拖拉机Ⅱ-Ⅲ档倒挡拨叉工艺及钻φ5孔夹具设计【版本2】带图纸
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系主任批准日期茂 名 学 院 毕 业 设 计(论 文)任 务 书 机电工程 系 机械设计制造及其自动化 专业 04-2 班 学生 周宏霄 一、毕业设计(论文)课题 车床拨叉上螺纹底孔加工钻床夹具的设计 二、毕业设计(论文)工作自 2008 年 3 月 17 日起至 2008 年6月 20 日止三、毕业设计(论文)进行地点 茂名学院机电工程学院 四、毕业设计(论文)的内容要求 (一)已知条件: (1)、被加工零件的工序图 (2) 成批生产 (二)、主要内容及要求: (1)、按要求写出开题报告; (2)、结合课题到工厂进行毕业实习; (3)、收集国内外有关情报资料,查阅文献资料15篇以上; (4)、翻译不少于5000字的英语科技文献; (5)、研究形成总体方案; (6)、设计绘制出夹具的总装工作图; (7)、绘制出主要零件图; (8)、按学校规定格式编写出不少于20000字的设计计算说明书(含文献综述); (9)、准备和参加毕业答辩。 (三)、主要参考资料: (1)机床夹具图册P8 孟宪栋等主编机械工业出版社 (2)巧改机床 陈榕林 张 磊 编著中国农业机械化出版社; (3)金属切削机床 上、下册 顾熙棠等主编 上海科技出版社; (4)组合机床设计手册 机械工业出版社; (5)组合机床设计图册 机械工业出版社; (6)机电传动与控制 邓星钟等 华中理工大学出版社; (7)新编机械设计手册 徐灏 机械工业出版社; (8) 机械可靠性设计 刘惟信主编 机械工业出版社; (9) 机械设计手册 机械工业出版社; (10) 机床夹具设计 龚定安等 西安交通大学出版社 (11) 机床夹具设计 李庆寿 机械工业出版社 (12)单独驱动的回转分度工作台 组合机床(1985)7 总137期P19 (13) 机床设计图册 华东五高校编 华东科技大学出版社 (14) 机电一体化系统设计手册 杨黎明 主编 国防工业出版社; 教研室负责人 指导教师 王安民(教授) 接受设计论文任务开始执行日期 2008 年 1 月 7 日学生签名 毕业设计(论文)开题报告题目车床拨叉上螺纹底孔加工钻床夹具的设计The Design of the Drilling Machine Fixture for Processing Lathe Shifting Fort Upper Thread Bottom Hole 学院茂名学院年级2004级专业机械设计制造及自动化学号04024020240姓名周宏霄指导教师王安民(教授)2008年3 月 25 日毕业设计(论文)开题报告题目车床拨叉上螺纹底孔加工钻床夹具的设计时间2008 年3月17日至 2008年 6月10日本课题的目的意义(含国内外的研究现状分析)机床夹具是机械制造工艺系统重要的组成部分,其质量的高低直接影响到零件制造的质量、工人的劳动强度、产品成本和生产率。通过机床夹具的设计着重培养同学们的设计、计算、分析问题和解决问题的能力,综合运用计算机绘图能力、表达技术问题的能力以及开拓创新的能力等。通过本夹紧机构的设计进而掌握一般机床夹具的一般方法、步骤和技巧,从而达到掌握一般机械的设计方法和技巧,使同学们综合运用所学的知识解决工程实际问题。机床夹具是用以装夹工件和引导刀具的附加装置。主要用于金属切削加工,在机床与工件、刀具之间起桥梁作用,是工艺系统中的一个重要环节。它可准确地确定工件与刀具、机床的相对位置,确保加工质量;它可以提高生产效率,确保劳动强度;它可以扩大或改变机床的使用范围等。因此,机床夹具是保证机械加工工艺过程正常进行的技术硬件之一。综上所诉,需要对零件进行加工工艺设计和机床夹具设计。设计(论文)的基本条件及设计(论文)依据已知条件:车床拨叉零件图和钻削工序图各1张,中批生产。设计工艺过程的主要依据 (1) 根据加工对象的尺寸公差、形状和位置公差、表面粗糙度、技术要求、工件材料、毛坯类型、热处理与表面保护等要求来设计工艺过程。 (2) 根据给定的生产量大小来确定工艺过程。 (3) 根据本单位的先有生产条件,注意充分发挥现场技术条件手段和技术力量的潜力来设计工艺过程。本课题的主要内容、重点解决的问题主要内容及要求: (1)查阅设计资料和进行参观补习; (2)夹具的方案设计;(3)夹具总装配图设计; (4)夹具主要零件图的绘制; (5)夹具可行性分析; (6)编写设计计算说明书;(7)外文翻译(不少于5000字符);(8)准备和参加答辩。重点解决问题:在保证零件加工质量前提下,提高生产效率,降低消耗,以取得较好的经济效益和社会效益.本课题欲达到的目的或预期研究的结果其主要目的:1)、培养学生综合分析和解决本专业的一般工程技术问题的独立工作能力,拓宽和深化学生的知识;2)、培养学生树立正确的设计思想,设计构思和创新思维,掌握工程设计的一般程序规范和方法;3)培养学生树立正确的设计思想和使用技术资料、国家标准等手册、图册工具书进行设计计算,数据处理,编写技术文件等方面的工作能力;4)培养学生进行调查研究,面向实际,面向生产,向工人和技术人员学习的基本工作态度,工作作风和工作方法。计 划 进 度时 间工 作 内 容备 注2008.3.172008.3.302007.4.312007.4.202007.4.212007.5.42007.552007.5.182007.5192007.6.8设计题目资料收集、写开题报告工艺过程规划工序设计与夹具方案的确定夹具设计与绘制装配图及零件图毕业论文的撰写整理及排版打印指导教师意见指导教师签名: 年 月 日I 摘要 本课题是车床拨叉上螺纹底孔加工钻床夹具设计,而车床拨叉它位于车床变速机 构中,主要起换档,使主轴回转运动按照工作者的要求工作,获得所需的速度和扭矩 的作用。 本设计中,根据拨叉尺寸公差、形状和位置公差、表面粗糙度、技术要求、工件 材料、毛坯类型、热处理与表面保护等要求来设计。夹具的总体设计包括从方案制定 到总装配图的设计的全部过程。包括确定工件的定位,选择或设计定位元件,计算定 位误差;确定刀具的导引和对刀方式,选取或色痕迹导引元件或对刀元件;确定工件 的夹紧方式,选择或设计夹紧机构或装置,计算夹紧力;确定夹具体及其他装置的结 构类型等。 通过合理的设计,在保证零件加工质量前提下,提高生产效率,降低消耗,以取得较 好的经济效益和社会效益。 关键词:夹具,设计,钻床,螺纹底孔; 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; 科技译文 3 目录 摘 要 .I ABSTRACT .II 第一章 绪论 .1 1.1 背景 .1 1.2 夹具的特点 .1 1.3 研究夹具的目的和意义 .4 1.4 论文构成及研究内容 .4 1.4.1 论文构成 .4 1.4.2 本设计的主要内容及要求 .5 第二章 机床夹具概述 .6 2.1 夹具的现状及生产对其提出新的要求 .6 2.2 夹具的国内外现状和发展趋势 .6 2.3 现代夹具的发展发向 .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 标准化 .7 2.4 机床夹具及其功用 .8 2.4.1 机床夹具 .8 2.4.2 机床夹具的功能 .8 2.5 机床夹具在机械加工中的作用 .8 2.6 机床夹具组成和分类 .9 2.6.1 机床夹具的基本组成部分 .9 2.6.2 机床夹具的其他组成部分 .9 2.7 机床夹具的分类 .10 2.7.1 按夹具的通用特性分类 .10 2.7.2 按夹具使用的机床分类 .11 2.8 机床夹具设计特点 .11 第三章 夹具设计 .12 3.1 夹具设计概述 .12 4 3.1.1 机床夹具设计的基本要求和步骤 .12 3.1.2 机床夹具的分类和组成 .13 3.1.3 工件安装与获得加工精度的方法 .13 3.1.4 工件在夹具中的定位原理 .14 3.1.5 常见定位方式及定位元件 .14 3.1.6 工件在夹具中的夹紧原理 .15 3.1.7 确定刀具位置及钻套的选择 .16 3.1.8 夹具总图的绘制及标注 .18 3.1.9 机床夹具总图上尺寸的标注 .19 3.1.10 机床夹具总图上技术条件的标注 .19 3.1.11 机床夹具调刀尺寸的标注 .20 3.2 夹具设计 .21 3.2.1 问题的提出 .21 3.2.2定位方案 设计 .22 3.2.3 定位元件设计 .23 3.2.4 切削力与夹紧力计算 .23 3.2.5 定位误差计算 .23 3.2.6 导向方案选择 .24 3.2.7 导向元件设计 .24 3.2.8 导向误差计算 .24 3.2.9 夹紧装置的设计 .24 3.2.10 设计夹具体 .25 3.2.11 夹具工作原理 .25 3.3 夹具在安装和操作时应注意的事项 .25 3.3.1 夹具的安装 .25 3.3.2 夹具在操作时应注意的事项 .26 3.4 夹具可行性分析 .26 3.4.1 夹具的经济效益分析 .26 3.4.2 夹具的可行性 .27 第四章 总结 .28 致谢 .29 参考文献 .30 科技译文 .31 科技译文 I 科技译文 科技译文 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 科技译文 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 parts 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 nodes charge. The contribution may be positive or negative, depending on the sign of the zones 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: ziki1 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: Pdnnm1210, 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 科技译文 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 objects 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:swiCi01 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). 科技译文 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
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