邊不同時(shí)乘以，我們得到</p><p><b>　　（4）</b></p><p>　　公式4能用；另一種方式寫為： （5）</p><p><b>　　這里</b

17、></p><p><b>　　于是</b></p><p><b>　?。?）</b></p><p>　　上述公式能被分別寫成：</p><p><b>　?。?）</b></p><p><b>　　這里</b><

18、/p><p>　　通過兩邊同時(shí)乘以，得到：</p><p><b>　?。?）</b></p><p>　　用公式（8）替換公式（7）,得到：</p><p><b>　?。?）</b></p><p><b>　　這里：</b></p>&l

19、t;p><b>　　然后得到：</b></p><p><b>　?。?0）</b></p><p>　　行程裝置上部的速度和下部的速度能表示成：</p><p><b>　?。?1）</b></p><p>　　把公式（7）和公式（10）代入公式（11）得到：</

20、p><p><b>　?。?2）</b></p><p><b>　　這里</b></p><p><b>　　由于</b></p><p><b>　　（13）</b></p><p>　　把公式（7）代入公式（13）得到</p

21、><p><b>　?。?4）</b></p><p>　　當(dāng)輸入運(yùn)動知道的前提下，可移動平臺的速度和角速度是確定的，對比公式（7）和公式（14），前面的速度公式可以寫成</p><p><b>　?。?5）</b></p><p>　　這里的，一個決定性的因素是，操縱者的位置和方向速度取決于輸入速度。

22、</p><p>　　如果坐標(biāo)系J是反向的，這相反的運(yùn)動方程可表示成：</p><p><b>　?。?6）</b></p><p>　　4.HMTs 的 CNC 系統(tǒng)的方案</p><p>　　這片文獻(xiàn)說的是對于1PS＋4TPS 型 HMTs的一個CNC系統(tǒng)方案。就和FIG4所示的一樣，</p><

23、p>　　圖3 HMTs的數(shù)控系統(tǒng)結(jié)構(gòu)</p><p>　　這個計(jì)劃包括設(shè)計(jì)想法目的是要利用傳統(tǒng)數(shù)字控制系統(tǒng)擴(kuò)充的成果，以便他能與傳統(tǒng)控制系統(tǒng)相兼容。也能在控制系統(tǒng)結(jié)構(gòu)，技術(shù)標(biāo)準(zhǔn)方面保持一致性，能采用兩者開放的標(biāo)準(zhǔn)系統(tǒng)結(jié)構(gòu)和標(biāo)準(zhǔn)設(shè)計(jì)理念。</p><p>　　HMTs的CNC系統(tǒng)計(jì)劃包括：CAD層次，CAM層次,CNC層次，補(bǔ)助層等，在他們之中，CAM層次的自動程序運(yùn)行模塊能在表面自動

24、產(chǎn)生運(yùn)行路徑，切削補(bǔ)償信息和速度控制信息，切削路徑資料都能自動產(chǎn)生。通過處理器的處理，G指令能從運(yùn)行路徑中得出，G指令也能通過機(jī)器的模擬得出，于是正確的切削路徑就能被核實(shí)。自動程序運(yùn)行模塊能夠直接輸出直線或曲線的插補(bǔ)指令，插補(bǔ)的G指令被輸入到插補(bǔ)層次，插補(bǔ)層次能高精度的產(chǎn)生切削路徑，然后分散粗糙的路徑能通過計(jì)算機(jī)硬件的處理得到修正。然后路徑的數(shù)據(jù)會被輸入到各個關(guān)節(jié)空間（等，移置和速度相反的分析模塊），分散關(guān)節(jié)空間的位置，在共同的空間里，

25、每一步精確的定位都是通過運(yùn)動控制卡發(fā)出的信號控制的。通過調(diào)節(jié)混合機(jī)制，HMTs就能實(shí)現(xiàn)高速高精確的切削。</p><p>　　傳統(tǒng)的數(shù)字控制系統(tǒng)積累了許多的研究成果，上述計(jì)劃繼承了一些傳統(tǒng)的數(shù)字控制系統(tǒng)的結(jié)構(gòu)，和一些特殊的HMTs的運(yùn)動控制裝置。所以對于HMTs 1PS+4TPS,上述CNC系統(tǒng)計(jì)劃是一個簡單的很實(shí)用的方法。</p><p><b>　　5．表面的插補(bǔ)運(yùn)算<

26、/b></p><p>　　5.1.基本的插補(bǔ)原理</p><p><b>　　表面方程定義如下</b></p><p><b>　?。?7）</b></p><p>　　這里，控制頂點(diǎn) 當(dāng)做一個 topological 矩形分配布署，</p><p>　　一個控制格

27、子，是由重力因素控制最高點(diǎn)，和，現(xiàn)在的標(biāo)準(zhǔn)齒條B由因素u和 v決定。所以有</p><p>　　如果切削方法適合表面加工，水平表面可以用來加工零件，也可以得到想要的切削路徑，曲線方程能表示成如下：</p><p><b>　?。?8）</b></p><p>　　普通表面的切削點(diǎn)能用如下方程表示</p><p><

28、b>　　（19）</b></p><p><b>　　上述方程又能寫成</b></p><p><b>　?。?0）</b></p><p>　　此外，單位內(nèi)的N數(shù)，也就是說 Ne能用下述方式表述</p><p><b>　?。?1）</b></p>

29、;<p><b>　　這里</b></p><p>　　切削的軸線要和被加工零件表面保持一致，如FIG5所示</p><p>　　圖4 切削的數(shù)學(xué)模型</p><p>　　根據(jù)幾何關(guān)系我們可以得到如下關(guān)系</p><p><b>　?。?2）</b></p><p&

30、gt;　　這里矢量是點(diǎn)P，是補(bǔ)償余量，是切削半徑，r是切削余量值。</p><p>　　5.2切削速度的控制</p><p>　　進(jìn)給速度v隨曲線方向能被定義為如下關(guān)系：</p><p>　?。?3） （24）</p><p><b>　　這里</b>

31、</p><p>　　所以 （25）</p><p>　　選取時(shí)間t=KT,使用Talor系列和包括兩個主要的延伸，我們得到</p><p><b>　?。?6）</b></p><p>　　上述方程對于因素u是不對稱的，曲線的進(jìn)給速度能通過機(jī)器控制給予一合適的增

32、量u。使進(jìn)給速度能在彎曲方向上持續(xù)運(yùn)行。所以光滑的切割就能完成。</p><p>　　5.3正確的插補(bǔ)運(yùn)算法則</p><p>　　PMAC運(yùn)動控制卡的PVT正確插補(bǔ)方法也同樣需要位置，速度，時(shí)間運(yùn)動方式。在這種PVT方式下，插補(bǔ)運(yùn)算是持續(xù)不斷進(jìn)行的，加速度與時(shí)間是呈線性關(guān)系的，前提是基于位置的約束和開始和結(jié)束點(diǎn)的速度。彎曲曲線能用插補(bǔ)進(jìn)行運(yùn)算，所以加速度.</p><

33、p><b>　?。?7）</b></p><p><b>　　這里的。</b></p><p>　　5.4切削路徑的間隔計(jì)算</p><p>　　圖5 切削路徑的間隔計(jì)算圖</p><p>　　FIG.6所示的情況，被加工面是一個平面，切削半徑是R，兩圓心之間的距離是L，余下的高度是h，在FI

34、G.6所示的基礎(chǔ)上，我們可以得到</p><p><b>　?。?8）</b></p><p>　　為了使高度小于被允許的最大高度，如下的關(guān)系式要滿足：</p><p><b>　　（29）</b></p><p>　　FIG.6b所示的情況，被加工的面是一個凸出的面，我們把面的曲率半徑定義為，基于

35、Fig.6所示的幾何關(guān)系，我們可以得到：</p><p><b>　?。?0）</b></p><p>　　通過上述的方程關(guān)系，我們可以把方程簡單的表示為：</p><p><b>　?。?1）</b></p><p>　　為了使高度小于被允許的最大高度，以下方程必須滿足：</p>&

36、lt;p><b>　?。?2）</b></p><p>　　FIG.6c所示的情況，被加工面是一個凹面，基于圖-6c所示的幾何關(guān)系，我們可以得到：</p><p><b>　?。?3）</b></p><p>　　通過以上兩個方程，我們可以用一個簡單的方程表示：</p><p><b&g

37、t;　?。?4）</b></p><p>　　為了使高度小于被允許的最大高度，必須滿足以下方程：</p><p><b>　?。?5）</b></p><p>　　6.錯誤分析和模擬計(jì)算</p><p>　　基于上述插補(bǔ)運(yùn)算的起源，我們可以看到插補(bǔ)點(diǎn)通常被設(shè)置在加工表面的彎曲處，那里沒有累計(jì)錯誤，并持續(xù)的給予

38、經(jīng)給速度，插補(bǔ)錯誤通常來自彎曲部分的經(jīng)向錯誤。如圖Fig.7所示，定義弦長為L，曲率是，曲線頂點(diǎn)到弦的距離是，通過上述關(guān)系，我們可以得到：</p><p><b>　?。?6）</b></p><p>　　定義加工點(diǎn)的曲率半徑是50mm，HMT的進(jìn)給速度是每分鐘10米，CNC系統(tǒng)的插補(bǔ)間隔時(shí)間是2毫秒，在公式（36）的基礎(chǔ)上，能計(jì)算出插補(bǔ)錯誤是0.278毫米，所以我們

39、能夠得出的結(jié)論是，機(jī)器的運(yùn)行速度很高，上述的插補(bǔ)方法能夠把插補(bǔ)錯誤控制在1毫米以內(nèi)。</p><p>　　為了證實(shí)插補(bǔ)運(yùn)算的正確性，我們做一個運(yùn)算模擬試驗(yàn)，為了模擬機(jī)器程序，切削軌跡被顯示在電腦屏幕上，模擬程序是用Delphi6.0計(jì)算機(jī)語言編寫的，F(xiàn)ig.8顯示的是模擬路徑的結(jié)果，為了清楚的顯示模擬結(jié)果，切削路徑和切削方向隔一定的時(shí)間就會被顯示，在圖Fig.8中，切削軸和切削表面是垂直的，數(shù)據(jù)顯示結(jié)果和數(shù)據(jù)抽樣

40、分析結(jié)果顯示，插補(bǔ)運(yùn)算在這里是正確的，合適的。</p><p>　　圖6 切削加工的路徑和方向</p><p><b>　　7.結(jié)論和討論</b></p><p>　　1PS+4TPS type HMTs的閉合相反的變位分析模型和相反的運(yùn)動模式是被確定的，對于1PS+4TPS type HMTs的高度的非線性和不確定性，我們在傳統(tǒng)數(shù)控機(jī)床的基礎(chǔ)

41、上，專門為1PS+4TPS type HMTs設(shè)計(jì)了一個計(jì)劃，及時(shí)五軸插補(bǔ)，它包括插補(bǔ)路徑的計(jì)算，相反的變位分析模式，相反的運(yùn)算分析模式和PVT插補(bǔ)模式。他們都被統(tǒng)一起來，通過數(shù)據(jù)實(shí)例和及時(shí)的插補(bǔ)能夠證實(shí)路徑的間隔計(jì)算和插補(bǔ)錯誤分析都是有根據(jù)的，正確的和合適的。</p><p>　　隨著平行機(jī)床的發(fā)展，新的軸數(shù)小于6的機(jī)床將會越來越受歡迎。所以混合機(jī)床正在展現(xiàn)它的潛力。1PS+4TPS type HMTs具有平行

42、的連續(xù)結(jié)構(gòu)，較好的運(yùn)動特性、高硬度、大的工作空間等特點(diǎn)。它是數(shù)控機(jī)床一種有前景的結(jié)構(gòu)。發(fā)展和應(yīng)用HMT技術(shù)，把理論和高速、高精度和高效率的技術(shù)應(yīng)用于數(shù)控機(jī)床中很有意義和價(jià)值。</p><p><b>　　參考文獻(xiàn)（略）</b></p><p>　　附件2：外文原文（復(fù)印件）</p><p>　　Study on Interpolation Pr

43、inciple and Method for 1PS+4TPS Type </p><p>　　Hybrid Machine Tool </p><p>　　Shouwen Fan Xiaobing Wang Mingquan Shi Hongzhong Huang </p><p>　　School of Mechatronics Engineering, <

44、;/p><p>　　University of Electronic Science and Technology of China </p><p>　　Chengdu, SiChuan, 610054, People’s Republic of China</p><p><b>　　ABSTRACT </b></p><p

45、>　　This paper presents a novel hybrid machine tool (HMT) based on a 4-dof 1PS+4TPS type spatial hybrid mechanism and a x-y worktable. This type HMT enjoys some advantages relative to its conventional counterparts: lar

46、ge workspace, good dexterity, etc. Closed-form solutions for both the inverse displacement model and inverse kinematic model are derived. A computerized numerical control (CNC) system scheme for motion control of HMTs is

47、 proposed focusing on motion control characteristics of HMTs and b</p><p>　　Keywords: Hybrid machine tool; Computerized Numerical Control; Interpolation; Error analysis; Cutter path interval </p><

48、p>　　1. INTRODUCTION </p><p>　　Parallel Machine Tool (PMT) is a creative application of parallel mechanism, NC technology and computer control technology in the area of machine tool [1-6]. As a new-style m

49、achine tool, PMT has advantages of simple structure, low cost, low moving inertia, high velocity, agile mobility, high techniques, etc. PMT complements the traditional NC machine tool perfectly and especially it is suita

50、ble for machining parts with complicated surfaces such as vane, impeller and propeller, etc[2]. </p><p>　　However, as the existing PMT which only adopts parallel architecture is restrained by hinge and inter

51、fered by chain, particularly is affected by some factors such as coupling of position and orientation, the mobile platform has a limited ability to realize orientation. Therefore, it is very difficult to meet the needs o

52、f multi-coordinate NC machining with large working space and complex surface. In order to solve this problem, researchers have made efforts on exploring new architectures. Many re</p><p>　　1PS+4TPS mechanism

53、 is a novel 4 DOFs hybrid mechanism[8], among the abbreviations ‘1PS+4TPS’, P represents prismical joint, S represents spherical joint, T represents hooke joint, it can implement one translatory movement and three rotary

54、 movements. The core architecture of novel HMT is a serial and parallel compound architecture which is composed of above 4 DOFs hybrid mechanism and a x-y worktable, shown as Fig.1. Mechanism design and kinematic analysi

55、s for this novel hybrid machine tool are d</p><p>　　2. DESCRIPTION OF NOVEL HMT’s ARCHITECTURE</p><p>　　A 4-DOF hybrid mechanism is shown in Fig. 1. </p><p>　　A3Fig.1. Structure sch

56、eme of novel hybrid machine tool </p><p>　　hybrid mechanism consists of five kinematic subchains, including four variable length driving legs with identical topology and one passive leg, connecting the fixed

57、 base to a moving platform. In this 4-DOF hybrid mechanism, each of the four identical legs consists of a fixed Hooke joint, an driving prismatic joint, a moving link and a spherical joint attached to the moving platform

58、. The fifth chain, which connects the fixed base center to the moving platform center, is a passive leg with a diffe</p><p>　　INVERSE DISPLACEMENT ANALYSIS MODEL AND INVERSE KINEMATIC MODEL FOR HMTs </p&g

59、t;<p>　　3.1. Inverse displacement analysis model </p><p>　　A fixed reference coordinate system and a movable reference coordinate system are set up on the center of fixed platform and movable platform

60、 respectively, shown as Fig 2. Position of four hooke joints of fixed platform with respect to the fixed frame can be described by ,position of four spherical joints of movable platform with respect to the movable frame

61、can be described by ,position of four spherical joints of movable platform with respect to the fixed frame can be described by ,original po</p><p>　　The coordineate of spherical joint in movable platform wit

62、h respect to the fixed frame can be denoted by </p><p>　　Inverse displacement analysis equation can be written as </p><p>　　where is the 3x3 rotation transformation matrix of coordinate system w

63、hich can be obtained using three sustain rotation transformation by three Euler angles and as follows (shown as Fig 3.) .</p><p>　　3.2. Inverse kinematic model </p><p>　　Definitions of parameter

64、s used in the kinematic analysis are listed as follows: length of actuating legs, input velocity of actuating legs ,angle velocity of movable platform ,velocity of center point P of movable platform ,angle velocity of ac

65、tuating leg, mass center velocity of upper section of actuating legs, mass center velocity of lower section of actuating legs, distance from mass center of upper section to point ,in actuating legs, distance from mass ce

66、nter of lower section to point in ac</p><p>　　because velocity of spherical joint point of movable table is equal to that of the same point in driving leg, we have </p><p>　　Dot multipling both

67、side of Eq.(3) using , we obtain </p><p>　　Eq.(4) can be rewritten using matrix form </p><p><b>　　where </b></p><p><b>　　Then </b></p><p>　　Abov

68、e equation can be written separately as </p><p><b>　　where </b></p><p>　　Cross multipling both side of Eq.(3) using derive </p><p>　　Substituting Eq.(7) into Eq.(8), we

69、obtain </p><p><b>　　where </b></p><p><b>　　Then </b></p><p>　　Mass center velocity of upper section and lower section of actuating legs can be expressed as &

70、lt;/p><p>　　Substituting Eq.(7) and Eq.(10) into Eq.(11), we get </p><p><b>　　where </b></p><p><b>　　Because </b></p><p>　　Substituting Eq.(7) into

71、 Eq.(13), we obtain </p><p>　　When input kinematic is known, the solution for velocity and angular velocity of movable platform is defined as forward velocity solution. Combining Eq.(7) and Eq.(14), forward

72、velocity model equation can be expressed as </p><p>　　Where one order influence coefficient matrix of end manipulator’s position and orientation velocity relative to input velocity ,If matrix is nonsingular,

73、 the inverse kinematic equation can be expressed as </p><p>　　SCHEME OF CNC SYSTEM FOR HMTs </p><p>　　A CNC system scheme for 1PS+4TPS type HMTs is proposed in this paper, illustrated as Fig.4.

74、The scheme includes such design ideas as to utilize the research fruits </p><p>　　of traditional numerical control system to maxium extend, to keep good compatibility with traditional numerical control syste

75、m, to keep accordance with traditional numerical control system in such aspects as control system structure, technique criterion etc, and to adopt both open modular system structure and standard hiberarchy design idea. T

76、he scheme of CNC system for HMTs is compoesd of CAD layer, CAM layer, CNC layer and Servo layer, etc. Among them, the automatic programming function modula</p><p>　　Traditional numerical control systems have

77、 accumulated many research fruits, above scheme inherits some system structure from traditional numerical control system, and some special requirements of motion control for HMTs are also taken into account, so above CNC

78、 system scheme is a simple and practical implementation strategy for motion control of 1PS+4TPS type HMTs. </p><p>　　SURFACE INTERPOLATION ALGORITHM </p><p>　　5.1. Basic principle for interpolat

79、ion </p><p>　　Nurbs Surface equation can be defined as </p><p>　　Where:control vertex distributing as a topological rectangle array, and forming a control gridding. are weighting factors connect

80、ing with control vertex ,and are normal B spline base for parameter u and v respectively. also have </p><p>　　If row cutting method is adapted for surface machining, parallel planes can be used for incising

81、surface of machining part, desired cutting path can be obtained. Curve equation located in the kth plane can be expressed as Normal vector N of cutting point of machining part surface can be calculated using following eq

82、uation .</p><p>　　Above equation can be rewriten as </p><p>　　Furthermore, unit normal of N, namely, Ne can be obtained </p><p><b>　　Where</b></p><p>　　Supp

83、osing that the axis of cutter keeps consistent with orientation of surface normal of machining parts (Showen as Fig.5), so, according to geometry relationship, we have </p><p>　　whereis position vector of cu

84、tter reference point P, is compensationvector of cutting remains ,is compensation vector of cutter radius, r is cutter radius.</p><p>　　5.2 control of cutting velocity</p><p>　　Feeding velocity

85、V(u) along curve direction can be defined as </p><p><b>　　Where </b></p><p><b>　　So </b></p><p>　　In sampling time t=kT, using Talor series and processing t

86、wo order expandedness, we obtain </p><p>　　Above equation is asymmetry iterative equation for parameter u. Feeding velocity along curve direction during machining process can be controlled by adjusting incre

87、ment of parameter u, and feeding velocity along curve direction can be made to keep constant. So, smooth cutting characteristic can be achieved. </p><p>　　5.3. Fine interpolation algorithm</p><p&g

88、t;　　PVT fine interpolation mode of pmac motion card is also called position, velocity, time motion mode. Under such PVT mode, interpolation period is set to be a constant, and acceleration is a linear function of time. B

89、ased on constrain condition of position and velocity of start point and end point, a smooth continuous spline curve can be obtained using Hermite interposition. So, acceleration velocity position of joint space under ata

90、in time can be expressed as</p><p><b>　　Where .</b></p><p>　　5.4 cutter path interval calculation</p><p>　　fig .6a shows the situation, in which machined surface is a pl

91、ane. Suppose radius of cutter is R, cutter path interval is L, remains height is h, based on geometry relationship in Fig.6a, we have </p><p>　　In order to make the remains height less than the allowed heigh

92、t H0, following condition must be met </p><p>　　Fig 6b shows the situation ,in which machined surface is a protruding surface . Suppose curvature radius of surface is ρ, based on geometry relationship in Fig

93、.6b, we have </p><p>　　Expand above equation using taylor series,the simplified equation can be expressed as </p><p>　　In order to make the remains height less than the allowed height H0, follow

94、ing condition must be met </p><p>　　Fig 6c shows the situation which machined surface is a concave surface. Based on geometry relationship in Fig.6c, we have </p><p>　　Expand above equation usin

95、g taylor series ,the simplified equation can be expressed as </p><p>　　In order to make the remains height less than the allowed height H0, following condition must be met </p><p>　　6 ERROR ANA

96、LYSIS AND SIMULATION CALCULATION</p><p>　　Based on derivation of above interpolation algorithm ,it ca be seen that interpolation point always located on section curve of machining surface, there is not di

97、rection keeps constant. Interpolation error mainly comes forth from radial error of chord and curve, shown as Fig. 7. Suppose length of chord is L, curvature radius is ρ, error is δ, based on error relationship between c

98、hord and arc, we have </p><p>　　feed speed of HMT is 10m/min, interpolation period of CNC system is 2ms, based on Eq.(36), it can be calculated that the interpolation error is 0.278μm. So, it can be conclude

99、d that even the machining speed is very high, above interpolation algorithm can also implement high precise machining with machining error less than 1μm.Interpolation algorithm, we proceeded a calculation</p><

100、p>　　simulation. In order to simulate machining process, cutter motion is displayed dynamicly on computer screen, simulation program is designed using Delphi 6.0 computer language. Fig. 8 shows simulation results of cu

101、tter motion path and cutter motion orientation (represented using cutter axis line), in order to display simulation results clearly, cutter motion path and cutter motion orientation are displayed after an interval of row

102、, in Fig. 8, cutter axis line keeps perpendicular to maching plane.</p><p>　　CONCLUSIONS AND DISCUSSION </p><p>　　Closed from inverse displacement analysis model and inverse kinematic model for

103、main feed mechanism of 1PS+4TPS type HMTs are established. Focusing on characteristics of 1PS+4TPS type HMTs such as highly nonlinear, tightly coupled and uncertain, we designed a CNC system scheme for 1PS+4TPS type HMTs

104、 based on research fruits of traditional numerical control machine tool. Real-time five-axis interpolator, which is composed of cutter path calculation, inverse displacement analysis model, inverse ki</p><p>

105、;　　chnology, new configurations for parallel machine tool with less than 6 axis (degree of freedom) would be more appropriate, so hybrid machine tool has shown its technical potential, 1PS+4TPS type HMTs, which combines

106、advantages of parallel structure with that of serial structure, possesses good kinematic characteristic, high stiffness, large workspace, is a promising structure type for numerical control machine tool. Development and