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系主任 批準(zhǔn)日期 茂 名 學(xué) 院 畢 業(yè) 設(shè) 計（論 文）任 務(wù) 書 機(jī)電工程 系 機(jī)械設(shè)計制造及其自動化 專業(yè) 04-2 班 學(xué)生 周宏霄 一、畢業(yè)設(shè)計(論文)課題 車床撥叉上螺紋底孔加工鉆床夾具的設(shè)計 二、畢業(yè)設(shè)計(論文)工作自 2008 年 3 月 17 日起至 2008 年6月 20 日止 三、畢業(yè)設(shè)計(論文)進(jìn)行地點(diǎn) 茂名學(xué)院機(jī)電工程學(xué)院 四、畢業(yè)設(shè)計(論文)的內(nèi)容要求 　　　　 (一)已知條件： 　　　　　 （1）、被加工零件的工序圖 （2） 成批生產(chǎn) (二)、主要內(nèi)容及要求： 　　 （1）、按要求寫出開題報告；　　　　　　　　　　　　　　　　　　　　　　　 （2）、結(jié)合課題到工廠進(jìn)行畢業(yè)實(shí)習(xí)；　　　　　　　　　　　　　　　　　　　 （3）、收集國內(nèi)外有關(guān)情報資料，查閱文獻(xiàn)資料15篇以上；　　　　　　　　　　 （4）、翻譯不少于5000字的英語科技文獻(xiàn)；　　　　　　　　　　　　　　　　　 （5）、研究形成總體方案；　　　　　　　　 　　　 （6）、設(shè)計繪制出夾具的總裝工作圖；　 　　　　　　　　　　　 （7）、繪制出主要零件圖；　　　　　　 　　　　　　　　　　　　　　　　　　 （8）、按學(xué)校規(guī)定格式編寫出不少于20000字的設(shè)計計算說明書（含文獻(xiàn)綜述）； （9）、準(zhǔn)備和參加畢業(yè)答辯?！　　　　　　　　　　　　　　　　　　　　　　? (三)、主要參考資料：　　　　　　　　　　　　　　　　　　　　　　　　　 （1）機(jī)床夾具圖冊P8 孟憲棟等主編　　機(jī)械工業(yè)出版社 　　　　　　 （2）巧改機(jī)床 陳榕林 張 磊 編著中國農(nóng)業(yè)機(jī)械化出版社；　　　　　　　　　 （3）金屬切削機(jī)床 上、下冊 顧熙棠等主編 上海科技出版社；　　　　　　　　 （4）組合機(jī)床設(shè)計手冊 機(jī)械工業(yè)出版社；　　　　　　　　　　　　　　　　　 （5）組合機(jī)床設(shè)計圖冊 機(jī)械工業(yè)出版社；　　　　　　　　　　　　　　　　　 （6）機(jī)電傳動與控制 鄧星鐘等 華中理工大學(xué)出版社；　　　　　　　　　　　 （7）新編機(jī)械設(shè)計手冊 徐灝 機(jī)械工業(yè)出版社；　　　　　　　　　　　　　　 （8） 機(jī)械可靠性設(shè)計 劉惟信主編 機(jī)械工業(yè)出版社；　　　　　　　　　　　　 （9） 機(jī)械設(shè)計手冊 機(jī)械工業(yè)出版社； （10） 機(jī)床夾具設(shè)計 龔定安等 西安交通大學(xué)出版社 　　 （11） 機(jī)床夾具設(shè)計 李慶壽 機(jī)械工業(yè)出版社 　　 （12）單獨(dú)驅(qū)動的回轉(zhuǎn)分度工作臺 組合機(jī)床（1985）7 總137期P19 （13） 機(jī)床設(shè)計圖冊 華東五高校編 華東科技大學(xué)出版社 （14） 機(jī)電一體化系統(tǒng)設(shè)計手冊 楊黎明 主編 國防工業(yè)出版社； 　　 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 教研室負(fù)責(zé)人 指導(dǎo)教師 王安民（教授） 接受設(shè)計論文任務(wù)開始執(zhí)行日期 2008 年 1 月 7 日 學(xué)生簽名 畢業(yè)設(shè)計（論文） 開題報告 題目 車床撥叉上螺紋底孔加工鉆床夾具的設(shè)計 The Design of the Drilling Machine Fixture for Processing Lathe Shifting Fort Upper Thread Bottom Hole 學(xué)院 茂名學(xué)院 年級 2004級 專業(yè) 機(jī)械設(shè)計制造及自動化 學(xué)號 04024020240 姓名 周宏霄 指導(dǎo)教師 王安民（教授） 2008年3 月 25 日 畢業(yè)設(shè)計（論文）開題報告 題目 車床撥叉上螺紋底孔加工鉆床夾具的設(shè)計 時間 2008 年3月17日至 2008年 6月10日 本課題的目的意義 （含國內(nèi)外的研究現(xiàn)狀分析） 機(jī)床夾具是機(jī)械制造工藝系統(tǒng)重要的組成部分，其質(zhì)量的高低直接影響到零件制造的質(zhì)量、工人的勞動強(qiáng)度、產(chǎn)品成本和生產(chǎn)率。通過機(jī)床夾具的設(shè)計著重培養(yǎng)同學(xué)們的設(shè)計、計算、分析問題和解決問題的能力，綜合運(yùn)用計算機(jī)繪圖能力、表達(dá)技術(shù)問題的能力以及開拓創(chuàng)新的能力等。通過本夾緊機(jī)構(gòu)的設(shè)計進(jìn)而掌握一般機(jī)床夾具的一般方法、步驟和技巧，從而達(dá)到掌握一般機(jī)械的設(shè)計方法和技巧，使同學(xué)們綜合運(yùn)用所學(xué)的知識解決工程實(shí)際問題。 機(jī)床夾具是用以裝夾工件和引導(dǎo)刀具的附加裝置。主要用于金屬切削加工，在機(jī)床與ＳＳ工件、刀具之間起橋梁作用，是工藝系統(tǒng)中的一個重要環(huán)節(jié)。它可準(zhǔn)確地確定工件與刀具、機(jī)床的相對位置，確保加工質(zhì)量；它可以提高生產(chǎn)效率，確保勞動強(qiáng)度；它可以擴(kuò)大或改變機(jī)床的使用范圍等。因此，機(jī)床夾具是保證機(jī)械加工工藝過程正常進(jìn)行的技術(shù)硬件之一。 綜上所訴，需要對零件進(jìn)行加工工藝設(shè)計和機(jī)床夾具設(shè)計。 設(shè)計(論文)的基本條件及設(shè)計(論文)依據(jù) 已知條件：車床撥叉零件圖和鉆削工序圖各1張，中批生產(chǎn)。 設(shè)計工藝過程的主要依據(jù) (1) 根據(jù)加工對象的尺寸公差、形狀和位置公差、表面粗糙度、技術(shù)要求、工件材料、毛坯類型、熱處理與表面保護(hù)等要求來設(shè)計工藝過程。 (2) 根據(jù)給定的生產(chǎn)量大小來確定工藝過程。 (3) 根據(jù)本單位的先有生產(chǎn)條件，注意充分發(fā)揮現(xiàn)場技術(shù)條件手段和技術(shù)力量的潛力來設(shè)計工藝過程。 本課題的主要內(nèi)容、 重點(diǎn)解決的問題 主要內(nèi)容及要求: (1)查閱設(shè)計資料和進(jìn)行參觀補(bǔ)習(xí)； (2)夾具的方案設(shè)計； (3)夾具總裝配圖設(shè)計； (4)夾具主要零件圖的繪制； (5)夾具可行性分析； (6)編寫設(shè)計計算說明書； (7)外文翻譯（不少于5000字符）； (8)準(zhǔn)備和參加答辯。 重點(diǎn)解決問題:在保證零件加工質(zhì)量前提下,提高生產(chǎn)效率,降低消耗,以取得較好的經(jīng)濟(jì)效益和社會效益. 本課題欲達(dá)到的目的 或預(yù)期研究的結(jié)果 其主要目的： 1）、培養(yǎng)學(xué)生綜合分析和解決本專業(yè)的一般工程技術(shù)問題的獨(dú)立工作能力，拓寬和深化學(xué)生的知識；2）、培養(yǎng)學(xué)生樹立正確的設(shè)計思想，設(shè)計構(gòu)思和創(chuàng)新思維，掌握工程設(shè)計的一般程序規(guī)范和方法；3）培養(yǎng)學(xué)生樹立正確的設(shè)計思想和使用技術(shù)資料、國家標(biāo)準(zhǔn)等手冊、圖冊工具書進(jìn)行設(shè)計計算，數(shù)據(jù)處理，編寫技術(shù)文件等方面的工作能力；4）培養(yǎng)學(xué)生進(jìn)行調(diào)查研究，面向?qū)嶋H，面向生產(chǎn)，向工人和技術(shù)人員學(xué)習(xí)的基本工作態(tài)度，工作作風(fēng)和工作方法。 計 劃 進(jìn) 度 時 間 工 作 內(nèi) 容 備 注 2008.3.17~2008.3.30 2007.4.31~2007.4.20 2007.4.21~2007.5.4 2007.5．5~2007.5.18 2007.5．19~2007.6.8 設(shè)計題目資料收集、寫開題報告 工藝過程規(guī)劃 工序設(shè)計與夾具方案的確定 夾具設(shè)計與繪制裝配圖及零件圖 畢業(yè)論文的撰寫整理及排版打印 指 導(dǎo) 教 師 意 見 指導(dǎo)教師簽名： 年 月 日 I 摘 要 本課題是車床撥叉上螺紋底孔加工鉆床夾具設(shè)計 而車床撥叉它位于車床變速機(jī) 構(gòu)中 主要起換檔 使主軸回轉(zhuǎn)運(yùn)動按照工作者的要求工作 獲得所需的速度和扭矩 的作用 本設(shè)計中 根據(jù)撥叉尺寸公差 形狀和位置公差 表面粗糙度 技術(shù)要求 工件 材料 毛坯類型 熱處理與表面保護(hù)等要求來設(shè)計 夾具的總體設(shè)計包括從方案制定 到總裝配圖的設(shè)計的全部過程 包括確定工件的定位 選擇或設(shè)計定位元件 計算定 位誤差 確定刀具的導(dǎo)引和對刀方式 選取或色痕跡導(dǎo)引元件或?qū)Φ对?確定工件 的夾緊方式 選擇或設(shè)計夾緊機(jī)構(gòu)或裝置 計算夾緊力 確定夾具體及其他裝置的結(jié) 構(gòu)類型等 通過合理的設(shè)計 在保證零件加工質(zhì)量前提下 提高生產(chǎn)效率 降低消耗 以取得較 好的經(jīng)濟(jì)效益和社會效益 關(guān)鍵詞 夾具 設(shè)計 鉆床 螺紋底孔 II Abstract The topic is The design of the drilling machine fixture for Processing lathe shifting fort upper thread bottom hole and lathe shifting fort located in the lathe speed institutions mainly from the shift so that the spindle rotary movement of workers in accordance with the requirements of work have the necessary speed and torque Role The design based on tolerance shifting fort size shape and location of tolerance surface roughness technical requirements the workpiece material rough type heat treatment and surface protection and other requirements of the design Fixture for the overall design including programming from the assembly to the design of the entire process Including the identification of the workpiece location location choice or design components calculated positioning error determine the tool and guided the knife or select the color traces of knife guided components or components determine the workpiece clamping choice or design clamping Or device calculated clamping force identify specific folders and other devices such as the type of structure Through rational design to ensure the quality of parts processing premise increase production efficiency and reduce consumption to achieve better economic and social benefits Keywords Fixture Design Drilling Machine Thread Bottom Hole 科技譯文 3 目錄 摘 要 I ABSTRACT II 第一章 緒論 1 1 1 背景 1 1 2 夾具的特點(diǎn) 1 1 3 研究夾具的目的和意義 4 1 4 論文構(gòu)成及研究內(nèi)容 4 1 4 1 論文構(gòu)成 4 1 4 2 本設(shè)計的主要內(nèi)容及要求 5 第二章 機(jī)床夾具概述 6 2 1 夾具的現(xiàn)狀及生產(chǎn)對其提出新的要求 6 2 2 夾具的國內(nèi)外現(xiàn)狀和發(fā)展趨勢 6 2 3 現(xiàn)代夾具的發(fā)展發(fā)向 7 2 3 1 精密化 7 2 3 2 高效化 7 2 3 3 柔性化 7 2 3 4 標(biāo)準(zhǔn)化 7 2 4 機(jī)床夾具及其功用 8 2 4 1 機(jī)床夾具 8 2 4 2 機(jī)床夾具的功能 8 2 5 機(jī)床夾具在機(jī)械加工中的作用 8 2 6 機(jī)床夾具組成和分類 9 2 6 1 機(jī)床夾具的基本組成部分 9 2 6 2 機(jī)床夾具的其他組成部分 9 2 7 機(jī)床夾具的分類 10 2 7 1 按夾具的通用特性分類 10 2 7 2 按夾具使用的機(jī)床分類 11 2 8 機(jī)床夾具設(shè)計特點(diǎn) 11 第三章 夾具設(shè)計 12 3 1 夾具設(shè)計概述 12 4 3 1 1 機(jī)床夾具設(shè)計的基本要求和步驟 12 3 1 2 機(jī)床夾具的分類和組成 13 3 1 3 工件安裝與獲得加工精度的方法 13 3 1 4 工件在夾具中的定位原理 14 3 1 5 常見定位方式及定位元件 14 3 1 6 工件在夾具中的夾緊原理 15 3 1 7 確定刀具位置及鉆套的選擇 16 3 1 8 夾具總圖的繪制及標(biāo)注 18 3 1 9 機(jī)床夾具總圖上尺寸的標(biāo)注 19 3 1 10 機(jī)床夾具總圖上技術(shù)條件的標(biāo)注 19 3 1 11 機(jī)床夾具調(diào)刀尺寸的標(biāo)注 20 3 2 夾具設(shè)計 21 3 2 1 問題的提出 21 3 2 2 定位方案 設(shè)計 22 3 2 3 定位元件設(shè)計 23 3 2 4 切削力與夾緊力計算 23 3 2 5 定位誤差計算 23 3 2 6 導(dǎo)向方案選擇 24 3 2 7 導(dǎo)向元件設(shè)計 24 3 2 8 導(dǎo)向誤差計算 24 3 2 9 夾緊裝置的設(shè)計 24 3 2 10 設(shè)計夾具體 25 3 2 11 夾具工作原理 25 3 3 夾具在安裝和操作時應(yīng)注意的事項(xiàng) 25 3 3 1 夾具的安裝 25 3 3 2 夾具在操作時應(yīng)注意的事項(xiàng) 26 3 4 夾具可行性分析 26 3 4 1 夾具的經(jīng)濟(jì)效益分析 26 3 4 2 夾具的可行性 27 第四章 總結(jié) 28 致謝 29 參考文獻(xiàn) 30 科技譯文 31 科技譯文 I 科技譯文 科技譯文 AUTOMATIC FIXTURE SYNTHESIS IN 3D Kamen Penev Programmable Automation Laboratory Computer Science Department and Institute for Robotics and Intelligent Systems University of Southern California Los Angeles CA 90089 0781Aristides A G Requicha Programmable Automation Laboratory Computer Science Department and Institute for Robotics and Intelligent Systems University of Southern California Los Angeles CA 90089 0781 ABSTRACT A fixture is an arrangement of fixturing modules that locate and hold a workpart during a manufacturing operation In this work we consider fixtures with frictionless point contacts and present a method for placement of contact points on a non prismatic 3D workpart It is a non deterministic potential field algorithm for contact point placement The method provides a basic framework for the integration of heterogeneous high level fixturing agents through an interface based on zones of attraction and repulsion on the workpart boundary The algorithm may produce redundant fixtures and can augment partial solutions to complete form closure fixtures 1 INTRODUCTION A fixture is an arrangement of fixturing modules that locate and hold a workpart during a manufacturing operation such as machining assembly and inspection Fixturing is of essential importance to industrial manufacturing and constitutes a significant part of all manufacturing costs Therefore fixture design automation is very important Fixture design involves a great variety of considerations such as restraint deterministic location loadability and tool accessibility Efficient algorithms that address the whole range of fixturing issues for a comprehensive domain of workparts do not yet exist Recently Brost and Peters published an algorithm Brost Peters 1996 that extends the earlier classic work of Brost and Goldberg Brost Goldberg 1994 to the 3D domain This algorithm however requires vertical and horizontal planar surfaces to constitute a substantial part of the workpart boundary It generates all possible fixtures and then rates them accordingly to certain metrics This is computationally expensive Wagner et al presented an algorithm that uses seven modular struts mounted in a box to fixture polyhedra Wagner et al 1995 This algorithm is not complete in the sense that it cannot effectively handle certain cases such as a cube with faces parallel to the box It also suffers from high computational complexity Wallack and Canny suggested another method with an enumerate and rate flavor Wallack Canny 1996 It can fixture prismatic workparts with planar and cylindrical vertical surfaces Ponce proposed an algorithm that utilizes curvature effects to compute fixtures with four fingers for polyhedral parts Ponce 96 The reduced number of contacts should provide for better complexity of this algorithm but the quality of the produced fixtures seems to be inferior to the ones that utilize more contacts and provide classical form closure In this paper we present a new potential field algorithm that efficiently produces quality fixture designs Our algorithm works for arbitrary workparts and provides convenient universal means for representing various fixturing requirements This algorithm is a direct generalization of the 2D potential field fixturing algorithm of Penev and Requicha Penev Requicha 1996 We consider fixtures with frictionless point contacts It has been proven that seven contacts are necessary1 Somoff 1900 and sufficient Markenscoff et al 1990 to immobilize any workpart2 in 3D Following a least commitment strategy the process of fixture synthesis may be separated into three stages fixturing task analysis contact point placement and fixture layout design In the fixturing task analysis phase the workpart geometry and manufacturing process are analyzed to identify various parameters of the fixturing problem such as cutting forces inaccessible or forbidden areas and also to find features that may be useful for applying fixturing devices such as machined flat surfaces horizontal and vertical surfaces pairs of parallel surfaces pairs of perpendicular surfaces etc Figure 1 Contact point placement In the contact point placement phase a number of contact points are placed on the workpart boundary Figure 1 so that the resulting configuration of contacts satisfies the constraints identified in the analysis phase as well as certain kinematic requirements that must be satisfied by any fixture such as total restraint ba Figure 2 From contact point configuration to fixture layout design In the layout design phase towers of fixturing components are built and placed around the workpart 科技譯文 so as to contact the part at the point locations computed in the contact point placement phase For example a contact point on a horizontal workpart surface Figure 2a may lead to the instantiation of an overhead clamp that contacts the workpart at that particular point Figure 2b This is a design for function problem constrained by the set of available fixturing modules and their parameters The set of contact points are the functional specification and the fixture layout is a configuration of components that achieves it In this research we focus on contact point placement and its integration with part and task analysis An arrangement of contact points must satisfy certain kinematic conditions in order to be a basis for a good fixture In particular it must provide form closure deterministic location clamping stability detachability and loadability Asada By The algorithm uses a discretization of the workpart boundary similar to the meshes used in FEA However unlike FEA our attention is on the mesh nodes rather than on the mesh elements Discretization was chosen for the following reasons First we can handle workparts with arbitrary geometry as long as the part s boundary is a collection of smooth surfaces which we know how to mesh This requirement is satisfied by all surfaces used in modern CAD systems Second discretization is necessary in order to avoid an expensive computation of geodesic curves Third discretization should not significantly affect the results as long as the number of discrete candidate locations on the boundary is much larger than the number of surfaces In our implementation the discretized boundary consists of several hundred points only Experimental evidence indicates that this is sufficient for realistic workparts We introduce a potential field on the workpart boundary defined by zones of attraction and repulsion which we call P zones The contacts are modeled as charged particles that move on the boundary driven by this potential field The contacts are also subject to mutual repulsion based on the distance between each two contacts in the wrench vector space The algorithm executes a series of simulation epochs Each epoch starts with a random configuration proceeds through a certain number of steps toward lower potential energy and ends with a test for kinematic conditions form closure The algorithm terminates when an epoch produces satisfactory configuration To spread the contact points on the boundary we simulate repulsion between each pair of them The intensity of repulsion between two contact points depends on the distance between their corresponding wrenches in the wrench vector space Our simulation proceeds in a limited number of steps or until equilibrium is reached The resulting placement should have a good chance of leading to a good fixture Such a randomized method assumes that the set of n tuples of contact points for n greater than three that satisfy the kinematic requirements has measure greater than zero and is relatively large That is the solution space is large Although we have not been able to prove this hypothesis mathematically our experiments have confirmed it Moreover the measure increases with the number of contact points e g it is easier to find a form closure arrangement with eight points than with seven The notion of repulsion is essential in our method as it allows other considerations to be accommodated easily We can put additional repulsion spots on the workpart boundary to represent forbidden regions We can also introduce centers of attraction These correspond to areas that were recommended by the analysis phase as desirable for placing contact points e g datum surfaces Thus we propose a potential field for uniformly representing heterogeneous fixturing information Regions of repulsion correspond to areas with positive potential Negative potential is associated with attraction Zero potential corresponds to neutral areas The initial randomly selected contact points are regarded as particles that are being attracted or repelled by a potential field that includes a pairwise repulsion The goal of the system of contact points is to minimize its total potential energy 2 THE INPUT The input to our algorithm consists of CAD models of the workpart boundary and a set of solid P zones Each P zone defines a potential field influencing region with non zero charge 3 DISCRETIZING THE WORKPART BOUNDARY The first step in our method is to discretize the boundary of the workpart thus creating the candidate contact point locations which we call nodes Discretization is done by invoking a standard faceter embedded in the geometric modeler we use The discretization is stored in an oriented graph data structure Each node of the graph corresponds to a node on the mesh The edges of the graph correspond to edges of the mesh connecting neighboring nodes At each node the screw representing the point contact is computed and stored A screw is a concise and convenient representation of the surface normal and the location of the node It is used in all kinematic tests based on screw theory 4 COMPUTING THE POTENTIAL FIELD The contact points in our algorithm are subject to the combined action of two components forming the potential field The background potential field is one of these components It is generated by the P zones and does not depend on the location of the contact points The background potential field is computed only once in the beginning of the algorithm The other component is dynamic and is due to the repulsion between the contacts The dynamic component is computed at each epoch The computation of the background potential field proceeds as follows First we find all nodes that lie inside P zones We perform membership classification of each node against each P zone Tilove 1980 If the node is inside a certain P zone the charge of the P zone contributes to the node s charge The contribution may be positive or negative depending on the sign of the zone s charge After this procedure the nodes that classify outside all P zones remain with zero charge If a node m classifies inside P zones z1 z2 zk its charge Cm equals the sum of the charges of those P zones ziki 1 After the charge of the nodes inside P zones is evaluated we proceed by computing the potential of all nodes We define the potential at a charged node to be initially equal to its charge Pm Cm For each charged node m with charge Cm we perform a breadth first traversal of its neighbors updating their potential according to the formula Pdnnm 1210 Here d m n is the distance between nodes m the charged node and n and d0 is a constant called distance of influence The distance between two nodes is defined as the number of edges on the 科技譯文 shortest path between them on the mesh boundary approximation Figure 3 n m d m n 7 Figure 3 Distance between two nodes on the mesh Assuming the mesh satisfies certain common quality requirements this distance approximates quite well the actual geodesic distance between two points on the object s boundary The breadth first traversal goes only d0 nodes deep Thus a charged node causes updates of the potential only in its d0 neighborhood For example if the three dark nodes in Figure 4 have charge 100 and d0 3 the potential in this part of the mesh will be as shown by the numbers next to each node 0 0 0 0 0 0 0 0 0 8 8 16 16 16 16 16 8 8 8 8 8 16 8 8 74 74 74 49 49 49 49 16 16 16 49 49 Figure 4 Potential field generated by three charged nodes The dynamic potential represents repulsion between the contact points The repulsion between two contacts depends on how distant their corresponding screws are as 6 dimensional vectors Pmnn 1142 Here is a small number to avoid division by zero is a scaling factor that makes the dynamic potential compatible with the background component and m n is the Euclidean distance between the screws at nodes m and n The rationale behind repulsion based on screw distance is the following A necessary and sufficient condition for form closure is that the set of contact screws positively spans the entire R6 Wagner et al 1995 As the contact screws repel each other they will tend to distribute regularly in the space thus increasing the possibility of form closure 5 EPOCHS Each epoch starts with a random initial placement of contact points Then these contact points are subjected to the combined forces due to the background potential field and the repulsion between the contact points themselves The algorithm proceeds in an iterative fashion First the dynamic component of the aggregated potential field is computed accordingly to 3 The dynamic potential is computed only at the contacts and their immediate neighbors After the combined potential is computed each contact is moved to the neighbor node with the lowest potential Thus a step is completed If the number of steps has reached a certain limit or no contact was moved i e equilibrium has been reached the epoch is completed Throughout this process special attention is paid to nodes that lie on edges and vertices of the workpart These nodes do not have a screw associated with them as there is no normal defined there Therefore they cannot be a possible contact location Instead they serve merely as transit nodes in the simulation This is achieved by always considering the neighbors of such a node whenever the node itself is addressed The net result of an epoch is that the initially random configuration transforms into one that has more regular distribution of contact screws in the screw vector space while at the same time keeping away from repulsion zones and providing contacts inside attraction zones 6 TEST In the test phase we check whether the placement of contact points provides form closure This is done using the method of Chou et al Chou et al 19 It tests whether there exists a non zero motion screw that complies with the constraints imposed by the contact wrenches swiCi 01 The existence of s is tested using linear programming techniques If no such motion exists the arrangement of contacts provides form closure If the test succeeds the algorithm terminates Otherwise a new epoch is initiated If the test fails and a certain number of generations have been tried we increase the number of contact points C Increasing C improves the probability of ending up with a form closure configuration as well as having more contacts in P zones of attraction The algorithm ensures that no two contact points are placed on the same mesh node Therefore in the extreme case there are three contacts on each face Such a placement obviously immobilizes any polyhedral part Hence the completeness of the algorithm at least for polyhedral parts After a redundant form closure configuration is computed the algorithm can remove the extra contacts in the order of decreasing background potential i e starting with the ones in P zones of highest repulsion Redundant fixtures are sometimes preferred as they minimize part deflection and vibration The system can operate with or without redundancy reduction The decision might be guided by the analysis phase based on the geometric shape of the part and the magnitude of the external forces or a human operator may allow redundancy manually and even force it by setting the initial number of contacts to be more than the theoretical minimum 7 in 3D 科技譯文 It is possible for the kinematic test to succeed but the potential at some contacts to be high This can happen if a contact is trapped in a local minimum of the potential field where the potential is high To handle such situations we introduce a threshold parameter called maximum allowable potential Arrangements with potential at any contact higher than the threshold are discarded This new test may lead to situations in which the algorithm does not terminate because no fixture exists with sufficiently small potential Imagine the extreme example that the entire workpart boundary is a forbidden region Therefore we limit the number of epochs to ensure termination In the case of such termination the algorithm outputs the solution with the lowest maximum potential 7 DISCUSSION The proposed algorithm solves the essential problem in fixture design placing contact points on the workpart that provide form closure It can be incorporated in a complete fixture design system that provides modules for fixturing task analysis and layout design The algorithm provides a simple but powerful interface to the fixturing task analysis modules based on zones of attraction and repulsion Admittedly not every contact configuration can be implemented by a certain fixturing toolkit in the layout design phase It may be necessary to invoke the contact placement algorithm several times until a feasible configuration is produced 7 1 Fixturing Task Analysis Various fixturing heuristics and requirements can be expressed in terms of zones of higher attraction or repulsion For example attraction zones may be used to represent datum surfaces machined surfaces surfaces with good orientation areas with good accessibility areas that need additional support to prevent deflection and deformation Repulsion zones can represent inaccessible areas forbidden areas due to tool accessibility requirements surfaces with poor orientation cast surfaces sensitive surfaces that are vulnerable to scratching etc An important open problem is how to assign numerical values to the P zone potential One possibility is to classify the constraints into a small number of categories e g strong repulsion repulsion neutral attraction strong attraction All constraints within the same category are assigned the same potential While such a scheme does not reflect subtle differences in priorities of the fixturing constraints it will probably capture the most important ones 7 2 Fixture Completion An important property of the algorithm is that it allows partial fixtures to be input Partial fixtures may be produced by other fixturing agents humans or computer programs who place certain fixels they know are necessary and hand the work over to our algorithm for completion The algorithm then places additional contacts so that form closure is achieved We represent the partial fixture as fixed contacts which participate in the mutual repulsion with the free contacts but are not allowed to move In this light the algorithm may be viewed as a fixture completion engine 7 3 Non determinism and Redundancy Due to the randomness of the initial placement in each generation the algorithm is non deterministic i e it can produce different solutions given the same input This is desirable as a contact point configuration may be rejected by the layout design module and the algorithm will have to produce another solution The algorithm may produce redundant fixtures in certain cases Redundant fixtures have drawbacks as well as advantages over the minimal ones Certainly they impair loadability and waste components However they may also minimize part deflection and deformation In practice human designers often produce redundant fixtures 7 4 Efficiency The running time of the algorithm does not depend directly on the complexity of the workpart boundary A simple cuboid and a complex curved workpart will be discretized with a comparable number of mesh nodes This decision is based on the intuitive assumption that a few hundred evenly distributed nodes on