（球閥閥體）閥體零件的銑上端面夾具設(shè)計

資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 機(jī)械加工工藝卡片 工件名稱 閥體 工序號 VII 零件名稱 閥體 零件號 零件重量 同時加工件數(shù) 1 材料 毛坯 牌號 硬度 型號 重量 鋼板 鑄件 1.98KG 設(shè)備 夾具 輔助工具 名稱 型號 專用夾具 立式銑床 X51 安裝 工步 安裝及工步說明 刀具 量具 走刀長度mm 走刀次數(shù) 切削深度mm 進(jìn)給量mm/r 主軸轉(zhuǎn)速r/min 切削速度m/min 基本工 時min 1 銑上端面 高速鋼端銑刀 游標(biāo)卡尺 21 1 設(shè)計者 指導(dǎo)老師 共 1 頁 第 1 頁 機(jī)械加工工藝過程卡片 零件號 工序號 工序名稱 設(shè)備 夾具 刀具 量具 名稱 型號 名稱 規(guī)格 名稱 規(guī)格 名稱 規(guī)格 Ⅰ 鑄造 Ⅱ 時效處理 Ⅲ 銑床96x80平面 立式銑床 X51 專用夾具 高速鋼端銑刀 Ⅳ 車Φ48的端面和外圓 臥式車床 CA6140 專用夾具 端面車刀 Ⅴ 鉆Φ25的孔 立式鉆床 Z525 專用夾具 錐柄麻花鉆 Ⅵ 車Φ54和Φ47的圓 臥式車床 CA6140 專用夾具 彎頭鏜刀 Ⅶ 銑上端面 立式銑床 X51 專用夾具 端銑刀 VIII 鉆Φ10孔锪孔Φ20深28再锪孔Φ27深15 立式鉆床 Z525 專用夾具 錐柄麻花鉆和锪孔鉆 游標(biāo)卡尺 IX 車退刀槽和螺紋孔 臥式車床 CA6140 專用夾具 鏜刀和螺紋車刀 游標(biāo)卡尺 X 鉆4-M12 鉆床 Z525 專用夾具 高速鋼錐柄麻花鉆 游標(biāo)卡尺 XI 終檢 鉆床 Z525 專用夾具 擴(kuò)孔鉆 游標(biāo)卡尺 XII 入庫 游標(biāo)卡尺 課程設(shè)計說明書 題目：閥體零件的銑上端面夾具設(shè)計 學(xué) 生： 學(xué) 號： 專 業(yè)： 班 級： 指導(dǎo)老師 ： 摘 要 本次設(shè)計內(nèi)容涉及了機(jī)械制造工藝及機(jī)床夾具設(shè)計、金屬切削機(jī)床、公差配合與測量等多方面的知識。 閥體加工工藝規(guī)程及其夾具設(shè)計是包括零件加工的工藝設(shè)計、工序設(shè)計以及專用夾具的設(shè)計三部分。在工藝設(shè)計中要首先對零件進(jìn)行分析，了解零件的工藝再設(shè)計出毛坯的結(jié)構(gòu)，并選擇好零件的加工基準(zhǔn)，設(shè)計出零件的工藝路線；接著對零件各個工步的工序進(jìn)行尺寸計算，關(guān)鍵是決定出各個工序的工藝裝備及切削用量；然后進(jìn)行專用夾具的設(shè)計，選擇設(shè)計出夾具的各個組成部件，如定位元件、夾緊元件、引導(dǎo)元件、夾具體與機(jī)床的連接部件以及其它部件；計算出夾具定位時產(chǎn)生的定位誤差，分析夾具結(jié)構(gòu)的合理性與不足之處，并在以后設(shè)計中注意改進(jìn)。 關(guān)鍵詞：工藝、工序、切削用量、夾緊、定位、誤差。 目 錄 序言……………………………………………………………………1 第一章 零件的分析…………………………………………2 1.1零件的作用…………………………………………………………2 1.2零件的主要技術(shù)條件分析…………………………………………2 第一章 零件工藝規(guī)程設(shè)計………………………………3 2.1確定零件的生產(chǎn)類型………………………………………………3 2.2確定零件毛坯的制造形式…………………………………………3 2.3制定工藝路線………………………………………………………4 2.4確定機(jī)械加工余量、工序尺寸及毛坯尺寸………………………5 2.5確定各序工藝裝備及切削用量……………………………………8 第三章 夾具設(shè)計………………………………………………14 3.1概述…………………………………………………………………14 3.2方案設(shè)計……………………………………………………………14 3.3切削力和夾緊力的計算……………………………………………14 3 .4 定位誤差分析……………………………………………………15 3.5 夾具設(shè)計及操作說明……………………………………………15 總 結(jié)……………………………………………………………17 致 謝………………………………………………………………18 參 考 文 獻(xiàn)………………………………………………………19 序 言 機(jī)械制造業(yè)是制造具有一定形狀位置和尺寸的零件和產(chǎn)品，并把它們裝備成機(jī)械裝備的行業(yè)。機(jī)械制造業(yè)的產(chǎn)品既可以直接供人們使用，也可以為其它行業(yè)的生產(chǎn)提供裝備，社會上有著各種各樣的機(jī)械或機(jī)械制造業(yè)的產(chǎn)品。我們的生活離不開制造業(yè)，因此制造業(yè)是國民經(jīng)濟(jì)發(fā)展的重要行業(yè)，是一個國家或地區(qū)發(fā)展的重要基礎(chǔ)及有力支柱。從某中意義上講，機(jī)械制造水平的高低是衡量一個國家國民經(jīng)濟(jì)綜合實力和科學(xué)技術(shù)水平的重要指標(biāo)。 閥體的加工工藝規(guī)程及其，鉆的夾具設(shè)計是在學(xué)完了機(jī)械制圖、機(jī)械制造技術(shù)基礎(chǔ)、機(jī)械設(shè)計、機(jī)械工程材料等進(jìn)行課程設(shè)計之后的下一個教學(xué)環(huán)節(jié)。正確地解決一個零件在加工中的定位，夾緊以及工藝路線安排，工藝尺寸確定等問題，并設(shè)計出專用夾具，保證零件的加工質(zhì)量。本次設(shè)計也要培養(yǎng)自己的自學(xué)與創(chuàng)新能力。因此本次設(shè)計綜合性和實踐性強(qiáng)、涉及知識面廣。所以在設(shè)計中既要注意基本概念、基本理論，又要注意生產(chǎn)實踐的需要，只有將各種理論與生產(chǎn)實踐相結(jié)合，才能很好的完成本次設(shè)計。 本次設(shè)計水平有限，其中難免有缺點(diǎn)錯誤，敬請老師們批評指正。 第一章 零件的分析 1.1零件的作用 閥體是整體裝置的重要零件，它支撐中心部分，承受著部分靜載荷，因為閥體與整個機(jī)體連接，并且中心部分與該零件是螺紋連接，因而該零件的螺紋承受著一定載荷，以及一定的沖擊力，所以該零件承受著靜、動載荷。 1.2零件的主要技術(shù)條件分析 1、 為了適合鑄件技術(shù)要求，因而采用精度等級為CT12。 2、 為了保證鑄件整個零件的中心高度，首先以底平面為基準(zhǔn)，粗鏜直徑為30的孔，再以該孔為基準(zhǔn)，粗銑底平面，最后以底平面為精基準(zhǔn)，精鏜以上的孔，再精銑底平面，以上步驟均需要專用銑夾具等。 3、 兩螺紋孔的中心距為46，該尺寸的要求較高，為了保證尺寸的配合，這兩個螺紋孔應(yīng)該到最后進(jìn)行鉆孔。 4、 內(nèi)孔承受著較高工作力，因而它的內(nèi)孔配合度較高，要求有較高的粗糙度，只有這樣的粗糙度才能滿足零件工作時的需要。 5、 有關(guān)螺紋的技術(shù)要求： 閥體在工作時，將受到一定的載荷，這一載荷又將傳到螺紋上，因此，對于安裝這兩個螺紋端面有一定的粗糙度，該粗糙度為3.2，屬于鑄造件中較高的粗糙度要求。 6、 有關(guān)結(jié)合面的技術(shù)要求： 閥體在工作中受到?jīng)_擊性質(zhì)動載荷以及靜載荷，結(jié)合面的歪斜將使中心部分不能正常工作，最終導(dǎo)致機(jī)體整體不能正常工作，因此，對結(jié)合面的平面度要求較高。 第二章 零件工藝規(guī)程設(shè)計 2.1確定零件的生產(chǎn)類型 生產(chǎn)綱領(lǐng)的確定： N零=Q* n（1+α+β） 式中：N零：零件的生產(chǎn)綱領(lǐng)； Q：產(chǎn)品的生產(chǎn)綱領(lǐng)，Q=5000臺/年； n:每一產(chǎn)品中包含該零件的數(shù)量 n=1； α：零件的備品率，一般情況下為α=3%～5% 取4% β：零件的平均廢品率，取β=1； ∴N零=5000*1（1+4%+1%） =5，025件/年 根據(jù)任務(wù)書可知零件為大量生產(chǎn)。 2.2確定零件毛坯的制造形式 影響毛坯選擇的因素通常包括： 1、零件材料的工藝性及對材料組織的要求。 2、零件的結(jié)構(gòu)形狀和外形尺寸。 3、零件對毛坯精度，表面粗糙度和表面層性能的要求。 4、零件生產(chǎn)綱領(lǐng)的大小。 5、現(xiàn)有生產(chǎn)能力和發(fā)展前途。 由于閥體要求有較高的強(qiáng)度和剛度，以及良好的耐磨性和疲勞強(qiáng)度，材料選擇HT200。 因為閥體在工作中承受靜載荷以及小量的動載荷，為了使金屬纖維盡量不被切斷，非加工表面對稱均勻，使零件工作可靠，并且鑄件的鑄造性能較好，。由于該零件的輪廓尺寸不大，生產(chǎn)類型為大量生產(chǎn)，又考慮零件的加工條件要求較高。為了保證加工質(zhì)量、提高生產(chǎn)率、降低成本、減少工人的勞動強(qiáng)度，確定采用鑄造成型。 2.3制定工藝路線 1、 工藝過程的安排： 在閥體加工中，影響加工精度的主要因素有： ① 閥體本身的剛度比較地，在外力（切削力、夾緊力）的作用下，容易變形。 ② 閥體是鑄造件，孔的加工余量大，切削時將產(chǎn)生的殘余內(nèi)應(yīng)力，并引起應(yīng)力重新分布。 因此，在安排工藝過程中，就需要把各主要表面的粗精加工工序分開，既把粗加工安排在前，半精加工安排在中間，精加工安排在后面。 這是由于粗加工工序的切削余量大，因此，切削力、夾緊力必然大，加工后容易變形。粗精加工分開后，粗加工產(chǎn)生的變形，可以在半精加工修正，半精加工中產(chǎn)生的變形可以在精加工中修正。這樣逐步減少加工余量，切削力及內(nèi)應(yīng)力作用。逐步修正加工的變形就能最后達(dá)到零件的技術(shù)要求。 2、 各主要表面的工序安排如下： ⑴一端面：銑。 ⑵鉆孔、鏜孔。 鉆Φ10孔，锪孔Φ20，再锪孔Φ27，車退刀槽，車螺紋 兩螺紋孔：鉆底孔、攻絲。 4一些次要表面的加工，則視需要和可能安排在工藝過程的中間或后面。 3、 閥體工藝路線的方案之一： ⑴鑄造 ⑵時效處理； ⑶銑床96x80平面； ⑷車Φ48的端面和外圓 ⑸鉆Φ25的孔 ⑹車Φ54和Φ47的圓 ⑺銑上端面 ⑻鉆Φ10孔锪孔Φ20深28再锪孔Φ27深15 ⑼車退刀槽和螺紋孔 ⑽鉆4-M12 11：檢驗 12;入庫 4、此方案具有如下特點(diǎn)： ⑴加工階段劃分得較合理： a.閥體本身的剛度比較地，在外力（切削力、夾緊力）的作用下，容易變形。 b.閥體是鑄造件，孔的加工余量大，切削時將產(chǎn)生的殘余內(nèi)應(yīng)力，并引起應(yīng)力重新分布。 因此，在安排工藝過程時，就需要把各表面的粗、精加工工序分開，即把粗加工安排在前，半精加工安排在中間，精加工安排在后面。這樣避免了由于粗加工工序切削余量大，切削力、夾緊力必然大，加工后易產(chǎn)生變形。 如：內(nèi)應(yīng)力引起的變形；夾緊力較大引起的變形；切削溫度過高引起的變形；工藝系統(tǒng)的熱變形等的影響。粗、精加工分開后，粗加工產(chǎn)生的變形可以在半精及精加工中得到修正，就能最后達(dá)到零件的技術(shù)要求。同時，還能合理地使用設(shè)備，保證加工質(zhì)量。在粗加工各表面后及早地發(fā)現(xiàn)毛坯缺陷，避免損失更多的工時和費(fèi)用。 ⑵定位基準(zhǔn)的選擇 閥體加工作為精基準(zhǔn)的表面是大端面，以及兩臺階面為定位面，而作為精基準(zhǔn)的表面應(yīng)該提前加工完。在選擇粗基準(zhǔn)時考慮的重點(diǎn)是如何保證各加工表面有足夠的余量，使不加工表面的尺寸、位置符合圖紙要求。因此按照粗基準(zhǔn)選擇原則，以端面為粗基準(zhǔn)來加工底平面——精基準(zhǔn)。在閥體的加工過程中定位基準(zhǔn)滿足基準(zhǔn)重合原則，簡化了工藝過程的制定，使夾具的設(shè)計、制造簡單，降低成本。 ⑶按照工序分散的原則來擬定工藝路線： 閥體的加工過程中，各加工工序的組合基本上是按照工序分散的原則進(jìn)行的。由于閥體的形狀復(fù)雜，要加工表面不便于集中加工，為了適應(yīng)大批量生產(chǎn)的快節(jié)奏，必須在各工序采用高效率的專用機(jī)床和夾具，以提高生產(chǎn)率，保證加工質(zhì)量，使各工序的時間趨于平衡，按一定的節(jié)拍組織流水生產(chǎn)。雖然現(xiàn)代生產(chǎn)的發(fā)展多趨向于工序集中，但工序分散在大批量生產(chǎn)中仍應(yīng)用很廣泛。 2.4確定機(jī)械加工余量、工序尺寸及毛坯尺寸 閥體材料為HT200。 機(jī)械加工余量對工藝過程有一定的影響，余量不夠，不能保證零件的加工質(zhì)量。余量過大，不但增加機(jī)械加工的勞動量，而且增加了成本。所以，必須合理地安排加工余量。 本設(shè)計采用查表法確定各表面的加工余量、工序尺寸、毛坯尺寸及公差等級。 （1） 單邊、雙邊的加工余量及工序尺寸的確定 由（Ⅰ）表2.2—4 α=6.5 α=4.5 鑄件機(jī)械加工余量 基本尺寸 加工余量數(shù)值 大于 至 --- 100 5.5 6.0 6.5 7.5 8.5 9.0 10 11 12 3.5 4.0 4.5 5.5 6.0 5.5 6.5 6.5 7.5 100 160 6.5 7.0 8.0 9.0 10 11 12 13 14 4.0 4.5 5.5 6.0 7.0 7.0 8.0 8.0 9.0 160 250 7.5 8.5 9.5 11 13 13 15 15 17 5.0 6.0 7.0 8.5 9.0 8.5 10 9.5 11 250 400 8.5 9.5 11 13 15 15 17 18 20 5.5 6.5 8.0 10 11 10 12 12 14 400 630 10 11 13 16 18 17 20 20 23 6.5 7.5 9.5 12 13 12 14 13 16 630 1000 12 13 15 18 20 20 23 23 26 7.5 9 11 14 15 14 17 15 18 基本尺寸 加工余量數(shù)值 大于 至 1000 1600 13 15 17 20 23 23 26 27 30 8.5 10 13 16 17 16 19 18 21 表2.2--4 注： 1、表中每攔有兩個加工余量數(shù)值，上面的 數(shù)值是以一側(cè)為基準(zhǔn)，進(jìn)行單側(cè)加工的加工余量，進(jìn)行單側(cè)加工的加工余量值。下面為雙側(cè)加工時，每側(cè)的加工余量值。 2、表中略去基本尺寸大于1600—10000mm的加工余量數(shù)值。 （2） 鑄件公差等級的確定 表（Ⅱ）2.2—5可知 成批和大量生產(chǎn)的鑄件機(jī)械加工余量等級 工藝方法尺寸公差 加工余量 加工余量等級 鑄鋼 灰鑄鐵 球墨鑄鐵 可鍛鑄鐵 銅合金 鋅合金 輕金屬合金 鎳基合金 鈷基合金 砂型手工造型 CT 11～13 11～13 11～13 10～12 10～12 ---- 9～11 --- --- MA J H H H H --- H --- --- 砂型機(jī)器造型及殼型 CT 8～10 8～10 8～10 8～10 8～10 ---- 7～9 --- --- MA H G G G G --- G --- --- 金屬型 CT --- 7～9 7～9 7～9 7～9 7～9 6～8 --- --- MA --- F F F F F F --- --- 低壓鑄造 CT --- 7～9 7～9 7～9 7～9 7～9 6～8 --- --- MA --- F F F F F F --- --- 壓力鑄造 CT --- --- --- --- 6～8 4～6 5～7 --- --- MA --- --- --- --- E E E --- --- 熔模鑄造 CT 5～7 5～7 5～7 --- 4～6 --- 4～6 5～7 5～7 MA E E E --- E --- E E E 表2.2---5 注： 1、 型鑄造的鑄件，頂面（相對澆注位置）的加工余量等級，比底、側(cè)面的加工余量等級需降低一級選用。例：尺寸公差為CT12級，加工余量底、側(cè)面為MA—H級。 2、 型鑄造鑄件的底、側(cè)面所采用加工余量等級為選定的尺寸公差等級所對應(yīng)的全部加工與量等級中最粗級時。例：底、側(cè)面加工與量為CT12級，MA—H級。 3、 砂型鑄造孔的加工余量等級可與底面、側(cè)面相同的等級。 （3） 鑄造孔的最小尺寸 在鑄造工藝上為制造方面，一般當(dāng)鑄造孔徑小于規(guī)定尺寸時可不鑄出，零件上的孔如難以機(jī)械加工，最小孔徑也可放寬到特殊情況數(shù)值。 （4） 鑄造壁的最小厚度 各種鑄造方法鑄件的最小壁厚可見表。 （5） 鑄造斜度 對于砂型及硬型鑄件常選用3°，壓鑄件常選用1°30′～2°。待加工表面的斜度數(shù)值可以大一些，非加工表面斜度數(shù)值可適當(dāng)減小。一般參照表選取。為便于模具制造及造型，各面斜度數(shù)值應(yīng)盡量一致。 2、 底面加工余量及工序尺寸的確定 查表2.2---4可得總余量A=6.5mm 由表可得精銑α=0.5 粗銑α=A-0.5=6mm 3、 螺紋孔加工余量及工序尺寸的確定 由表可得鉆孔直徑為8.5，加工余量α=2.5 4、 臺階孔加工余量的確定 由表查得總余量為A=6.5 精銑α=0.5（單面） 粗銑α=A-2α=6.5-1=5.5 2.5確定各序工藝裝備及切削用量 工序三：銑96x80的平面 銑φ96x80底平面 查參考文獻(xiàn)[14]表2.4-73 刀具：硬質(zhì)合金銑刀（面銑刀），材料：，D=68mm ，齒數(shù)，此為粗齒銑刀。 因其單邊余量：Z=3.5mm 所以銑削深度：=3.5mm 每齒進(jìn)給量：根據(jù)參考文獻(xiàn)[7]表2.4-75，取，銑削速度：參照參考文獻(xiàn)[7]表30—34，取V=1.33m/s 機(jī)床主軸轉(zhuǎn)速： 式（2.1） 式中 V—銑削速度； d—刀具直徑。 機(jī)床主軸轉(zhuǎn)速： 按照參考文獻(xiàn)[3]表3.1-74 實際銑削速度： 進(jìn)給量： 工作臺每分進(jìn)給量：6.7mm/s×60=402mm/min ：根據(jù)參考文獻(xiàn)[7]表2.4-81, 被切削層長度：由毛坯尺寸可知 銑刀切入時取： ， 銑刀切出時取： 根據(jù)《機(jī)械制造工藝學(xué)》表可得： =0.22min 由表3.3-7得：操作機(jī)床時間為：0.83 min 由表3.3-8得：測量工件時間為：0.14 min T1=0.97min 則T總=T1+T2 =1.19min 工序四：車Φ48的外圓和端面 工序①車、：（T1=T輔助時間 T2=T機(jī)床時間） 粗車φ48外圓時：因為單邊與量: Z=2mm 根據(jù)參考文獻(xiàn)表[3]中3-1得：：f=0.5 m/r 根據(jù)參考文獻(xiàn)[5]中5.3-20得：v=82 m/r 則機(jī)床主軸轉(zhuǎn)速 工時定額： 根據(jù)參考文獻(xiàn)表[3]中 3.3-3得：操作機(jī)床時間為： 0.02+0.04+0.03+0.07+0.06+0.02+0.01+0.02+0.03+0.04=0.64 min 根據(jù)參考文獻(xiàn)由表[3]中 3.3-4得： 測量工件時間為：0.08+0.08=0.16 min 所以T1=0.64+0.16=0.8 min 根據(jù)參考文獻(xiàn)表5.4-1得機(jī)動時間為： T2=0.05+0.02+0.03=0.1 m/r 根據(jù)文獻(xiàn)[13] 表2-24得T基公式- 則T總=T1+T2+T基=0.347 min 工序五：鉆Φ25孔 鉆孔 切削深度： 進(jìn)給量：根據(jù)參考文獻(xiàn)[7]《機(jī)械加工工藝手冊》表2.4-52，取 切削速度：參照參考文獻(xiàn)[7]《機(jī)械加工工藝手冊》表2.4-53，取 機(jī)床主軸轉(zhuǎn)速，由式（1.1）有： ，取 實際切削速度，由式（1.2）有： 被切削層長度： 刀具切入長度： 式（1.8） 刀具切出長度： 取 走刀次數(shù)為1 基本工時： 式（1.9） 工序六 鏜φ54和φ47內(nèi)孔時； 鏜φ54時： 切削用量：ap=3 毛坯孔徑d=50 由表8.2-1得：f=0.5 m/r v=80 m/r 則n=318V/D=1817.1m/r 取D=1800r/min 實際切削速度 工作臺每分鐘進(jìn)給量 被切削層長度 刀具切入長度 刀具切出長度 取 行程次數(shù)： 基本工時，由式（1.5）有： 鏜Φ47孔時 切削用量：ap=3 毛坯孔徑d=43 由表8.2-1得：f=0.5 m/r v=80 m/r 則n=318V/D=1817.1m/r 取D=1800r/min 實際切削速度 工作臺每分鐘進(jìn)給量 被切削層長度 刀具切入長度 刀具切出長度 取 行程次數(shù)： 基本工時，由式（1.5）有： ，工序七和工序三的計算相同，在此不在累述 工序十:鉆4-M12螺紋孔 鉆M12螺紋孔底孔Φ10.2； 根據(jù)《機(jī)械加工工藝手冊》表查得：進(jìn)給量,切削速度，切削深度 機(jī)床主軸轉(zhuǎn)速 取 實際切削速度 被切削層長度： 刀具切入長度： 刀具切出長度： 取 根據(jù)《機(jī)械制造工藝學(xué)》表可得： =0.09 攻絲M12 選擇M12mm高速鋼機(jī)用絲錐 f等于工件螺紋的螺距p，即 按機(jī)床選取 基本工時： 由表3.3-9得：裝夾工件時間為0.17min 由表3.3-10得：松開卸下工件時間為0.15min 由表3.3-12得：測量工件時間為：0.04min 所以輔助時間是T1=1.34 min T2=0.09×4=0.36min 則T總=T1+T2=1.80min 第三章：夾具設(shè)計 3.1概述 在機(jī)床對零件進(jìn)行機(jī)械加工時，為保證工件加工精度，首先要保證工件在 機(jī)床上占有正確的位置，然后通過夾緊機(jī)構(gòu)使工件的正確位置固定不動，這一 任務(wù)就是由夾具來完成。 對于單件、小批生產(chǎn)，應(yīng)盡量使用通用夾具，這樣可以降低工件的生產(chǎn)成本。 但由于通用夾具適用各種工件的裝夾，所以夾緊時往往比較費(fèi)時間，并且操作復(fù) 雜，生產(chǎn)效率低。 本零件屬于大量生產(chǎn)，零件外形也不適于使用通用夾具，為了保證工件精度， 提高生產(chǎn)效率，設(shè)計專用夾具就顯得非常必要。 3.2方案設(shè)計 方案設(shè)計是夾具設(shè)計的第一步，也是夾具設(shè)計關(guān)鍵的一步，方案設(shè)計的 好、壞將直接影響工件的加工精度、加工效率，稍不注意就會造成不能 滿足工件加工要求，或加工精度不能達(dá)到設(shè)計要求，因此必須慎重考慮。 設(shè)計方案的擬定必須遵循下列原則： 1、 定位裝置要確保工件定位準(zhǔn)確和可靠，符合六位定位原理。 2、 夾具的定位精度能滿足工件精度的要求。 3、 夾具結(jié)構(gòu)盡量簡單，操縱力小而夾緊可靠，力爭造價低 3.3切削力和夾緊力的計算 2 ） 切削力及夾緊力計算 粗銑時受力最大，　選用高速端面銑刀 刀具：高速鋼端面銑刀，φ38mm。 銑時的軸向力 查文獻(xiàn)[２]表15-31， 由于工件所受加緊力與切削力方向相互垂直，為防止工件在切削力作用下沿φ90mm段較小平面?zhèn)冗厓A斜，使工件離開基面所需的夾緊力 ， 摩擦系數(shù)查[4]表3-19，=0.25。 安全系數(shù) ， 式中 K————基本安全系數(shù)1.5； K————加工狀態(tài)系數(shù)1.2； K————刀具鈍化系數(shù)1.5，由文獻(xiàn)[4]表3-20查得； K————切削特點(diǎn)系數(shù)1.0； K————考慮加緊動力穩(wěn)定性系數(shù)1.3。 L=20mm, H=42mm, l=34mm 查文獻(xiàn)[4]表3-26，知d=10mm的螺栓許用加緊力，因 ，此選用該螺栓加緊足以滿足加緊要求。 3 .4 定位誤差分析 夾具的主要定位元件為心軸和定位塊，該定位心軸是根據(jù)零件定位方案設(shè)計的專用件，定位精度較高，同時銑面時，面自身沒有精度要求，因此定位誤差可以不予考慮。 3.5 夾具設(shè)計及操作說明 如前所述，在設(shè)計夾具時，為提高生產(chǎn)率，首先想到是怎么樣方便的安裝和拆卸，本道工序就是采用了開口壓板壓緊的方式。由于本夾具是對工件進(jìn)行銑上端面，因此在鉛直方向受到很大的沖擊力，故在其相應(yīng)的方向上應(yīng)適當(dāng)?shù)目紤]強(qiáng)度上的要求。并設(shè)法減少夾具的的占地面積，使之很方便的操作和快速的切換工件。 夾具體上用Φ40孔定，定位釘定位，加一定位塊限制2個自由度，靠銑削時的里來限擠進(jìn)工件，即滿足定位要求又能增加定位穩(wěn)定性。夾緊裝置使用移動壓板，操作方便。夾具體也是由定位夾緊需要設(shè)計而成，工件的拆裝也比較方便，總體上這套夾具方案能夠滿足生產(chǎn)要求。 裝配圖附圖如下 總 結(jié) 課程設(shè)計即將結(jié)束了，時間雖然短暫但是它對我們來說受益菲淺的，通過這次的設(shè)計使我們不再是只知道書本上的空理論，不再是紙上談兵，而是將理論和實踐相結(jié)合進(jìn)行實實在在的設(shè)計，使我們不但鞏固了理論知識而且掌握了設(shè)計的步驟和要領(lǐng)，使我們更好的利用圖書館的資料，更好的更熟練的利用我們手中的各種設(shè)計手冊和AUTOCAD等制圖軟件，為我們踏入設(shè)計打下了好的基礎(chǔ)。 畢業(yè)設(shè)計使我們認(rèn)識到了只努力的學(xué)好書本上的知識是不夠的，還應(yīng)該更好的做到理論和實踐的結(jié)合。因此同學(xué)們非常感謝老師給我們的辛勤指導(dǎo)，使我們學(xué)到了好多，也非常珍惜學(xué)院給我們的這次設(shè)計的機(jī)會，它將是我們畢業(yè)設(shè)計完成的更出色的關(guān)鍵一步。 致 謝 這次課程設(shè)計使我收益不小，為我今后的學(xué)習(xí)和工作打下了堅實和良好的基礎(chǔ)。但是，查閱資料尤其是在查閱切削用量手冊時，數(shù)據(jù)存在大量的重復(fù)和重疊，由于經(jīng)驗不足，在選取數(shù)據(jù)上存在一些問題，不過我的指導(dǎo)老師每次都很有耐心地幫我提出寶貴的意見，在我遇到難題時給我指明了方向，最終我很順利的完成了畢業(yè)設(shè)計。 這次課程設(shè)計成績的取得，與指導(dǎo)老師的細(xì)心指導(dǎo)是分不開的。在此，我衷心感謝我的指導(dǎo)老師，特別是每次都放下她的休息時間，耐心地幫助我解決技術(shù)上的一些難題，她嚴(yán)肅的科學(xué)態(tài)度，嚴(yán)謹(jǐn)?shù)闹螌W(xué)精神，精益求精的工作作風(fēng)，深深地感染和激勵著我。從課題的選擇到項目的最終完成，她都始終給予我細(xì)心的指導(dǎo)和不懈的支持。多少個日日夜夜，她不僅在學(xué)業(yè)上給我以精心指導(dǎo)，同時還在思想、生活上給我以無微不至的關(guān)懷，除了敬佩指導(dǎo)老師的專業(yè)水平外，她的治學(xué)嚴(yán)謹(jǐn)和科學(xué)研究的精神也是我永遠(yuǎn)學(xué)習(xí)的榜樣，并將積極影響我今后的學(xué)習(xí)和工作。在此謹(jǐn)向指導(dǎo)老師致以誠摯的謝意和崇高的敬意。 參 考 文 獻(xiàn) 1. 切削用量簡明手冊,艾興、肖詩綱主編,機(jī)械工業(yè)出版社出版，1994年 2.機(jī)械制造工藝設(shè)計簡明手冊，李益民主編，機(jī)械工業(yè)出版社出版，1994年 3.機(jī)床夾具設(shè)計，哈爾濱工業(yè)大學(xué)、上海工業(yè)大學(xué)主編，上?？茖W(xué)技術(shù)出版社出版，1983年 4.機(jī)床夾具設(shè)計手冊，東北重型機(jī)械學(xué)院、洛陽工學(xué)院、一汽制造廠職工大學(xué)編，上?？茖W(xué)技術(shù)出版社出版，1990年 5.金屬機(jī)械加工工藝人員手冊，上?？茖W(xué)技術(shù)出版社，1981年10月 6.機(jī)械制造工藝學(xué)，郭宗連、秦寶榮主編，中國建材工業(yè)出版社出版，1997年 Robotics and Computer-Integrated Manufacturing 21 (2005) 368378Locating completeness evaluation and revision in fixture planH. Song?, Y. RongCAM Lab, Department of Mechanical Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USAReceived 14 September 2004; received in revised form 9 November 2004; accepted 10 November 2004AbstractGeometry constraint is one of the most important considerations in fixture design. Analytical formulation of deterministiclocation has been well developed. However, how to analyze and revise a non-deterministic locating scheme during the process ofactual fixture design practice has not been thoroughly studied. In this paper, a methodology to characterize fixturing systemsgeometry constraint status with focus on under-constraint is proposed. An under-constraint status, if it exists, can be recognizedwith given locating scheme. All un-constrained motions of a workpiece in an under-constraint status can be automatically identified.This assists the designer to improve deficit locating scheme and provides guidelines for revision to eventually achieve deterministiclocating.r 2005 Elsevier Ltd. All rights reserved.Keywords: Fixture design; Geometry constraint; Deterministic locating; Under-constrained; Over-constrained1. IntroductionA fixture is a mechanism used in manufacturing operations to hold a workpiece firmly in position. Being a crucialstep in process planning for machining parts, fixture design needs to ensure the positional accuracy and dimensionalaccuracy of a workpiece. In general, 3-2-1 principle is the most widely used guiding principle for developing a locationscheme. V-block and pin-hole locating principles are also commonly used.A location scheme for a machining fixture must satisfy a number of requirements. The most basic requirement is thatit must provide deterministic location for the workpiece 1. This notion states that a locator scheme producesdeterministic location when the workpiece cannot move without losing contact with at least one locator. This has beenone of the most fundamental guidelines for fixture design and studied by many researchers. Concerning geometryconstraint status, a workpiece under any locating scheme falls into one of the following three categories:1. Well-constrained (deterministic): The workpiece is mated at a unique position when six locators are made to contactthe workpiece surface.2. Under-constrained: The six degrees of freedom of workpiece are not fully constrained.3. Over-constrained: The six degrees of freedom of workpiece are constrained by more than six locators.In 1985, Asada and By 1 proposed full rank Jacobian matrix of constraint equations as a criterion and formed thebasis of analytical investigations for deterministic locating that followed. Chou et al. 2 formulated the deterministiclocating problem using screw theory in 1989. It is concluded that the locating wrenches matrix needs to be full rank toachieve deterministic location. This method has been adopted by numerous studies as well. Wang et al. 3 consideredARTICLE IN PRESS front matter r 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.rcim.2004.11.012?Corresponding author. Tel.: +15088316092; fax: +15088316412.E-mail address: hsongwpi.edu (H. Song).locatorworkpiece contact area effects instead of applying point contact. They introduced a contact matrix andpointed out that two contact bodies should not have equal but opposite curvature at contacting point. Carlson 4suggested that a linear approximation may not be sufficient for some applications such as non-prismatic surfaces ornon-small relative errors. He proposed a second-order Taylor expansion which also takes locator error interaction intoaccount. Marin and Ferreira 5 applied Chous formulation on 3-2-1 location and formulated several easy-to-followplanning rules. Despite the numerous analytical studies on deterministic location, less attention was paid to analyzenon-deterministic location.In the Asada and Bys formulation, they assumed frictionless and point contact between fixturing elements andworkpiece. The desired location is q*, at which a workpiece is to be positioned and piecewisely differentiable surfacefunction is gi(as shown in Fig. 1).The surface function is defined as giq? 0: To be deterministic, there should be a unique solution for the followingequation set for all locators.giq 0;i 1;2;.;n,(1)where n is the number of locators and q x0;y0;z0;y0;f0;c0? represents the position and orientation of theworkpiece.Only considering the vicinity of desired location q?; where q q? Dq; Asada and By showed thatgiq giq? hiDq,(2)where hiis the Jacobian matrix of geometry functions, as shown by the matrix in Eq. (3). The deterministic locatingrequirement can be satisfied if the Jacobian matrix has full rank, which makes the Eq. (2) to have only one solutionq q?:rankqg1qx0qg1qy0qg1qz0qg1qy0qg1qf0qg1qc0:qgiqx0qgiqy0qgiqz0qgiqy0qgiqf0qgiqc0:qgnqx0qgnqy0qgnqz0qgnqy0qgnqf0qgnqc026666666664377777777758:9=; 6.(3)Upon given a 3-2-1 locating scheme, the rank of a Jacobian matrix for constraint equations tells the constraint statusas shown in Table 1. If the rank is less than six, the workpiece is under-constrained, i.e., there exists at least one freemotion of the workpiece that is not constrained by locators. If the matrix has full rank but the locating scheme hasmore than six locators, the workpiece is over-constrained, which indicates there exists at least one locator such that itcan be removed without affecting the geometry constrain status of the workpiece.For locating a model other than 3-2-1, datum frame can be established to extract equivalent locating points. Hu 6has developed a systematic approach for this purpose. Hence, this criterion can be applied to all locating schemes.ARTICLE IN PRESSX Y Z O X Y Z O (x0,y0,z0) gi UCS WCS Workpiece Fig. 1. Fixturing system model.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378369Kang et al. 7 followed these methods and implemented them to develop a geometry constraint analysis module intheir automated computer-aided fixture design verification system. Their CAFDV system can calculate the Jacobianmatrix and its rank to determine locating completeness. It can also analyze the workpiece displacement and sensitivityto locating error.Xiong et al. 8 presented an approach to check the rank of locating matrix WL(see Appendix). They also intro-duced left/right generalized inverse of the locating matrix to analyze the geometric errors of workpiece. It hasbeen shown that the position and orientation errors DX of the workpiece and the position errors Dr of locators arerelated as follows:Well-constrained :DX WLDr,(4)Over-constrained :DX WTLWL?1WTLDr,(5)Under-constrained :DX WTLWLWTL?1Dr I6?6? WTLWLWTL?1WLl,(6)where l is an arbitrary vector.They further introduced several indexes derived from those matrixes to evaluate locator configurations, followed byoptimization through constrained nonlinear programming. Their analytical study, however, does not concern therevision of non-deterministic locating. Currently, there is no systematic study on how to deal with a fixture design thatfailed to provide deterministic location.2. Locating completeness evaluationIf deterministic location is not achieved by designed fixturing system, it is as important for designers to knowwhat the constraint status is and how to improve the design. If the fixturing system is over-constrained, informa-tion about the unnecessary locators is desired. While under-constrained occurs, the knowledge about all the un-constrained motions of a workpiece may guide designers to select additional locators and/or revise the locatingscheme more efficiently. A general strategy to characterize geometry constraint status of a locating scheme is describedin Fig. 2.In this paper, the rank of locating matrix is exerted to evaluate geometry constraint status (see Appendixfor derivation of locating matrix). The deterministic locating requires six locators that provide full rank locatingmatrix WL:As shown in Fig. 3, for given locator number n; locating normal vector ai;bi;ci? and locating position xi;yi;zi? foreach locator, i 1;2;.;n; the n ? 6 locating matrix can be determined as follows:WLa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775.(7)When rankWL 6 and n 6; the workpiece is well-constrained.When rankWL 6 and n46; the workpiece is over-constrained. This means there are n ? 6 unnecessary locatorsin the locating scheme. The workpiece will be well-constrained without the presence of those n ? 6 locators. Themathematical representation for this status is that there are n ? 6 row vectors in locating matrix that can be expressedas linear combinations of the other six row vectors. The locators corresponding to that six row vectors consist oneARTICLE IN PRESSTable 1RankNumber of locatorsStatuso 6Under-constrained 6 6Well-constrained 646Over-constrainedH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378370locating scheme that provides deterministic location. The developed algorithm uses the following approach todetermine the unnecessary locators:1. Find all the combination of n ? 6 locators.2. For each combination, remove that n ? 6 locators from locating scheme.3. Recalculate the rank of locating matrix for the left six locators.4. If the rank remains unchanged, the removed n ? 6 locators are responsible for over-constrained status.This method may yield multi-solutions and require designer to determine which set of unnecessary locators shouldbe removed for the best locating performance.When rankWLo6; the workpiece is under-constrained.3. Algorithm development and implementationThe algorithm to be developed here will dedicate to provide information on un-constrained motions of theworkpiece in under-constrained status. Suppose there are n locators, the relationship between a workpieces position/ARTICLE IN PRESSFig. 2. Geometry constraint status characterization.X Z Y (a1,b1,c1) 2,b2,c2) (x1,y1,z1) (x2,y2,z2) (ai,bi,ci) (xi,yi,zi) (aFig. 3. A simplified locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378371orientation errors and locator errors can be expressed as follows:DX DxDyDzaxayaz2666666666437777777775w11:w1i:w1nw21:w2i:w2nw31:w3i:w3nw41:w4i:w4nw51:w5i:w5nw61:w6i:w6n2666666666437777777775?Dr1:Dri:Drn2666666437777775,(8)where Dx;Dy;Dz;ax;ay;azare displacement along x, y, z axis and rotation about x, y, z axis, respectively. Driisgeometric error of the ith locator. wijis defined by right generalized inverse of the locating matrix Wr WTLWLWTL?15.To identify all the un-constrained motions of the workpiece, V dxi;dyi;dzi;daxi;dayi;dazi? is introduced such thatV DX 0.(9)Since rankDXo6; there must exist non-zero V that satisfies Eq. (9). Each non-zero solution of V represents an un-constrained motion. Each term of V represents a component of that motion. For example, 0;0;0;3;0;0? says that therotation about x-axis is not constrained. 0;1;1;0;0;0? means that the workpiece can move along the direction given byvector 0;1;1?: There could be infinite solutions. The solution space, however, can be constructed by 6 ? rankWLbasic solutions. Following analysis is dedicated to find out the basic solutions.From Eqs. (8) and (9)VX dxDx dyDy dzDz daxDax dayDay dazDaz dxXni1w1iDri dyXni1w2iDri dzXni1w3iDri daxXni1w4iDri dayXni1w5iDri dazXni1w6iDriXni1Vw1i;w2i;w3i;w4i;w5i;w6i?TDri 0.10Eq. (10) holds for 8Driif and only if Eq. (11) is true for 8i1pipn:Vw1i;w2i;w3i;w4i;w5i;w6i?T 0.(11)Eq. (11) illustrates the dependency relationships among row vectors of Wr: In special cases, say, all w1jequal to zero,V has an obvious solution 1, 0, 0, 0, 0, 0, indicating displacement along the x-axis is not constrained. This is easy tounderstand because Dx 0 in this case, implying that the corresponding position error of the workpiece is notdependent of any locator errors. Hence, the associated motion is not constrained by locators. Moreover, a combinedmotion is not constrained if one of the elements in DX can be expressed as linear combination of other elements. Forinstance, 9w1ja0;w2ja0; w1j ?w2jfor 8j: In this scenario, the workpiece cannot move along x- or y-axis. However, itcan move along the diagonal line between x- and y-axis defined by vector 1, 1, 0.To find solutions for general cases, the following strategy was developed:1. Eliminate dependent row(s) from locating matrix. Let r rank WL; n number of locator. If ron; create a vectorin n ? r dimension space U u1:uj:un?rhi1pjpn ? r; 1pujpn: Select ujin the way that rankWL r still holds after setting all the terms of all the ujth row(s) equal to zero. Set r ? 6 modified locating matrixWLMa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775r?6,where i 1;2;:;niauj:ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 3683783722. Compute the 6 ? n right generalized inverse of the modified locating matrixWr WTLMWLMWTLM?1w11:w1i:w1rw21:w2i:w2rw31:w3i:w3rw41:w4i:w4rw51:w5i:w5rw61:w6i:w6r26666666664377777777756?r3. Trim Wrdown to a r ? rfull rank matrix Wrm: r rankWLo6: Construct a 6 ? r dimension vector Q q1:qj:q6?rhi1pjp6 ? r; 1pqjpn: Select qjin the way that rankWr r still holds after setting all theterms of all the qjth row(s) equal to zero. Set r ? r modified inverse matrixWrmw11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r26666664377777756?6,where l 1;2;:;6 laqj:4. Normalize the free motion space. Suppose V V1;V2;V3;V4;V5;V6? is one of the basic solutions of Eq. (10) withall six terms undetermined. Select a term qkfrom vector Q1pkp6 ? r: SetVqk ?1;Vqj 0 j 1;2;:;6 ? r;jak;(5. Calculated undetermined terms of V: V is also a solution of Eq. (11). The r undetermined terms can be found asfollows.v1:vs:v62666666437777775wqk1:wqki:wqkr2666666437777775?w11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r2666666437777775?1,where s 1;2;:;6saqj;saqk;l 1;2;:;6 laqj:6. Repeat step 4 (select another term from Q) and step 5 until all 6 ? r basic solutions have been determined.Based on this algorithm, a C+ program was developed to identify the under-constrained status and un-constrained motions.Example 1. In a surface grinding operation, a workpiece is located on a fixture system as shown in Fig. 4. The normalvector and position of each locator are as follows:L1:0, 0, 10, 1, 3, 00,L2:0, 0, 10, 3, 3, 00,L3:0, 0, 10, 2, 1, 00,L4:0, 1, 00, 3, 0, 20,L5:0, 1, 00, 1, 0, 20.Consequently, the locating matrix is determined.WL0013?100013?300011?20010?203010?2012666666437777775.ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378373This locating system provides under-constrained positioning since rankWL 5o6: The program then calculatesthe right generalized inverse of the locating matrix.Wr000000:50:5?1?0:51:50:75?1:251:5000:250:25?0:5000:5?0:50000000:5?0:526666666643777777775.The first row is recognized as a dependent row because removal of this row does not affect rank of the matrix. Theother five rows are independent rows. A linear combination of the independent rows is found according therequirement in step 5 of the procedure for under-constrained status. The solution for this special case is obvious that allthe coefficients are zero. Hence, the un-constrained motion of workpiece can be determined as V ?1; 0; 0; 0; 0; 0?:This indicates that the workpiece can move along x direction. Based on this result, an additional locator should beemployed to constraint displacement of workpiece along x-axis.Example 2. Fig. 5 shows a knuckle with 3-2-1 locating system. The normal vector and position of each locator in thisinitial design are as follows:L1:0, 1, 00, 896, ?877, ?5150,L2:0, 1, 00, 1060, ?875, ?3780,L3:0, 1, 00, 1010, ?959, ?6120,L4:0.9955, ?0.0349, 0.0880, 977, ?902, ?6240,L5:0.9955, ?0.0349, 0.0880, 977, ?866, ?6240,L6:0.088, 0.017, ?0.9960, 1034, ?864, ?3590.The locating matrix of this configuration isWL010515:000:8960010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:9960866:6257998:24660:093626666666643777777775,rankWL 5o6 reveals that the workpiece is under-constrained. It is found that one of the first five rows can beremoved without varying the rank of locating matrix. Suppose the first row, i.e., locator L1is removed from WL; theARTICLE IN PRESSXZYL3L4L5L2L1Fig. 4. Under-constrained locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378374modified locating matrix turns intoWLM010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:996866:6257998:24660:09362666666437777775.The right generalized inverse of the modified locating matrix isWr1:8768?1:8607?20:666521:37160:49953:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775.The program checked the dependent row and found every row is dependent on other five rows. Without losinggenerality, the first row is regarded as dependent row. The 5 ? 5 modified inverse matrix isWrm3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:028402666666437777775.The undetermined solution is V ?1; v2; v3; v4; v5; v6?:To calculate the five undetermined terms of V according to step 5,1:8768?1:8607?20:666521:37160:499526666666643777777775T?3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775?1 0; ?1:713; ?0:0432; ?0:0706; 0:04?.Substituting this result into the undetermined solution yields V ?1;0; ?1:713; ?0:0432; ?0:0706; 0:04?ARTICLE IN PRESSFig. 5. Knuckle 610 (modified from real design).H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378375This vector represents a free motion defined by the combination of a displacement along ?1, 0, ?1.713 directioncombined and a rotation about ?0.0432, ?0.0706, 0.04. To revise this locating configuration, another locator shouldbe added to constrain this free motion of the workpiece, assuming locator L1was removed in step 1. The program canalso calculate the free motions of the workpiece if a locator other than L1was removed in step 1. This provides morerevision options for designer.4. SummaryDeterministic location is an important requirement for fixture locating scheme design. Analytical criterion fordeterministic status has been well established. To further study non-deterministic status, an algorithm for checking thegeometry constraint status has been developed. This algorithm can identify an under-constrained status and indicatethe un-constrained motions of workpiece. It can also recognize an over-constrained status and unnecessary locators.The output information can assist designer to analyze and improve an existing locating scheme.Appendix. Locating matrixConsider a general workpiece as shown in Fig. 6. Choose reference frame fWg fixed to the workpiece. Let fGg andfLig be the global frame and the ith locator frame fixed relative to it. We haveFiXw;Hw;rwi fiXli;Hli;rli,(12)where Xw2 3?1and Hw2 3?1(Xli2 3?1and Hli2 3?1) are the position and orientation of the workpiece(the ith locator) in the global frame fGg; rwi2 3?1(rli2 3?1) is the position of the ith contact point between theworkpiece and the ith locator in the workpiece frame fWg (the ith locator frame fLig).Assume that DXw2 3?1(DHw2 3?1) and Drwi2 3?1are the deviations of the position Xw2 3?1(orientationHw2 3?1) of the workpiece and the position of the ith contact point rwi2 3?1; respectively. Then we have the actualcontact on the wor