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外文翻譯
譯文題目 一種自動化夾具設(shè)計方法
原稿題目A Clamping Design Approach for Automated Fixture Design
原稿出處 Int J Adv Manuf Technol (2001)18:784–789
一種自動化夾具設(shè)計方法
塞西爾
美國，拉斯克魯塞斯，新墨西哥州立大學(xué)，，工業(yè)工程系，虛擬企業(yè)工程實驗室（VEEL）
在這片論文里，描述了一種新的計算機輔助夾具設(shè)計方法。對于一個給定的工件，這種夾具設(shè)計方法包含了識別加緊表面和夾緊位置點。通過使用一種定位設(shè)計方法去夾緊和支撐工件，并且當機器正在運行的時候，可以根據(jù)刀具來正確定位工件。該論文還給出了自動化夾具設(shè)計的詳細步驟。幾何推理技術(shù)被用來確定可行的夾緊面和位置。要識別所完成工件和定位點就還需要一些輸入量包括CAD模型的技術(shù)要求、特征。
關(guān)鍵詞：夾緊；夾具設(shè)計
1. 動機和目標
夾具設(shè)計是連接設(shè)計與制造間的一項重要任務(wù)。自動化夾具設(shè)計和計算機輔助夾具設(shè)計開發(fā)（夾具CAD）是下一代制造系統(tǒng)成功實現(xiàn)目標的關(guān)鍵。在這片論文里，討論了一種夾具設(shè)計的方法，這種方法有利于在目前環(huán)境下夾具設(shè)計的自動化。
夾具設(shè)計方法的研究已成為國內(nèi)多家科研工作的重點。作者：周在[1]中對工件的穩(wěn)定和總需求約束了雙重標準，突出重點的工作。在夾具設(shè)計中廣泛的運用了人工智能（AI）以及專家系統(tǒng)。部分CAD模型幾何信息也被用于夾具設(shè)計。Bidanda [4]描述了一個基于規(guī)則的專家系統(tǒng)，以確定回轉(zhuǎn)體零件的定位和夾緊。夾緊機制同時用于執(zhí)行定位和夾緊功能。其他研究者（如DeVor等，[5,6]）分析了切削力鉆井機械和建筑模型及其他金屬切削加工?？涤袨榈仍赱2]中定義了裝配約束建模的模塊化與夾具元件之間的空間關(guān)系。一些研究人員采用模塊化夾具設(shè)計原則，用以生成[2,7-11]，另一些夾具設(shè)計工作者已經(jīng)報告了[1,3,9,12-23]。可以在[21,24]中找到夾具設(shè)計相關(guān)的大量的審查工作。
在第二節(jié)中，對夾具設(shè)計任務(wù)中各種步驟進行了概述。在第3節(jié)和第四節(jié)中描述了工件的加工過程，要夾緊工件表面，否則將面臨工件的全面自動測定。第5節(jié)討論了對工件的夾緊點的測定。
2. 夾具設(shè)計的整體方法
在本節(jié)中，描述了整體夾緊的設(shè)計方法。通常對較理想的位置的那一部分進行夾緊，并減低切削力的影響。夾緊的位置和夾具設(shè)計中定位的位置是高度相關(guān)的。通常，夾緊和定位可以通過同樣的方法來完成。但是，不明白這兩個是夾具設(shè)計中不同的方面，可能導(dǎo)致夾具設(shè)計的失敗。多數(shù)人的在規(guī)劃過程中首先解決定位問題，這樣可以使開發(fā)的定位與設(shè)計的定位相契合。不過，整體定位及設(shè)計方法不在本文討論范文內(nèi)。
除了零件的設(shè)計（為此夾具設(shè)計有待開發(fā)），公差規(guī)格，過程序列，定位點和設(shè)計等因素外，還應(yīng)投入CAD模型到夾具設(shè)計方法中。這樣的夾具可以夾緊并支撐定位器。指導(dǎo)使用的主要內(nèi)容應(yīng)盡量不抵制切割或加工過程和中所涉及的操作。相反，應(yīng)定位夾具，使切削力在正確的方向，這將有助于保持在一個特定的部分加工操作安全。通過引導(dǎo)對定位器的切割力量，部分（或工件）被固定，固定定位點，因此不能移動的定位器。
在這里討論的夾具的設(shè)計方法必須在整體夾具設(shè)計方法的范圍內(nèi)。在此之前進行定位器/支撐和夾具設(shè)計的初步階段，涉及到的分析和識別的功能、相關(guān)的公差和其他規(guī)范是必要的。根據(jù)初步的評估和測定，定位/支撐設(shè)計與夾具設(shè)計結(jié)果的在此基礎(chǔ)上可以同時進行。本文對所描述夾具設(shè)計的方法討論基于定位器/支撐設(shè)計與先前已經(jīng)確定的假設(shè)（包括適當?shù)亩ㄎ缓椭С譁y定一個工件的定位，以及識別和夾具，如V元素的支持面塊，基礎(chǔ)板，定位銷等）。
（1） 夾具設(shè)計的輸入
輸入包括對特定產(chǎn)品的設(shè)計翼邊模型，公差信息，提取的特征，過程順序和部分在給定的每一個設(shè)計的相關(guān)特性的加工方向，面向的位置和定位裝置，以及加工過程中的各種工序，須出示每個相應(yīng)的功能。
（2）夾具設(shè)計的方法
圖一是自動化夾具設(shè)計主要步驟總結(jié)圖。對這些步驟概述如下：
第1步：設(shè)置配置清單以及相關(guān)的[進程_功能]條目。
第2步：確定方向和夾緊力。輸入必要的加工方向向量mdv1，mdv2……mdvn，面對nvs的支持力，并確定法向量。如果加工方向向下（對應(yīng)的方向向量[0，0，-1]），和面的支持向量平行于加工方向，那么，夾緊力方向平行向下加工方向[0，0，-1]。如果必需要側(cè)面夾緊并沒有可夾緊的地方，那么在其中放置一個夾具夾緊下調(diào)，然后邊鉗方向計算如下。讓sv和tv輔助常規(guī)的向量代替次要的和三級定位孔。然后，使用夾緊機構(gòu)夾緊一個方向，例如，av應(yīng)平行于這兩個法向量，即，正常向量應(yīng)分別與每塊表面的sv和tv向量平行。側(cè)面夾緊面應(yīng)該是一對分別平行于面sv和tv的平面孔。
第三步：從列表中選出最大有效加工力。這樣能夠有效的平衡各加工力。
第四步：利用計算出的最高有效加工力，才能確定用來支撐工件加工的面積的夾具尺寸（例如，一個帶夾子可以作為一個夾緊機構(gòu)使用）。
第五步：確定給定工件的夾緊面。這一步在第4步中所述過。
第六步：該夾具的夾緊面的實際位置自動在第5節(jié)中確定。考慮接下來的步驟并返回第一步。
3. 判斷夾具尺寸
在這項工作中所用到的夾具都來自一個系列。夾具的原理與圖二相同。在這一節(jié)里，描述了一個自動化夾具。鎖模力所需的有關(guān)螺桿的螺紋裝置大小或保存到位鉗。夾緊力平衡加工工件使工件保持恰當?shù)奈恢?。讓鎖模力為W和螺桿直徑為D。各種螺絲夾緊力大小，可以按以下方式確定：最初，極限拉伸強度（抗拉強度）和該夾具的材料（供應(yīng)情況而定）可以從數(shù)據(jù)檢索庫檢索。各種材料有不同的拉伸強度。該夾具材料的選擇，也可直接采用啟發(fā)式規(guī)則進行。例如，如果部分材料是低碳鋼，那么鉗材料可低碳鋼或機器鋼。為了確定設(shè)計應(yīng)力，抗拉強度值應(yīng)除以安全系數(shù)（如4或5）。根區(qū)的螺絲格A1（如一個螺絲鉗）可以被確定：[鎖模力/設(shè)計應(yīng)力]。隨后，螺栓截面全面積可以計算為等于{格A1 /（65％），}（因為螺絲的地方可能會發(fā)生根切面積約為65％螺栓的總面積） 。螺釘?shù)闹睆紻可以被確定等同于（D2的3.14 / 4）。另一項涉及可用于方程有關(guān)的寬度B，高度H和跨度的鉗L的螺絲直徑為D（B，H和L可以為不同的值計算D）：d2 =4/3 BH2/L.
4. 判斷夾緊表面
確定夾具經(jīng)常出現(xiàn)的相關(guān)參數(shù)包括了產(chǎn)品的CAD模型，提取的特征信息，特征尺寸，定位面和定位器的選擇?？紤]所有潛在的加緊面，如圖3。最關(guān)鍵的是夾緊表面不應(yīng)重疊或與該面相交，如圖4所示。夾緊面積是與工件表面（或PCF）接觸的是一個二維輪廓線段組成的（見圖6）。利用線段相交測試，可以測定在給定的光子晶體光纖的任何范圍內(nèi)是否可能有接觸面夾緊面重疊。
夾緊面的確定可以如下所示：
第1步：鑒別平行于二級和三級定位面（lf1和lf2）是分別到lf1和tcj最遠的距離的面。如下所示：（一）鑒別面tci,tcj,使面tci和 tcj平行l(wèi)f1和tcj平行l(wèi)f2。（二）在TCF中列出面對tci的面。（三）通過檢查所有TCF中面對tci的面，確定的面對tci和tcj的面是到lf1和lf2分別最遠的面，并舍棄所有其他TCF中的面。
第2步：鑒別平行面的位置，除了不相鄰的附加面。最好是選擇一個不與其他定位面垂直相鄰的面。這一步如下所示：
(a) 考慮TCF列表中的tci面，獲得與每個tci面垂直或相鄰的面然后，在FCF列表中插入每個fci面。
(b) 檢查每個FCI面，并執(zhí)行以下測試：如果FCI是相鄰、垂直于lf1或lf2，然后從列表中舍棄它并插入NTCF列表中。
第3步:確定加緊面都在有效的加緊面上，如下所述夾緊面：
例1:如果沒有條目在列表NTCF中，就使用TCF中的面并繼續(xù)執(zhí)行步驟4。如果任何面發(fā)現(xiàn)，垂直于第二，第三位置的面孔lf1和lf2，這將要面臨的是下次選擇可行的夾具。在這種情況下，唯一剩下的選擇是重新審視在列表NTCF的面。
例2：如果列表中NTCF條目數(shù)為1時，可行夾緊面為FCI。與TCI的法向量垂直相鄰的相應(yīng)軸是夾緊軸。
例3：如果在列表NTCF項數(shù)大于1，確定最大的TCI加緊面再進行步驟4。
例4：:夾緊力的方向可以是[1，0，0]或[0，1，0]，可以夾緊TCI面的中心位置。
在其他幾何位置可確定使用零件幾何形狀和拓撲信息，這在下一節(jié)中描述。
5. 判斷夾緊表面上的夾緊點
確定夾緊面后，必須確定實際夾緊位置。輸入夾具側(cè)面積，沿著[x，Y，Z]和潛在的夾緊面CF方向。容下使用CF幾何獲得夾具側(cè)面積：
第一步是確定一個箱體的大小，這是用來測試它是否包含在它里面的任何部分。相交測試也可以在前面介紹的方法使用。如果相交測試返回一個負的結(jié)果，那么有部分箱體與夾具相交，如圖4所示。如果相交測試返回一個正的結(jié)果，可以執(zhí)行下列步驟：
1． 劃分成更小的矩形大小條（1 W）夾框輪廓(圖5和圖6)。
2． 執(zhí)行指定與功能配置文件出現(xiàn)在CF面的零件設(shè)計的相交測試。
3． 沒有功能相交的條形區(qū)域，都是可行夾緊區(qū)域。如果有一個以上的長方形候選
面，矩形配置文件，向中沿軸夾緊CF面點的是夾緊配置文件（夾點）。
如果沒有發(fā)現(xiàn)配置文件，夾具寬度可減少一半，夾具數(shù)可以增加兩個。使用這些修改過的夾具尺寸，執(zhí)行前面描述的特征相交測試。如果此測試也失敗了，那么可以用相鄰的面作為夾緊面用于執(zhí)行端夾緊。這面可以重復(fù)進行PCF和功能相交測試。
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5.1試驗曲線的交點
輸入需要的二維輪廓P1、P2，使用下列方法可以自動確定該配置文件的交集。每一個輸入的資料組成一個封閉環(huán)。此配置文件測試的步驟如下：
(T1) 考慮P1線段中的L（i，1）和P2線段中的L（2，j）。
(T2) 采用L（i，1）線段和L（2，j）線段的相交段。如果邊緣相交測試返回一個正值，那么特征面和潛在面相交。如果它返回一個負值，繼續(xù)執(zhí)行步驟3。
（T3）重復(fù)與步驟（T1）相同的部分或者緩慢走過其余P1中的(Li,1)段直到P2中的 [(L2, j+1) till j =n–1]段。
(T4) 其余部分邊和P1中的L12、L13到L1n段重復(fù)（T1）和（T2）步驟。
如果特征面與夾緊面重復(fù)，線相交測試將決定該事件。相交的邊可以進行自動檢測兩個面是否相互交叉。輸入所需的邊L12{連接 (x1, y1) 和 (x2, y2)}和L34{連接 (x3, y3) 和(x4, y4)}。
L12型方程的可表示為：
F(x,y) =0 (1)
L34型方程的可表示為：
H(x,y) =0 (2)
. 第一步：使用等式（1）計算R3 =F(x3, y3)，用X和Y取代X3和Y3;計算R4 =F(x4, y4)，用X和Y取代X4和Y4。
第二步：如果R3和R4都與0不相等，但R3與R4結(jié)果相同（R1與R2在相同的一邊），則邊L12與L34不相交。如果這樣不滿足條件，那么進行第三步。
第三步：使用等式（2）計算R1 =H(x1, y1)。接著，計算R2 =G(x2, y2)再進行第四步。
第四步：如果R1與R2都不等于0，且R1與R2的結(jié)果相同，那么把R1與R2放在相同的一邊并輸入不相交。如果，這個也不滿足條件，那么進行第五步。
第五步：給定相交線段。這樣就完成了測試?？紤]如圖7所示的一部分樣品。將要生產(chǎn)一個盲孔。起初，完成定位設(shè)計。定位器的（或主要定位器）是一個基盤（放在F4面）和二級和三級定位器面臨F6和F5（對應(yīng)到定位面lf1和lf2在第4節(jié)中討論）。一個輔助定位器也被使用，這是一個V型塊（對F3和F5面輔助定位），如圖8所示。在前面討論的夾具設(shè)計方法中所述的步驟的基礎(chǔ)上，候選面孔（這是平行的，并在從lf1和lf2最遙遠的距離）是面對F3和F5面。沒有面孔，這是平行到定位面，但他們不相鄰。在這種情況下使用的優(yōu)先權(quán)規(guī)則（如步驟3第4步討論），剩余的候選面面對的是F2面。夾具方向向下的V型塊徑向定位器和其他與對工件夾緊底面提供所需位置。
根據(jù)第五步選擇夾具的位置。如果沒有功能發(fā)生在面F2上，那么也沒有必要進行相交測試確定夾具優(yōu)美加緊。夾具位置應(yīng)遠離V型定位器（這是輔助定位位置）的夾緊面毗鄰輔助定位面（這確保了更好的快速夾緊）。最終位置和夾具的設(shè)計如圖8所示。
本文討論的方法，毫不遜色于其他夾具設(shè)計文獻中討論的方法。本文所討論的方法的獨特性是零件的夾緊面的幾何形狀，拓撲和功能發(fā)生了被加工為基礎(chǔ)的系統(tǒng)鑒定。其他方法都沒有利用了定位器的位置，該方法使用定位器在對持有一級，二級和三級定位器加工的工件。這種方法的另一個好處是在可行的候選面上確定在面上用夾具面交點測試（如前所述），并迅速和有效地確定潛在的下游過程中可能出現(xiàn)問題，夾緊和加工的功能檢測。
6. 總結(jié)
在這篇論文中，對在一個夾具設(shè)計方法的總體框架內(nèi)進行了夾具設(shè)計方面的討論。
設(shè)計定位器，規(guī)范零件設(shè)計，和其他相關(guān)被用來確定夾緊面和夾緊方向。并討論了各種自動化步驟。
Int J Adv Manuf Technol (2001) 18:784789 2001 Springer-Verlag London LimitedA Clamping Design Approach for Automated Fixture DesignJ. CecilVirtual Enterprise Engineering Lab (VEEL), Industrial Engineering Department, New Mexico State University, Las Cruces, USAIn this paper, an innovative clamping design approach isdescribed in the context of computer-aided fixture design activi-ties. The clamping design approach involves identification ofclamping surfaces and clamp points on a given workpiece.This approach can be applied in conjunction with a locatordesign approach to hold and support the workpiece duringmachining and to position the workpiece correctly with respectto the cutting tool. Detailed steps are given for automatedclamp design. Geometric reasoning techniques are used todetermine feasible clamp faces and positions. The requiredinputs include CAD model specifications, features identified onthe finished workpiece, locator points and elements.Keywords: Clamping; Fixture design1.Motivation and ObjectivesFixture design is an important task, which is an integration linkbetween design and manufacturing activities. The automation offixture design activities and the development of computer-aidedfixture design (CAFD) methodologies are key objectives to beaddressed for the successful realisation of next generationmanufacturing systems. In this paper, a clamp design approachis discussed, which facilitates automation in the context of anintegrated fixture design methodology.Clamp design approaches have been the focus of severalresearch efforts. The work of Chou 1 focused on the twincriteria of workpiece stability and total restraint requirement.The use of artificial intelligence (AI) approaches as well asexpert system applications in fixture design has been widelyreported 2,3. Part geometry information from a CAD modelhas also been used to drive the fixture design task. Bidanda4 described a rule-based expert system to identify the locatingand clamping faces for rotational parts. The clamping mech-anism is used to perform both the locating and clampingCorrespondence and offprint requests to: Dr J. Cecil, Virtual EnterpriseEngineering Lab (VEEL), Industrial Engineering Department, NewMexico State University, Las Cruces, NM 88003, USA. E-mail:jcecil?nmsu.edufunctions. Other researchers (e.g. DeVor et al. 5,6) haveanalysed the cutting forces and built mechanistic models fordrilling, and other metal cutting processes. Kang et al. 2defined assembly constraints to model spatial relationshipsbetween modular fixture elements. Several researchers haveemployed modular fixturing principles to generate fixturedesigns 2,711.Other fixturedesign effortshave beenreported in 1,3,9,1223. An extensive review of fixture designrelated work can be found in 21,24.In Section 2, the various steps in the overall approach toautomate the clamping design task are outlined. Section 3describes the determination of the clamp size to hold a work-piece during machining and in Section 4, the automatic determi-nation of the clamping surface or face region on a workpieceis detailed. Section 5 discusses the determination of the clamp-ing points on a workpiece.2.Overall Approach to Clamp DesignIn this section, the overall clamping design approach isdescribed. Clamping is usually carried out to hold the part ina desired position and to resist the effects of cutting forces.Clamping and locating problems in fixture design are highlyrelated. Often, the clamping and locating can be accomplishedby the same mechanism. However, failure to understand thatthese two tasks are separate aspects of fixture design may leadto infeasible fixture designs. Human process planners generallyresolve the locating problem first. The approach developed canwork in conjunction with a locator design strategy. However,the overall locator and support design approach is beyond thescope of this paper.CAD models of the part design (for which the clamp designhas to be developed), the tolerance specifications, processsequence, locator points and design, among other factors, arethe inputs to the clamp design approach. The purpose ofclamping is to hold the parts against locators and supports.The guiding theme used is to try not to resist the cutting ormachining forces involved during a machining operation.Rather, the clamps should be positioned such that the cuttingforces are in the direction that will assist in holding the partsecurely during a specific machining operation. By directingA Clamping Design Approach785the cutting forces towards the locators, the part (or workpiece)is forced against solid, fixed locating points and so cannotmove away from the locators.The clamp design approach discussed here must be viewedin the context of the overall fixture design approach. Priorto performing locator/support and clamp design, a prelimi-nary phase involving analysis and identification of features,associated tolerances and other specifications is necessary.Based on the outcome of this preliminary evaluation anddetermination, the locator/support design and clamp design canbe carried out. The clamp design approach described in thispaper is discussed based on the assumption that locator/supportdesign attributes have been determined earlier (this includesdetermination of appropriate locator and support faces on aworkpiece as well as identification of locator and supportfixturing elements such as V-blocks, base plates, locatingpins, etc).2.1Inputs to Clamp DesignThe inputs include the winged-edge model of the given productdesign, the tolerance information, the extracted features, theprocess sequence and the machining directions for each of theassociated features in the given part design, the location facesand locator devices, and the machining forces for the variousprocesses required to produce each corresponding feature.2.2Clamp Design StrategyThe main steps in the automation of the clamping design taskare summarised in Fig. 1. An overview of these steps isas follows:Step 1. Consider the set-up SUi in the set-up configuration listalong with the associated process ? feature entries.Step 2. Identify the direction and type of clamping. The inputsrequiredarethemachiningdirectionvectorsmdv1,mdv2,. . .,mdvn and identified normal vectors of support face nvs. Ifthe machining directions are downward (which correspond tothe direction vector 0, 0, 1), and the normal vector of thesupport face is parallel to the machining direction, then thedirection of clamping is parallel to the downward machiningdirection 0, 0, 1. If sideways clamping is required, and ifthere are no feasible regions at which to position a clamp fordownward clamping, then a side-clamp direction is obtainedas follows. Let sv and tv be the normal vectors of the secondary(sv) and tertiary (tv) locating faces. Then, the direction ofclamping used by a side-clamping mechanism such as a v-block should be parallel to both these normal vectors, i.e. thenormal vectors of the each of the v-surfaces in the v-blockwill be parallel to sv and tv, respectively. The side clampingface should be a pair of faces parallel to the faces sv andtv, respectively.Step 3. Determine the highest machining force from the mach-ining forces list (for each feature) MFi (i = 1, . . .,n). This willbe the effective force FE that must be balanced while designingthe clamp for this set-up SUi.Step 4. Using the value of the calculated highest machiningforce FE, the dimensions of the clamp to be used to hold theFig. 1. The clamp design activities.workpiece can be determined (for example, a strap clamp canbe used as a clamping mechanism). The approach for this taskis explained in Section 3.Step 5. Determine the clamping face on a given workpiece.This step can be automated as described in Section 4.Step 6. The actual position of the clamp on the clampingface is determined in an automated manner as explained inSection 5.Consider next set-up SU(i + 1) and proceed to step 1.3.Determination of the Clamp SizeIn this work, the clamps used belong to the family of clampsreferred to as strap clamps. A strap clamp is based on thesame principle as that of the lever (see Fig. 2). In this section,the automated design of a strap clamp is described. Theclamping force required is related to the size of the screw ora threaded device that holds the clamp in place. The clampingforce should balance the machining force to hold the workpiecein position. Let the clamping force be W and the screwdiameter be d. The dimensions of the various screw sizes forvarious clamping forces can be determined in the followingmanner. Initially, the ultimate tensile strength (UTS) of thematerial of the clamp (depending on availability) can beretrieved from a data library. Various materials have differenttensile strengths. The selection of the clamp material can alsobe performed directly using heuristic rules. For example, if thepart material is mild steel, then the clamp material can be low786J. CecilFig. 2. The strap clamp.carbon steel or machine steel. To determine the design stress,the UTS value can be divided by a safety factor (such as 4or 5). The root area A1 of the screw (for a clamp such asa screw clamp) can then be determined: Clamping forcerequired/Design Stress DS. Subsequently, the full area FA ofthe bolt cross-section can be computed as equal to A1/(65%)(since the root area of the screw where shearing can occur isapproximately 65% of the total area of the bolt). The diameterof the screw d can then be determined by equating FA to(3.14 d2/4). Another equation which can be used involvesrelating the width B, height H and span L of the clamp to thescrew diameter d (B, H, and L can be computed for variousvalues of d): d2= 4/3 BH2/L.4.The Determination of the ClampingFaceThe required inputs to determine the clamping region includethe CAD model of the product, the extracted features infor-mation, the feature dimensions and faces on which they occur,the locating faces and locators selected. Consider a potentialclamping face PCF as shown in Fig. 3. The crucial criterionto be satisfied is that the clamping surface should not overlapor intersect with the features on that face, as shown in Fig. 4.The clamping surface area, which is in contact with theworkpiece surface (or PCF) is a 2D profile consisting of linesegments (see Fig. 6). By using line segment intersection tests,it can be determined whether the potential clamping area ofcontact overlaps any of the features on the given PCF.The determination of clamping faces can be automated as fol-lows:Fig. 3. Potential clamping face and feature profiles.Fig. 4. Potential clamping face and clamp box profile.Step 1. Identify faces that are parallel to the secondary andtertiary locator faces (lf1 and lf2) and at the farthest distancefrom lf1 and tcj, respectively. This is performed as shownbelow:(a)Identify faces tci, tcj such that tci is parallel to lf1 andtcj is parallel to lf2.(b)Insert candidate faces tci in list TCF.(c)By examining all faces tci listed in TCF, determine facestci and tcj that are farthest from face lf1 and lf2, respect-ively, and discard all other faces from list TCF.Step 2. Identify the face that is parallel to the location facesbut not adjacent to the additional locator faces. It is preferableto select a clamp face that does not have to share the adjacentperpendicular face with a locator. This step can be automatedas shown below:(a)Consider each face tci in list TCF and obtain correspond-ing faces fci that are adjacent and perpendicular to eachtci. Then, insert each face fci in list FCF.(b)Examine each fci and perform the following test:If fci is adjacent, perpendicular to lf1 or lf2,then discard it from list FCF and insert it in list NTCF.Step 3. Determine the clamping faces, based on the availabilityof potential clamping faces, as described below.Case (a). If there are no entries in list NTCF, then use thefaces in list TCF and proceed to step 4. If any faces werefound that were perpendicular to the secondary and tertiarylocation faces lf1 and lf2, such faces are the next feasiblechoices to be used for clamping.In this case, the only remaining choice is to re-examine thefaces in list NTCF.Case (b). If the number of entries in list NTCF is 1, thefeasible clamping face is fci. The normal vector of thecorresponding adjacent, perpendicular face tci is the axis ofclamping.Case (c). If number of entries in list NTCF is greater than 1,determine the face tci with larger area and proceed to step 4.Step 4. Depending on the direction of clamping which is either(+ or )1, 0, 0 or (+ or ) 0, 1, 0, the clamp can bepositioned along the centre of the face tci. The candidategeometrical positions of the clamp can be determined usingpart geometry and topological information, which is describedin the next section.A Clamping Design Approach787Fig. 5. Determination of the clamp profile dimensions.5.Determination of the Clamping Pointson a Clamping FaceAfter the clamp face has been determined, the actual clampingpositions on that face must be determined. The inputs are theclamp profile dimensions, clamp directions x, y, z, and poten-tial clamping face CF. The clamp profile dimensions areobtained (as in case (g) using CF geometry as follows.The first step is to determine a box size, which is tested todetermine whether it contains any features inside it. Profileintersection tests can also be performed using the methoddescribed earlier. If the intersection test returns a negativeresult, then no feature intersects with the clamp box profile,as shown in Fig. 4. If the intersection test returns a positiveresult, the following steps can be performed:1. Divide the clamp box profile into smaller rectangular stripsof size (1 w) (Figs 5 and 6).2. Perform the intersection tests with the feature profiles offeatures that occur on the face CF for the given part design.Fig. 6. Profiles intersection test of feature and clamp regions.3. The rectangular strips, where no feature intersection occurs,are feasible clamping regions. If there is more than onecandidate rectangle for clamping, the rectangle profile thatis toward the mid-point of the CF face along the clampingaxis is the clamp profile (and clamp points).If no profile Pi can be found that does not intersect with thefeature profiles, clamp width can be reduced by half and thenumber of clamps increased to two on that face. Using thesemodified clamp dimensions, perform the feature intersectiontest described earlier. If this test also fails, then the side faceadjacent to the PCF can be used as the clamping surface toperform side clamping. The side face then becomes the PCFand the feature intersection test can be repeated.5.1The Intersection of Profiles TestThe required inputs include the 2D profile P1 another 2Dprofile P2. The intersection of profiles can be determined inan automated manner using the following approach. Each inputprofile Pi consists of a closed loop of line segments Lij. Thesteps in this profile test are as follows:(T1) Consider a line segment L(i,1) in P1 and another linesegment L(2, j) in P2.(T2) For inputs L(i,1) and L(2, j), the intersection of edgescan be employed. If the edge intersection test returns a positivevalue, then the feature profile intersects with the candidate orpotential clamp profile under evaluation. If it returns a negativevalue, proceed to step 3.(T3) Repeat step (T1) for the same segment or edge (Li,1) inP1 with all remaining segments (L2, j+1) till j = n1 in P2.(T4) Repeat steps (T1) and (T2) for the remaining edges orsegments L12, L13,. . .,L1n in profile P1.If the feature profiles overlap the clamping profiles, the lineintersection tests will determine that occurrence. The inter-section of edges test can be performed automatically to detectwhether two edges intersect with each other. The inputsrequired for this test are the line segments L12 connecting(x1, y1) and (x2, y2) and L34 connecting (x3, y3) and(x4, y4).Let the equation of L12 be represented by:F(x,y) = 0(1)and that of L34 by:H(x,y) = 0(2)Step 1. Using Eq. (1) compute r3 = F(x3, y3) by substitutingx3 and y3 for x and y and compute r4 = F(x4, y4) by substitut-ing x4 and y4 for x and y.Step 2. If r3 is not equal to 0, r4 is not equal to 0, and thesigns of r3 and r4 are the same, (which indicate r1 and r2lie on same side), then the edges L12 and L34 do not intersect.If this is not satisfied, then step (3) is performed.Step 3. Using Eq. (2), compute r1 = H(x1, y1). Then, computer2 = G(x2, y2) and proceed to step 4.Step 4. If r1 is not equal to zero, r2 is not equal to zero, andthe signs of both r1 and r2 are the same , then r1, r2 lie on788J. CecilFig. 7. Sample part to illustrate the clamping design approach.the same side and the input line segments do not intersect.Else, if this condition is not satisfied, proceed to step 5.Step 5. The given line segments do intersect. This completesthe test.Consider the same sample part shown in Fig. 7. The featuresto be produced are a step and hole. Initially, the locator designis completed. The support locator (or primary locator) is abase plate (placed against face f4) and the secondary andtertiary locators are placed against faces f6 and f5 (whichcorrespond to the locator faces lf1 and lf2 discussed in Section4). An ancillary locator is also used, which is a v-block(positioned against the ancillary faces f3 and f5), shown inFig. 8. Based on the steps outlined in the clamp designFig. 8. Fixture design for the sample part in Fig. 7.approach discussed earlier, the candidate faces (which areparallel and at the farthest distance from lf1 and lf2) are facef3 and f5. There are no faces which are parallel to the locatorfaces but not adjacent to them. Using the priority rules in suchcases (as discussed in step 3 of Section 4), the remainingcandidate face is face f2. The clamp direction is downward;the v-block radial locator and other locators provide therequired location with the clamp holding the workpiece down-ward against the baseplate.The position of the clamp is determined based on the stepsdescribed in Section 5. As there are no feaures occurring onface f2, there is no need for feature intersection tests todetermine collision-free clamping. The position of the clampshould be away from the v-locator (which is positioned alongthe ancillary location faces) as the clamping face is adjacentto the ancillary location faces (this ensures better access forquick clamping). The final location and clamping design isshown in Fig. 8.The method discussed in this paper compares favourablywith the other clamp design methods discussed in the literature.The uniqueness of the discussed approach is the systematicidentification of the clamping faces based on part geometry,topology, and the occurrence of features to be machined. Whileother approaches have not exploited the position of the locatorsadequately, the proposed method uses the locators to hold theworkpiece during machining against the primary, secondary,and tertiary locators. Another advantage of this approach isthe determination of candidate feasible locations on clampfaces using the detection of profile intersections test (describedearlier), which quickly and efficiently identifies potential down-stream problems which may occur during clamping and mach-ining of features.6.ConclusionIn this paper, the clamping design aspects in the overall contextof a fixture design methodology was discussed. The locatordesign, the part design specifications, and other inputs areconsidered in identifying the clamping faces and directions.The various steps to automate this approach are also discussed.References1. Y. C. Chou, V. Chandru and B. Barash, “A mathematical approachto automatic configuration of machining fixtures: analysis andsynthesis”, Transactions ASME, Journal of Engineering for Indus-try, 111(4), pp. 299306, 1989.2. Y. Kang, Y. Rong and M. Sun, “Constraint based modular fixtureassembly modelling and automated design”, Proceedings of theASMEManufacturingScienceandEngineeringDivisio
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