搖臂鉆床自動送料裝置設(shè)計【半自動鉆床】,半自動鉆床,搖臂鉆床自動送料裝置設(shè)計【半自動鉆床】,搖臂,鉆床,自動,裝置,設(shè)計,半自動 任務(wù)書 題目 搖臂鉆床的自動送料機構(gòu)設(shè)計 （任務(wù)起止日期2010年 月 日～2011年 月 日） 專業(yè) 班 學生姓名 學 號 指導教師 系主任 院 長 課題內(nèi)容： 1、分析搖臂鉆床的工作原理和操作流程，論證進行自動送料的意義；提出一種合適的自動送料方案。 2、進行自動送料機構(gòu)的設(shè)計。 課題任務(wù)要求： 1、針對課題內(nèi)容撰寫一篇文獻綜述； 2、完成一篇與設(shè)計相關(guān)的英文文獻翻譯； 3、自動送料機構(gòu)設(shè)計：送料機構(gòu)工作原理圖、控制電路圖、裝配圖及零件圖。 4、在完成上述工作基礎(chǔ)上，撰寫設(shè)計說明書； 5、畢業(yè)答辯準備。 主要參考文獻（由指導教師選定）： 1. 數(shù)控技術(shù) 2. [維普]中文科技期刊全文數(shù)據(jù)庫（參考關(guān)鍵詞：搖臂鉆床） 3. [cnki]中文學術(shù)期刊全文數(shù)據(jù)庫 同組設(shè)計者 注：1、此任務(wù)書應由指導教師填寫。 2、此任務(wù)書最遲必須在畢業(yè)設(shè)計開始前一周下達給學生。 工作進度計劃表 序 號 畢業(yè)設(shè)計（論文）工作任務(wù) 工作進度日程安排 周 次 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 資料收集，完成開題報告等 2 正式設(shè)計 3 撰寫畢業(yè)論文和準備答辯 4 畢業(yè)答辯 5 6 7 8 9 注：1、此表由指導教師填寫； 2、此表每個學生一份，作為畢業(yè)設(shè)計（論文）檢查工作進度之依據(jù)； 3、進度安排請用“—”在相應位置畫出。 工作情況檢查表 時間 第一階段（1～3周） 第二階段（4～14周） 第三階段（15～17周） 內(nèi)容 組織紀律 完成任務(wù)情況 組織紀律 完成任務(wù)情況 組織紀律 完成任務(wù)情況 檢 查 情 況 教師簽字 簽字 日期 簽字 日期 簽字 日期 注：1、此表應由教師認真填寫； 2、“組織”紀律一欄根據(jù)學生具體執(zhí)行情況如實填寫； 3、“完成任務(wù)情況”一欄按學生是否按進度保質(zhì)保量完成任務(wù)的情況填寫； 4、對違紀和不能按時完成任務(wù)者，指導教師可根據(jù)情節(jié)輕重對該生提出警告或不能參加答辯的建議。 半自動鉆床 2.1設(shè)計題目 設(shè)計加工圖1所示工件ф12mm孔的半自動鉆床。進刀機構(gòu)負責動力頭的升降，送料機構(gòu)將被加工工件推入加工位置，并由定位機構(gòu)使被加工工件可靠固定。 圖1 加工工件 半自動鉆床設(shè)計數(shù)據(jù)參看表3。 表3 半自動鉆床凸輪設(shè)計數(shù)據(jù) 方案號 進料機構(gòu) 工作行程 mm 定位機構(gòu) 工作行程 mm 動力頭 工作行程 mm 電動機轉(zhuǎn)速 r/mm 工作節(jié)拍（生產(chǎn)率） 件/min A 40 30 15 1450 1 B 35 25 20 1400 2 C 30 20 10 960 1 2.2設(shè)計任務(wù) 1.半自動鉆床至少包括凸輪機構(gòu)、齒輪機構(gòu)在內(nèi)的三種機構(gòu)。 2.設(shè)計傳動系統(tǒng)并確定其傳動比分配。 3. 圖紙上畫出半自動鉆床的機構(gòu)運動方案簡圖和運動循環(huán)圖。 4.凸輪機構(gòu)的設(shè)計計算。按各凸輪機構(gòu)的工作要求，自選從動件的運動規(guī)律，確定基圓半徑，校核最大壓力角與最小曲率半徑。對盤狀凸輪要用電算法計算出理論廓線、實際廓線值。畫出從動件運動規(guī)律線圖及凸輪廓線圖。 5.設(shè)計計算其他機構(gòu)。 6.編寫設(shè)計計算說明書。 7.學生可進一步完成：凸輪的數(shù)控加工，半自動鉆床的計算機演示驗證等。 2.3設(shè)計提示 1.鉆頭由動力頭驅(qū)動，設(shè)計者只需考慮動力頭的進刀（升降）運動。 2. 除動力頭升降機構(gòu)外，還需設(shè)計送料機構(gòu)、定位機構(gòu)。各機構(gòu)運動循環(huán)要求見表4。 3. 可采用凸輪軸的方法分配協(xié)調(diào)各機構(gòu)運動。 表4 機構(gòu)運動循環(huán)要求 凸輪軸 轉(zhuǎn)角 10o 20o 30o 45o 60o 75o 90o 105o～270o 300o 360o 送料 快進 休止 快退 休止 定位 休止 快進 休止 快退 休止 進刀 休止 快進 快進 快退 休止 三．運動方案的選擇與比較 方案的分析與比較： (1) 減速機構(gòu)： 由于電動機的轉(zhuǎn)速是1450r/min，而設(shè)計要求的主軸轉(zhuǎn)速為2r/min，利用行星輪進行大比例的降速，然后用圓錐齒輪實現(xiàn)方向的轉(zhuǎn)換。 圖4-1 （1） 對比機構(gòu)： 對比機構(gòu)：定軸輪系傳動；傳動比 =n輸入/n輸出 =700 傳動比很大，要用多級傳動。如圖4-2. 圖4-2 (3) 進刀機構(gòu) 采用一個擺動滾子從動件盤行凸輪機構(gòu)來傳遞齒輪齒條機構(gòu).因為我們用一個擺動滾子從動件盤行凸輪機構(gòu)來傳遞齒輪機構(gòu)，當進刀的時候，凸輪在推程階段運行，很容易通過機構(gòu)傳遞帶動齒輪齒條嚙合.帶動動刀頭來完成鉆孔，擺桿轉(zhuǎn)動的幅度也是等于齒廓轉(zhuǎn)動的幅度，兩個齒輪來傳動也具有穩(wěn)性。 圖4-3 （4） 對比機構(gòu)： 在擺桿上加一個平行四邊行四桿機構(gòu)，這樣也可以來實現(xiàn)傳動，但是當加了四桿機構(gòu)以后并沒有達到改善傳動的效果，只是多增加了四桿機構(gòu)，為了使機構(gòu)結(jié)構(gòu)緊湊，又能完成需要的傳動，所以選擇了一個擺動滾子從動件盤行凸輪機構(gòu)。 § 方案一： § D1為了達到輸出間歇運動同時能夠做到循環(huán)往復運動，采用凸輪機構(gòu)和扇形齒與齒條配合，中間采用連桿帶動。先把回轉(zhuǎn)運動動力轉(zhuǎn)化為扇形齒的往復擺動，在通過齒輪傳遞給齒條，增加一個齒輪的目的是為了使傳動更加的平穩(wěn)可靠。 圖4-4 （5） 送料系統(tǒng)： 采用一個六桿機構(gòu)來代替曲柄滑塊機構(gòu)，由于設(shè)計的鉆床在空間上傳動軸之間的距離有點大，故一般四桿機構(gòu)很難實現(xiàn)這種遠距離的運動。再加上用四桿機構(gòu)在本設(shè)計中在尺寸上很小。所以考慮到所設(shè)計的機構(gòu)能否穩(wěn)定的運行因此優(yōu)先選用了如下圖的六桿機構(gòu)來實現(xiàn)。由于本設(shè)計送料時不要求在傳動過程中有間歇，所以不需要使用凸輪機構(gòu)。如圖4-5。 圖4-5 （6）對比機構(gòu)： 所選用的對比四桿機構(gòu)如下圖(圖4-6)，由于在空間上軸與軸之間的距離較大，但選用下來此四桿的尺寸太小。故優(yōu)先選用六桿機構(gòu)。 § 方案二： § B2采用凸輪與四桿機構(gòu)的組合結(jié)構(gòu)實現(xiàn)既有快慢變化的運動又有休止的間歇運動。 圖4-6 （7）定位系統(tǒng)： 定位系統(tǒng)采用的是一個偏置直動滾子從動件盤型凸輪，因為定位系統(tǒng)要 有間歇，所以就要使用凸輪機構(gòu)，但如果是平底推桿從動件，則凸輪就會失真，若增加凸輪的基圓半徑，那么凸輪機構(gòu)的結(jié)構(gòu)就會很大，也不求實際，所以就采用一個偏置直動滾子從動件盤型凸輪，它就可以滿足我們的實際要求了。 圖4-7 （8）對比機構(gòu)： 采用彈力急回間歇機構(gòu)來代替偏置直動滾子從動件盤型凸輪，它是將旋轉(zhuǎn)運動轉(zhuǎn)換成單側(cè)停歇的往復運動。這樣也可以完成實際要求，但是為了使設(shè)計的機構(gòu)結(jié)構(gòu)緊湊，又能節(jié)省材料，所以還是選偏置直動滾子從動件盤型凸輪來完成定位。 圖4-8 § 方案一： § C1利用四桿機構(gòu)中死點的積極作用，選取凸輪結(jié)合夾緊機構(gòu)共同作用達到定位機構(gòu)和間歇定位的要求。 四.機構(gòu)運動總體方案圖（機構(gòu)運動簡圖） 根據(jù)前面表3-3中實線連接的方案的運動簡圖確定本設(shè)計中半自動鉆床的總體方案圖如圖5-1 圖5-1 五．工作循環(huán)圖 圖5-1所示的機械系統(tǒng)方案的執(zhí)行件需要進行運動協(xié)調(diào)設(shè)計 其運動循環(huán)如圖6-1 凸輪軸轉(zhuǎn)角 00～1000 1000～1500 1500～2700 2700～3000 3000～3600 送料 快進 快退 定位 休止 快進 休止 快退 進刀 休止 快進 慢進 休止 快退 圖6-1 六．執(zhí)行機構(gòu)設(shè)計過程及尺寸計算 1．送料機構(gòu)機構(gòu)采用如下分析 送料連桿機構(gòu)：采用如下機構(gòu)來送料，根據(jù)要求，進料機構(gòu)工作行程為40mm，可取ABCD4桿機構(gòu)的極位夾角為12度，則由 得K=1.14，急回特性不是很明顯，但對送料機構(gòu)來說并無影響。 各桿尺寸：（如圖6-1） AB=8.53 BC=84.42 CD=60 DA=60 CE=40 EF=8 該尺寸可以滿足設(shè)計要求，即滑塊的左右運動為40，ABCD的極位夾角為12度。 圖6-1 2.凸輪擺桿機構(gòu)的設(shè)計： (1).由進刀規(guī)律，我們設(shè)計了凸輪擺桿機構(gòu)，又以齒輪齒條的嚙合來實現(xiàn)刀頭的上下運動； (2).用凸輪擺桿機構(gòu)和圓弧形齒條所構(gòu)成的同一構(gòu)件，凸輪擺桿從動件的擺動就可以實現(xiàn)弧形齒條的來回擺動，從而實現(xiàn)要求；采用滾子盤行凸輪，且為力封閉凸輪機構(gòu)，利用彈簧力來使?jié)L子與凸輪保持接觸.刀具的運動規(guī)律就與凸輪擺桿的運動規(guī)律一致； (3).弧形齒條所轉(zhuǎn)過的弧長即為刀頭所運動的的距離。具體設(shè)計步驟如下： 1.根據(jù)進刀機構(gòu)的工作循環(huán)規(guī)律,設(shè)計凸輪基圓半徑r0=40mm，中心距A=80mm，擺桿長度d=65mm，最大擺角β為18°, 凸輪轉(zhuǎn)角λ=0-60°,β=0°; 凸輪轉(zhuǎn)角λ=60°-270°，刀具快進，β=5°， 凸輪轉(zhuǎn)角λ=270°-300°； 凸輪轉(zhuǎn)角λ=300°-360°，β=0° 2.設(shè)計圓形齒條,根據(jù)刀頭的行程和凸輪的擺角,設(shè)計出圓形齒輪的半徑r=l/β,由β=18°, l=10mm， 3.得到r=63.69mm，如圖7-2 圖7-2 3.凸輪推桿機構(gòu)的設(shè)計： 凸輪機構(gòu)采用直動滾子盤行凸輪，且為力封閉凸輪機構(gòu)，利用彈簧力來使?jié)L子與凸輪保持接觸，實現(xiàn)定位功能。只要適當?shù)卦O(shè)計出凸輪的輪廓曲線，就可以使推桿得我們所需要的運動規(guī)律，滿足加工要求，而且響應快速，機構(gòu)簡單緊湊。具體設(shè)計如下: 設(shè)計基圓半徑r0=40mm,偏心距e=25 凸輪轉(zhuǎn)角λ=0°-100°,定位機構(gòu)休止,推桿行程h=0mm; 凸輪轉(zhuǎn)角λ=100°-285°,定位機構(gòu)快進,推桿行程h=20mm; 凸輪轉(zhuǎn)角λ=285°-300°,定位機構(gòu)休止,推桿行程h=0mm; 凸輪轉(zhuǎn)角λ=300°-360°,定位機構(gòu)快退,推桿行程h=-20mm; 設(shè)計偏心距e=20的原因是因為此凸輪執(zhí)行的是定位，其定位桿的行程為20故如此設(shè)計。 4．行星輪系的計算: （1）用定軸輪系傳動 傳動比 =n輸入/n輸出 =700 傳動比很大，要用多級傳動。 （2）用行星輪系傳動 Z1=35 Z2=20 Z2’=20 Z3=35 傳動比iH3=700 根據(jù)行星輪傳動公式：i（H3）=1-i(31)H=1-Z2’Z1/Z3Z2 由i(1H)=1-Z2'Z1/Z3Z2，考慮到齒輪大小與傳動的合理性，經(jīng)過比較設(shè)計皮帶傳動機構(gòu)與齒輪系傳動機構(gòu)的相應參數(shù)如下表： 皮帶輪參數(shù) 名稱 皮帶輪1 皮帶輪2 半徑（mm） 100 100 齒輪參數(shù) 模數(shù)（mm） 壓力角（°） 齒數(shù)（個） 直徑（mm） 齒輪1 2. 20 35 70 齒輪2 2 20 20 40 齒輪2’ 2 20 20 40 齒輪3 2 20 35 70 七. 凸輪設(shè)計分段圖輪廓圖和設(shè)計結(jié)果 一.定位凸輪 圖8-1為定位凸輪分段圖和設(shè)計結(jié)果圖 圖8-1 圖8-2和8-3為定位凸輪的輪廓圖（8-2內(nèi)包絡(luò)線圖，8-3外包絡(luò)線圖） 圖8-2 圖8-3 二.進刀凸輪 進刀凸輪類型設(shè)計結(jié)果如圖8-4，凸輪運動分段如圖8-5. 圖8-4， 圖8-5 進刀凸輪的輪廓線設(shè)計如圖8-6（內(nèi)包絡(luò)線）和圖8-7（外包絡(luò)線） 圖8-6 圖8-7 I 變速機構(gòu) § 方案一： § A1由于電動機的轉(zhuǎn)速是1450r/min，而選用設(shè)計要求的主軸轉(zhuǎn)速為1r/min。可以考慮利用行星輪進行大比例的降速，然后采用蝸輪變向。 機構(gòu)簡圖 Ⅱ送料機構(gòu)的選型： § 方案一： § B1直接采用凸輪滑塊機構(gòu)，并且在輪同軸的齒輪組合中加入不完全齒輪以滿足間歇休止運動要求。 § 方案二： § B2采用凸輪與四桿機構(gòu)的組合結(jié)構(gòu)實現(xiàn)既有快慢變化的運動又有休止的間歇運動。 § 方案三： § B3采用一個六桿機構(gòu)來代替曲柄滑塊機構(gòu)，由于設(shè)計的鉆床在空間上傳動軸之間的距離有點大，故一般四桿機構(gòu)很難實現(xiàn)這種遠距離的運動。再加上用四桿機構(gòu)在本設(shè)計中在尺寸上很小。所以考慮到所設(shè)計的機構(gòu)能否穩(wěn)定的運行因此優(yōu)先選用了如下圖的六桿機構(gòu)來實現(xiàn) 。 § Ⅲ 定位機構(gòu)選型 § 方案一： § C1利用四桿機構(gòu)中死點的積極作用，選取凸輪結(jié)合夾緊機構(gòu)共同作用達到定位機構(gòu)和間歇定位的要求。 § 方案二： § C2定位系統(tǒng)采用的是一個偏置直動滾子從動件盤型凸輪，因為定位系統(tǒng)要 有間歇，所以就要使用凸輪機構(gòu)，但如果是平底推桿從動件，則凸輪就會失真，若增加凸輪的基圓半徑，那么凸輪機構(gòu)的結(jié)構(gòu)就會很大，也不求實際，所以就采用一個偏置直動滾子從動件盤型凸輪，它就可以滿足實際要求了。 Ⅳ 進刀機構(gòu) § 方案一： § D1為了達到輸出間歇運動同時能夠做到循環(huán)往復運動，采用凸輪機構(gòu)和扇形齒與齒條配合，中間采用連桿帶動。先把回轉(zhuǎn)運動動力轉(zhuǎn)化為扇形齒的往復擺動，在通過齒輪傳遞給齒條，增加一個齒輪的目的是為了使傳動更加的平穩(wěn)可靠。 § 方案二 § D2采用一個擺動滾子從動件盤行凸輪機構(gòu)來傳遞齒輪齒條機構(gòu).因為我們用一個擺動滾子從動件盤行凸輪機構(gòu)來傳遞齒輪機構(gòu)，當進刀的時候，凸輪在推程階段運行，很容易通過機構(gòu)傳遞帶動齒輪齒條嚙合.帶動動刀頭來完成鉆孔，擺桿轉(zhuǎn)動的幅度也是等于齒廓轉(zhuǎn)動的幅度，兩個齒輪來傳動也具有穩(wěn)性。 PDF created with pdfFactory trial version ? 產(chǎn)品名稱： 二相步進電機2HB110系列 規(guī)格型號： 2HB110系列 產(chǎn)品簡介： 2HB110系列步進電機為二相四出線電機，輸出力矩10N.M-27N.M,并廣泛應用于數(shù)控機床、激光雕刻、電腦繡花、紡織、印刷、包裝機械、標記機、雕刻機、繞線機械、坐標測量儀器、三維工作臺、機器人、醫(yī)療設(shè)備、陶瓷機械等行業(yè)中。 ? ? ? ? 詳細資料： ? 通用規(guī)格 (General specifications) 步距精度　　　　5% 溫??? 升　　　　80℃ Max 環(huán)境溫度　　　　-20℃~+50℃ 絕緣電阻　　　　100M Ω Min 500VDC 耐??? 壓　　　　500V AC 1minute 徑向跳動　　　　最大0.06mm（450g負載） 軸向跳動　　　　最大0.08mm（450g負載） 技術(shù)數(shù)據(jù)(Specifications) ? ?※? 以上僅為代表性產(chǎn)品，可按要求另行制作。 ?外形尺寸(Dimension) ※? 110系列四款電機軸徑均為16mm，軸鍵為平鍵6×25mm。 矩頻特性曲線圖(Frequency-torque characteristics) 接線圖(Connections) 注意事項： 1.電機特性數(shù)據(jù)和技術(shù)數(shù)據(jù)都是在YKA2811MA驅(qū)動器驅(qū)動的情況下測得，測試電壓為110ADC。 2.電機安裝時務(wù)必用電機前端蓋安裝止口定位，并注意公差配合，嚴格保證電機軸與負載軸的同心度。 3.對于電機引線方式，如果客戶有特殊需求，請在訂貨前事先聲明，由廠家接好線，用戶不必自己改動。 4.電機與驅(qū)動器連接時，請勿接錯相。 ? PDF created with pdfFactory trial version 任務(wù)書任務(wù)書搖臂鉆床的自動卸料機構(gòu)搖臂鉆床的自動卸料機構(gòu)搖臂鉆床的自動卸料機構(gòu)搖臂鉆床的自動卸料機構(gòu)設(shè)計設(shè)計設(shè)計設(shè)計說明書說明書說明書說明書2011年3月20日自動卸料機構(gòu)總體結(jié)構(gòu)設(shè)計工作臺數(shù)控升降控制系統(tǒng)基座自動卸料機：1 基座；2 數(shù)控升降控制系統(tǒng)；3 工作臺數(shù)控升降控制系統(tǒng)工作原理步進電機固緊螺釘固緊螺釘液壓機固緊螺釘數(shù)控升降控制系統(tǒng)由步進電機與液壓機構(gòu)成；步進電機由兩顆螺釘固定與基座；液壓機由四顆螺釘固定與基座。工作臺工作原理步進電機卸料盤齒輪-皮帶傳動機構(gòu)工作臺由1 步進電機；2 卸料盤；3 齒輪-皮帶傳動機構(gòu)；4 工作臺面構(gòu)成。步進電機驅(qū)動齒輪-皮帶傳動機構(gòu)對卸料盤進行旋轉(zhuǎn)控制。卸料盤對加工料進行預緊，定位及卸料。工作臺臺面的幾何中心設(shè)置有過孔，可通過螺釘固緊與液壓機進行裝配臺面卸料盤工作原理電磁-彈簧執(zhí)行器電磁-彈簧預緊裝置臺面臺面過孔卸料盤十字對稱4個卸料孔1：卸料盤由4個十字對稱的卸料孔及16個電磁-彈簧執(zhí)行器構(gòu)成。2：在工作臺的臺面縱向位置有一過孔，用于加工完畢工件的卸料。3：送料裝置將待加工工件送與卸料孔，4個對稱的電磁-彈簧預緊裝置；由于所有電磁-彈簧執(zhí)行器采用相同彈性模量的彈簧構(gòu)成，以及工作臺面的具有一定的平滑度（摩擦力?。?，將保證待加工工件的幾何中心高度配合與卸料孔的幾何中心。工作前，通過搖臂鉆床的定位機構(gòu)對卸料孔的1個幾何中心進行定位即可完成對待加工工件的精密定位。4：在電磁-彈簧執(zhí)行器通電時，彈簧處于縮緊狀態(tài)，此時進行送料，送料完畢，斷電，彈簧膨脹，壓緊及定位工件。步進電機控制驅(qū)動卸料盤旋轉(zhuǎn)90度，給處于臺面孔過上方的電磁-彈簧執(zhí)行器進行通電，彈簧縮緊，完成卸料。 A 1 D e 5 A i B a A 1 e A e Z T V s v , A 7 1 e a A 1 e # A e b ? 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Q , Q | 1 _ b . : k T c ! . | H , m/ L L U 0 T 6 b | B | h , 5 L : k b T | Q _ , 5 0 T / b B ) H V b A 1 e Y e | 3 L l v i ? Z b = , e 1 B t , y 3 L = 1 p , H 1 , Y e c4 1 pb = 0 f = B = V B m/ A | A z d A V , f # A B 1 Y y , 1 p f - f f % B A Q 7 S M b B A f | L C b , 1 p | | B A % , ie | f v 8 B M S = b - f | , v s A | ? 1 p, h , P 3 T s B K b B ! ! ! . , M l 3 Z T 3 , 5 T , | B # x A f | , . 1 D e r Z T b H A ! M | B S - f | , B T f 7 % b V I A , V E b A z d # e d , V | A z , f 1 p, i? v 1 v f S b B 6 V | z Z T b B a d # e Z T 4 V | 1 pV , q Q 1 M , f f / , z 9 v 7 1 9 F b c , | _ 1 / b B e _B m_ BB _B BB B F S , K v H % 英文原文 Kinematic and dynamic synthesis of a parallel kinematic high speed drilling machine Abstract Typically, the term‘‘high speed drilling’’ is related to spindle capability of high cutting speeds. The suggested high speed drilling machine (HSDM) extends this term to include very fast and accurate point-to-point motions. The new HSDM is composed of a planar parallel mechanism with two linear motors as the inputs. The paper is focused on the kinematic and dynamic synthesis of this parallel kinematic machine (PKM). The kinematic synthesis introduces a new methodology of input motion planning for ideal drilling operation and accurate point-to-point positioning. The dynamic synthesis aims at reducing the input power of the PKM using a spring element. Keywords: Parallel kinematic machine; High speed drilling; Kinematic and dynamic synthesis 1. Introduction During the recent years, a large variety of PKMs were introduced by research institutes and by industries. Most, but not all, of these machines were based on the well-known Stewart platform [1] configuration. The advantages of these parallel structures are high nominal load to weight ratio, good positional accuracy and a rigid structure [2]. The main disadvantages of Stewart type PKMs are the small workspace relative to the overall size of the machine and relatively slow operation speed [3,4]. Workspace of a machine tool is defined as the volume where the tip of the tool can move and cut material. The design of a planar Stewart platform was mentioned in [5] as an affordable way of retrofitting non-CNC machines required for plastic moulds machining. The design of the PKM [5] allowed adjustable geometry that could have been optimally reconfigured for any prescribed path. Typically, changing the length of one or more links in a controlled sequence does the adjustment of PKM geometry. The application of the PKMs with ‘‘constant-length links’’ for the design of machine tools is less common than the type with ‘‘varying-length links’’. An excellent example of a ‘‘constant-length links’’ type of machine is shown in [6]. Renault-Automation Comau has built the machine named ‘‘Urane SX’’. The HSDM described herein utilizes a parallel mechanism with constant-length links. Drilling operations are well introduced in the literature [7]. An extensive experimental study of highspeed drilling operations for the automotive industry is reported in [8]. Data was collected fromhundreds controlled drilling experiments in order to specify the parameters required for quality drilling. Ideal drilling motions and guidelines for performing high quality drilling were presented in [9] through theoretical and experimental studies. In the synthesis of the suggested PKM, we follow the suggestions in [9]. The detailed mechanical structures of the proposed new PKM were introduced in [10,11]. One possible configuration of the machine is shown in Fig. 1; it has large workspace, highspeed point-to-point motion and very high drilling speed. The parallel mechanism provides Y, and Z axes motions. The X axis motion is provided by the table. For achieving highspeed performance, two linear motors are used for driving the mechanism and a highspeed spindle is used for drilling. The purpose of this paper is to describe new kinematic and dynamic synthesis methods that are developed for improving the performance of the machine. Through input motion planning for drilling and point-to-point positioning, the machining error will be reduced and the quality of the finished holes can be greatly improved. By adding a well-tuned spring element to the PKM, the input power can be minimized so that the size the machine and the energy consumption can be reduced. Numerical simulations verify the correctness and effectiveness of the methods presented in this paper. 2. Kinematic and dynamic equations of motion of the PKM module The schematic diagram of the PKM module is shown in Fig. 2. In consistent with the machine tool conventions, the z-axis is along the direction of tool movement. The PKM module has two inputs (two linear motors) indicated as part 1 and part 6, and one output motion of the tool. The positioning and drilling motion of the PKM module in this application is characterized by (y axis motion for point-to-point positioning) and (z axis motion for drilling). Motion equations for both rigid body and elastic body PKM module are developed. The rigid body equations are used for the synthesis of input motion planning of drilling and input power reduction. The elastic body equations are used for residual vibration control after point-to-point positioning of the tool. 2.1. Equations of motion of the PKM module with rigid links Using complex-number representation of mechanisms [12], the kinematic equations of the tool unit (indicated as part 3 which includes the platform, the spindle and the tool) are developed as follows. The displacement of the tool is and where b is the distance between point B and point C, r is the length of link AB (the lengths of link AB, CD and CE are equal). The velocity of the tool is where The acceleration of the tool is where The dynamic equations of the PKM module are developed using Lagrange’s equation of the second kind [13] as shown in Eq. (7). ·echanism can be derived using the finite element method and take the form of where [M], [C] and [K] are system mass, damping and stiffness matrix, respectively; {D} is the set of generalized coordinates representing the translation and rotation deformations at each element node in global coordinate system; {R} is the set of generalized external forces corresponding to {D}; n is the number of the generalized coordinates (elastic degrees of freedom of the mechanism). In our FEA model, we use frame element shown in Fig. 3 in which EIe is the bending stiffness (E is the modulus of elasticity of the material, Ie is the moment of inertia), q is the material density, le is the original length of the element. are nodal displacements expressed in local coordinate system(x, y). The mass matrix and stiffness matrix for the frame element will be 66 symmetric matrices which can be derived fromthe kinetic energy and strain energy expressions as Eqs. (12) and (13) where T is the kinetic energy and U is the strain energy of the element; are the linear 1 2 3 4 5 6 and angular deformations of the node at the element local coordinate system. Detailed derivations can be found in [14]. Typically, a compliant mechanism is discretized into many elements as in finite element analysis. Each element is associated with a mass and a stiffness matrix. Each element has its own local coordinate system. We combine the element mass and stiffness matrices of all elements and perform coordinate transformations necessary to transform the element local coordinate systemto global coordinate system. This gives the systemmass [M] and stiffness [K] matrices. Capturing the damping characteristics in a compliant systemis not so straightforward. Even though, in many applications, damping may be small but its effect on the systemstability and dynamic response, especially in the resonance region, can be significant. The damping matrix [C] can be written as a linear combination of the mass and stiffness matrices [15] to form the proportional damping [C] which is expressed as where a and b are two positive coefficients which are usually determined by experiment. An alternate method [16] of representing the damping matrix is expressing [C]as The element of [C’] is defined as,where signKij=(Kij/|Kij|), Kij and Mij are the elements of [K] and [M], ζis the damping ratio of the material. The generalized force in a frame element is defined as where Fj and Mj are the jth external force and moment including the inertia force and moment on the element acting at (xj ,yj), and m is the number of the externalforces acting on the element. The element generalized forces ,are then combined to formthe systemgeneralized force {R}. The second order ordinary differential equations of motion of the system, Eq. (11), can be directly integrated with a numerical method such as Runge-Kutta method. For the PKM we studied, each link was discreted as 15 frame elements. Both Matlab and ADAMS software are used for programming and solving these equations. 3. Input motion planning for drilling Suppose we know the ideal motion function of the drilling tool. How to determine the input motor motion so that the ideal tool motion can be realized is critical for high quality drillings. The created explicit input motion function also provides the necessary information for machine controls. According to the study done in [9], the drilling process can be divided into three phases: entrance phase, middle phase, and exit phase. In order to increase the productivity and quality of the drilling, many operation constraints such as minimum tool life constraint, hole location error constraint, exit burr constraint, drill torsion breakage constraint, etc. must be considered and satisfied. Under these conditions, the feed velocity of the tool should be slow at the entrance phase to reduce the hole location errors. The tool velocity should also be slow at the exit phase to reduce the exit burr. At the middle phase, the tool drilling velocity should be fast and kept constant. The retraction of the tool after finishing the drilling should be done as quickly as possible to increase the productivity. Based on these considerations, we assume that the ideal drilling and retracting velocities of the tool are given by Eq. (17). where vT1 is the maximum drilling velocity, T1, T2,and T3 are the times corresponding to the entrance phase, the middle phase and the exit phase. vT2 is the maximum retracting velocity. T4, T5, and T6 are corresponding to accelerating, constant velocity, and decelerating times for retracting operation. is the cycle time for a single drilling. As a numerical example, suppose we drill a 25.4 mm (1 in) deep hole with Tc=0.4s, 0.3s for drilling, 0.1s for retracting. Set T1=T3 0.06s, T4=T6=0.03s. Under these con-ditions, vT1=106(mm/s), vT2=-363(mm/s). The graphical expression of the ideal tool motion is shown in Fig. 4. If the link length in PKM r=500 mm, the angleβ=53° at the starting point of drilling, the corresponding input motor velocity relative to the idealtool motion is shown in Fig. 5. Generally, the curve fitting method can be used to create the input motion function. But according to the shape of the curve shown in Fig. 5, we create the linear motor velocity function manually section by section as shown in Eq. (18). where vB=143.48mm/s, vC=165.77mm/s, vE=-557.36mm/s, vF=-499.44mm/s. When plotting the velocity curve with Eq. (18), no visual difference can be found with the curve shown in Fig. 5. Eq. (18) is composed of six parts with four cycloidal functions and two linear functions. If we control the two linear motors to have the same motion as described in Eq. (18), the drilling and retracting velocity of the tool will be almost the same as shown in Fig. 4. The absolute errors between the ideal and real tool velocity are shown in Fig. 6, in which the maximum error is less than 8 mm/s, the relative error is less than 1.5%. At the start and the end positions of the drilling, the errors are zero. These small absolute and relative errors illustrate the created input motion and are quite acceptable. The derived function is simple enough to be integrated into the control algorithmof the PKM. 4. Input motion planning for point-to-point positioning In order to achieve fast and accurate positioning operation in the whole drilling process, the input motion should be appropriately planned so that the residual vibration of the tool tip can be minimized. Conventionally the constant acceleration motion function is commonly used for driving the axes motions in machine tools. Although this kind of motion function is simple to be controlled, it may excite the elastic vibration of the systemdue to the sudden changes in acceleration. Take the same PKM module used in previous for example. A FEA model is built using ADMAS with frame elements. The positioning motion is the y-axis motion, which is realized by the two linear motors moving in the same direction. Suppose the positioning distance between the two holes is 75mm, the constant acceleration is 3g(approximated as 30m/s2 here). The input motion of the linear motors with constant acceleration and deceleration is shown in Fig. 7, in which the maximum velocity is 1500 mm/s, the positioning time is 0.1 s. Assuming the material damping ratio as 0.01, the residual vibration of the tool tip is shown in Fig. 8. In order to reduce the residual vibration and make the positioning motion smoother, a six order polynomial input motion function is built as Eq. (19) where the coeffcients ci are the design variables which have to be determined by minimizing the residual vibration of the tool tip. Selecting the boundary conditions as that when t=0, sin=0, vin=0, ain=0; and when t=Tp, sin=h, vin=0, ain=0, where Tp is the point-to-point positioning time, the first six coeffcients are resulted: Logically, set the optimization objective as where c6 is the independent design variable; is the maximum fluctuation of residual vibrations of the tool tip after the point-to-point positioning. Set and start the calculation from c6=0. The optimization results in c6=-10mm/s . Consequently, c5=7.5×10mm/s , c4 =-1.425×10mm/s , c3=8.5×10mm/s , c2=c1=c0=0. It can be seen that the optimization calculation brought the design variable c6 to the boundary. If further loosing the limit for c6, the objective will continue reduce in value, but the maximum value of acceleration of the input motion will become too big. The optimal input motions after the optimization are shown in Fig. 9. The corresponding residual vibration of the tool tip is shown in Fig. 10. It is seen from comparing Fig. 8 and Fig. 10 that the amplitude and tool tip residual vibration was reduced by 30 times after optimization. Smaller residual vibration will be very useful for increasing the positioning accuracy. It should be mentioned that only link elasticity is included in above calculation. The residual vibration after optimization will still be very small if the compliance from other sources such as bearings and drive systems caused it 10 times higher than the result shown in Fig. 10. 5. Input power reduction by adding spring elements Reducing the input power is one of many considerations in machine tool design. For the PKM we studied, two linear motors are the input units which drive the PKM module to perform drilling and positioning operations. One factor to be considered in selecting a linear motor is its maximum required power. The input power of the PKM module is determined by the input forces multiplying the input velocities of the two linear motors. Omitting the friction in the joints, the input forces are determined from balancing the drilling force and inertia forces of the links and the spindle unit. Adding an energy storage element such as a spring to the PKM may be possible to reduce the input power if the stiffness and the initial (free) length of the spring are selected properly. The reduction of the maximum input power results in smaller linear motors to drive the PKM module. This will in turn reduce the energy consumption and the size of the machine structure. A linear spring can be added in the middle of the two links as shown in Fig. 11(a). Or two torsional springs can be added at points B and C as shown in Fig. 11(b). The synthesis process is the same for the linear or torsional springs. We will take the linear spring as an example to illustrate the design process. The generalized force in Eq. (10) has the form of where l0 and k are the initial length and the stiffness of the linear spring. The input power of the linear motors is determined by In order to reduce the input power, we set the optimization objective as follows: where v is a vector of design variables including the length and the stiffness of the spring, . For the PKM module we studied, the mass properties are listed in Table 1. The initial values of the design variables are set as . The domains for design variables are set as [lmin;lmax]=[400, 500 ]mm, [kmin; kmax]=[1,20 ]N/mm. The PKM module is driven by the input motion function described as Eq. (18). Through minimizing objective (24), the optimal spring parameters are obtained as and k=14.99 N/mm. The input powers of the linear motors with and without the optimized spring are shown in Fig. 12, in which the solid lines represents the input power without spring, the dotted lines represents the input power with the optimal spring. It can be seen from the result that the maximum input power of the right linear motor is reduced from 122.37 to 70.43 W. A 42.45% reduction is achieved. For the left linear motor, the maximum input power is reduced from 114.44 to 62.72 W. A 45.19% reduction is achieved. The effectiveness of the presented method by adding a spring element to reduce the input power of the machine is verified. Torsional springs may be sued to reduce the inertial effect and the size of the spring attachment. 6. Conclusions The paper presents a new type of high speed drilling machine based on a planar PKM module. The study introduces synthesis technology for planning the desirable motion functions of the PKM. The method allows both the point-to-point positioning motion and the up-and-down motion required for drilling operations. The result has shown that it is possible to reduce substantially the residual vibration of the tool tip by optimizing a polynomial motion function. Reducing residual vibration is critical when tool positioning requirement for the HSDM is in the range of several microns. By adding a ‘‘well-tuned’’ optimal spring to the structure, it was possible to reduce the required input power for driving the linear motors. The simulation has demonstrated that more than 40% reduction in the required input power is achieved relative to the structure without the spring. The reduction of required input power may allow choosing smaller motors and as a result reducing costs of hardware and operations. In order to better understand the properties of the HSDM and to complete its design, further study is required. It will include error analysis of the machine as well as the control strategies and control design of the system. 7. Acknowledgements The authors gratefully acknowledge the financial support of the NSF Engineering Research Center for Reconfigurable Machining Systems (US NSF Grant EEC95-92125) at the University of Michigan and the valuable input fromthe Center’s industrial partners. 中文翻譯 高速鉆床的動力學分析 摘要 通常情況下，術(shù)語“高速鉆床”就是指具有較高切削速率的鉆床。高速鉆床(HSDM)也是指具有非?？斓暮驼_的點到點運動的鉆床。新的HSDM是由帶有兩個直線電動機的平面并聯(lián)機構(gòu)組成。本文主要就是對并聯(lián)機器(PKM)的動力學分析。運動合成是為了介紹一種新方法，它能夠完善鉆孔操作和點到點定位的準確性。動態(tài)合成旨在減少因使用彈簧機械時PKM的輸入功率。 關(guān)鍵詞: 并聯(lián)運動機床; 高速鉆床; 動力學的合成 1.介紹 在最近的幾年里，研究所和工業(yè)協(xié)會介紹了各式各樣的PKM。其中大部分（但不是所有）,以眾所周知的斯圖爾特月臺[1]為基礎(chǔ)結(jié)構(gòu)。這一做法的好處是高公稱的負載重量比，良好的位置精度和結(jié)構(gòu)剛性[2]。斯圖爾特式PKM的主要缺點是相對小的工作空間和相對慢的操作速度 [3,4]。機床刀具的工作空間是指刀尖能夠移動和切削材料所需要的容積。平面的斯圖爾特月臺的設(shè)計在[5]中被提到，像是對無CNC機器作翻新改進的方法需要塑料的鑄模機制一樣。PKM[5]的設(shè)計允許可以調(diào)整幾何學已經(jīng)被規(guī)定了的最佳的再配置的任何路徑。 一般的，改變一根或較多連桿的長度是以PKM受約束的順序來做幾何學的調(diào)整。 在機床設(shè)計中，“定長度連桿”的PKM應用比“不定長度連桿”的共同點要少的多。一個優(yōu)秀“定長度連桿”型的機器例子被顯示在[6]。Renault-Automation Comau已經(jīng)建造叫做“Urane SX”的機器。在此HSDM被描述成是一個采用“定長度連桿”組成的并聯(lián)機械裝置。 鉆床操作在文學[7]中被很好的介紹了。汽車工業(yè)中，一項關(guān)于高速鉆孔的操作的廣泛的實驗研究在[8]中被報告。數(shù)據(jù)從數(shù)百個鉆床控制實驗上收集起來，是為了具體指定鉆床質(zhì)量所必須的參數(shù)。理想的鉆床運動和制造高質(zhì)量鉆床的指導方針通過理論和實驗的研究被呈現(xiàn)在[9]中。在被建議的PKM綜合中，我們遵循[9]中的結(jié)論。 新推出的PKM的詳細機械結(jié)構(gòu)在[10,11]被介紹，機器的大致結(jié)構(gòu)顯示在圖1中；它有很大的工作空間，點到點的高速運動和非常高的鉆速。并聯(lián)的機械裝置提供給了Y和Z軸的動作，X軸動作是由工作臺提供的。為了達成高速的運轉(zhuǎn)，用了兩個線性馬達來驅(qū)駛機械裝置和用一個高速的主軸來鉆孔。這篇文章的目的就是描述新的運動學的和動力學合成的方法的發(fā)展，為了改良機器的運轉(zhuǎn)。通過輸入運動，規(guī)劃鉆井和點對點定位，機器的誤差將會被減少，而且完成孔的質(zhì)量能被極大的提高。通過增加一個彈簧機械要素到PKM，輸入動力就能被最小，以便機器的尺寸和能量損耗降低。數(shù)字模擬的正確查證和