夹具类外文翻译-一种自动化夹具设计方法【中文4660字】【PDF+中文WORD】
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【中文4660字】一种自动化夹具设计方法塞西尔美国，拉斯克鲁塞斯，新墨西哥州立大学，工业工程系，虚拟企业工程实验室（VEEL）本文描述了一种新的计算机辅助夹具设计方法。对于一个给定的工件，这种夹具设计方法包含了识别加紧表面和夹紧位置点。通过使用一种定位设计方法去夹紧和支撑工件，并且当机器正在运行的时候，可以根据刀具来正确定位工件。该论文还给出了自动化夹具设计的详细步骤。几何推理技术被用来确定可行的夹紧面和位置。要识别所完成工件和定位点就还需要一些输入量包括CAD模型的技术要求、特征。关键词：夹紧；夹具设计1.动机和目标夹具设计是连接设计与制造的一项重要任务。自动化夹具设计和计算机辅助夹具设计开发（夹具CAD）是下一代制造系统成功实现目标的关键。在这篇论文里，讨论了一种夹具设计的方法，这种方法有利于在目前环境下夹具设计的自动化。夹具设计方法的研究已成为国内多家科研工作的重点。作者周在1中对工件的稳定和总需求约束了双重标准，突出重点的工作。在夹具设计中广泛地运用了人工智能（AI）以及专家系统。部分CAD模型几何信息也被用于夹具设计。Bidanda 4描述了一个基于规则的专家系统，以确定回转体零件的定位和夹紧。夹紧机制同时用于执行定位和夹紧功能。其他研究者（如DeVor等，5,6）分析了切削力钻井机械和建筑模型及其他金属切削加工。康有为等在2中定义了装配约束建模的模块化与夹具元件之间的空间关系。一些研究人员采用模块化夹具设计原则，用以生成2,7-11，另一些夹具设计工作者已经报告了1,3,9,12-23。可以在21,24中找到夹具设计相关的大量的审查工作。在第二节中，对夹具设计任务中各种步骤进行了概述。在第三节和第四节中描述了工件的加工过程，要夹紧工件表面，否则将面临工件的全面自动测定。第五节讨论了对工件的夹紧点的测定。2.夹具设计的整体方法在本节中，描述了整体夹紧的设计方法。通常对较理想的位置的那一部分进行夹紧，并减低切削力的影响。夹紧的位置和夹具设计中定位的位置是高度相关的。通常，夹紧和定位可以通过同样的方法来完成。但是，不明白这两个是夹具设计中不同的方面，则可能导致夹具设计的失败。多数人的在规划过程中首先解决定位问题，这样可以使开发的定位与设计的定位相契合。不过，整体定位及设计方法不在本文讨论范围内。除了零件的设计（为此夹具设计有待开发），公差规格，过程序列，定位点和设计等因素外，还应投入CAD模型到夹具设计方法中。这样的夹具可以夹紧并支撑定位器。指导使用的主要内容应尽量不抵制切割或加工过程和其中所涉及的操作。相反，应定位夹具，使切削力在正确的方向，这将有助于保持在一个特定的部分加工操作安全。通过引导对定位器的切割力量，部分（或工件）被固定，固定定位点，因此不能移动的定位器。在这里讨论的夹具的设计方法必须在整体夹具设计方法的范围内。在此之前进行定位器/支撑和夹具设计的初步阶段，涉及到的分析和识别的功能、相关的公差和其他规范是必要的。根据初步的评估和测定，定位/支撑设计与夹具设计结果的在此基础上可以同时进行。本文对所描述夹具设计的方法讨论基于定位器/支撑设计与先前已经确定的假设（包括适当的定位和支持测定一个工件的定位，以及识别和夹具，如V元素的支持面块，基础板，定位销等）。 （1） 夹具设计的输入输入包括对特定产品的设计翼边模型，公差信息，提取的特征，过程顺序和部分在给定的每一个设计的相关特性的加工方向，面向的位置和定位装置，以及加工过程中的各种工序，须出示每个相应的功能。（2） 夹具设计的方法 图一是自动化夹具设计主要步骤总结图。对这些步骤概述如下： 第一步：设置配置清单以及相关的进程_功能条目。 第二步：确定方向和夹紧力。输入必要的加工方向向量mdv1，mdv2mdvn，面对nvs的支持力，并确定法向量。如果加工方向向下（对应的方向向量0，0，-1），和面的支持向量平行于加工方向，那么，夹紧力方向平行向下加工方向0，0，-1。如果必需要侧面夹紧并没有可夹紧的地方，那么在其中放置一个夹具夹紧下调，然后边钳方向计算如下。让sv和tv辅助常规的向量代替次要的和三级定位孔。然后，使用夹紧机构夹紧一个方向，例如，av应平行于这两个法向量，即，正常向量应分别与每块表面的sv和tv向量平行。侧面夹紧面应该是一对分别平行于面sv和tv的平面孔。第三步：从列表中选出最大有效加工力。这样能够有效的平衡各加工力。第四步：利用计算出的最高有效加工力，才能确定用来支撑工件加工的面积的夹具尺寸（例如，一个带夹子可以作为一个夹紧机构使用）。第五步：确定给定工件的夹紧面。这一步在第四步中所述过。第六步：该夹具的夹紧面的实际位置自动在第5节中确定。考虑接下来的步骤并返回第一步。3.判断夹具尺寸在这项工作中所用到的夹具都来自一个系列。夹具的原理与图二相同。在这一节里，描述了一个自动化夹具。锁模力所需的有关螺杆的螺纹装置大小或保存到位钳。夹紧力平衡加工工件使工件保持恰当的位置。让锁模力为W和螺杆直径为D。各种螺丝夹紧力大小，可以按以下方式确定：最初，极限拉伸强度（抗拉强度）和该夹具的材料（供应情况而定）可以从数据检索库检索。各种材料有不同的拉伸强度。该夹具材料的选择，也可直接采用启发式规则进行。例如，如果部分材料是低碳钢，那么钳材料可低碳钢或机器钢。为了确定设计应力，抗拉强度值应除以安全系数（如4或5）。根区的螺丝格A1（如一个螺丝钳）可以被确定：锁模力/设计应力。随后，螺栓截面全面积可以计算为等于格A1 /（65）（因为螺丝的地方可能会发生根切面积约为65螺栓的总面积）。螺钉的直径D可以被确定等同于（D2的3.14 / 4）。另一项涉及可用于方程有关的宽度B，高度H和跨度的钳L的螺丝直径为D（B，H和L可以为不同的值计算D）：d2=4/3 BH2/L.4.判断夹紧表面确定夹具经常出现的相关参数包括了产品的CAD模型，提取的特征信息，特征尺寸，定位面和定位器的选择。考虑所有潜在的加紧面，如图3。最关键的是夹紧表面不应重叠或与该面相交，如图4所示。夹紧面积是与工件表面（或PCF）接触的是一个二维轮廓线段组成的（见图6）。利用线段相交测试，可以测定在给定的光子晶体光纤的任何范围内是否可能有接触面夹紧面重叠。夹紧面的确定可以如下所示：第1步：鉴别平行于二级和三级定位面（lf1和lf2）是分别到lf1和tcj最远的距离的面。如下所示：（一）鉴别面tci,tcj,使面tci和 tcj平行lf1和tcj平行lf2。（二）在TCF中列出面对tci的面。（三）通过检查所有TCF中面对tci的面，确定的面对tci和tcj的面是到lf1和lf2分别最远的面，并舍弃所有其他TCF中的面。 第2步：鉴别平行面的位置，除了不相邻的附加面。最好是选择一个不与其他定位面垂直相邻的面。这一步如下所示：(a) 考虑TCF列表中的tci面，获得与每个tci面垂直或相邻的面然后，在FCF列表中插入每个fci面。(b) 检查每个FCI面，并执行以下测试：如果FCI是相邻、垂直于lf1或lf2，然后从列表中舍弃它并插入NTCF列表中。第3步: 确定加紧面都在有效的加紧面上，如下所述夹紧面：例1:如果没有条目在列表NTCF中，就使用TCF中的面并继续执行步骤4。如果任何面发现，垂直于第二，第三位置的面孔lf1和lf2，这将要面临的是下次选择可行的夹具。在这种情况下，唯一剩下的选择是重新审视在列表NTCF的面。例2：如果列表中NTCF条目数为1时，可行夹紧面为FCI。与TCI的法向量垂直相邻的相应轴是夹紧轴。例3：如果在列表NTCF项数大于1，确定最大的TCI加紧面再进行步骤4。例4：:夹紧力的方向可以是1，0，0或0，1，0，可以夹紧TCI面的中心位置。在其他几何位置可确定使用零件几何形状和拓扑信息，这在下一节中描述。5.判断夹紧表面上的夹紧点确定夹紧面后，必须确定实际夹紧位置。输入夹具侧面积，沿着X，Y，Z和潜在的夹紧面CF方向。容下使用CF几何获得夹具侧面积：第一步是确定一个箱体的大小，这是用来测试它是否包含在它里面的任何部分。相交测试也可以在前面介绍的方法使用。如果相交测试返回一个负的结果，那么有部分箱体与夹具相交，如图4所示。如果相交测试返回一个正的结果，可以执行下列步骤： 1. 划分成更小的矩形大小条（1 W）夹框轮廓(图5和图6)。 2. 执行指定与功能配置文件出现在CF面的零件设计的相交测试。 3. 没有功能相交的条形区域，都是可行夹紧区域。如果有一个以上的长方形候选面，矩形配置文件，向中沿轴夹紧CF面点的是夹紧配置文件（夹点）。 如果没有发现配置文件，夹具宽度可减少一半，夹具数可以增加两个。使用这些修改过的夹具尺寸，执行前面描述的特征相交测试。如果此测试也失败了，那么可以用相邻的面作为夹紧面用于执行端夹紧。这面可以重复进行PCF和功能相交测试。5.1试验曲线的交点输入需要的二维轮廓P1、P2，使用下列方法可以自动确定该配置文件的交集。每一个输入的资料组成一个封闭环。此配置文件测试的步骤如下：(T1) 考虑P1线段中的L（i，1）和P2线段中的L（2，j）。(T2) 采用L（i，1）线段和L（2，j）线段的相交段。如果边缘相交测试返回一个正值，那么特征面和潜在面相交。如果它返回一个负值，继续执行步骤3。（T3）重复与步骤（T1）相同的部分或者缓慢走过其余P1中的(Li,1)段直到P2中的(L2, j+1) till j=n1段。 (T4) 其余部分边和P1中的L12、L13到L1n段重复（T1）和（T2）步骤。如果特征面与夹紧面重复，线相交测试将决定该事件。相交的边可以进行自动检测两个面是否相互交叉。输入所需的边L12连接 (x1, y1) 和 (x2, y2)和L34连接 (x3, y3) 和(x4, y4)。L12型方程的可表示为：F(x,y) =0 （1） L34型方程的可表示为：H(x,y) =0 （2） 第一步：使用等式（1）计算R3 = F(x3, y3)，用X和Y取代X3和Y3；计算R4 = F(x4, y4)，用X和Y取代X4和Y4。 第二步：如果R3和R4都与0不相等，但R3与R4结果相同（R1与R2在相同的一边），则边L12与L34不相交。如果这样不满足条件，那么进行第三步。第三步：使用等式（2）计算R1 = H(x1, y1)。接着，计算R2 = G(x2, y2)再进行第四步。第四步：如果R1与R2都不等于0，且R1与R2的结果相同，那么把R1与R2放在相同的一边并输入不相交。如果，这个也不满足条件，那么进行第五步。 第五步：给定相交线段。这样就完成了测试。考虑如图7所示的一部分样品。将要生产一个盲孔。起初，完成定位设计。定位器的（或主要定位器）是一个基盘（放在F4面）和二级和三级定位器面临F6和F5（对应到定位面lf1和lf2在第4节中讨论）。一个辅助定位器也被使用，这是一个V型块（对F3和F5面辅助定位），如图8所示。在前面讨论的夹具设计方法中所述的步骤的基础上，候选面孔（这是平行的，并在从lf1和lf2最遥远的距离）是面对F3和F5面。没有面孔，这是平行到定位面，但他们不相邻。在这种情况下使用的优先权规则（如步骤3第4步讨论），剩余的候选面面对的是F2面。夹具方向向下的V型块径向定位器和其他与对工件夹紧底面提供所需位置。根据第五步选择夹具的位置。如果没有功能发生在面F2上，那么也没有必要进行相交测试确定夹具优美加紧。夹具位置应远离V型定位器（这是辅助定位位置）的夹紧面毗邻辅助定位面（这确保了更好的快速夹紧）。最终位置和夹具的设计如图8所示。本文讨论的方法，毫不逊色于其他夹具设计文献中讨论的方法。本文所讨论的方法的独特性是零件的夹紧面的几何形状，拓扑和功能发生了被加工为基础的系统鉴定。其他方法都没有利用了定位器的位置，该方法使用定位器在对持有一级，二级和三级定位器加工的工件。这种方法的另一个好处是在可行的候选面上确定在面上用夹具面交点测试（如前所述），并迅速和有效地确定潜在的下游过程中可能出现问题，夹紧和加工的功能检测。6.总结 本文在一个夹具设计方法的总体框架之下进行了夹具设计方面的讨论。设计定位器，规范零件设计，和其他相关被用来确定夹紧面和夹紧方向。各种自动化步骤也有涉及。8Int 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 is described in the context of computer-aided fixture design activi- ties. The clamping design approach involves identification of clamping surfaces and clamp points on a given workpiece. This approach can be applied in conjunction with a locator design approach to hold and support the workpiece during machining and to position the workpiece correctly with respect to the cutting tool. Detailed steps are given for automated clamp design. Geometric reasoning techniques are used to determine feasible clamp faces and positions. The required inputs include CAD model specifications, features identified on the finished workpiece, locator points and elements.Keywords: Clamping; Fixture design1. Motivation and ObjectivesFixture design is an important task, which is an integration link between design and manufacturing activities. The automation of fixture design activities and the development of computer-aided fixture design (CAFD) methodologies are key objectives to be addressed for the successful realisation of next generation manufacturing systems. In this paper, a clamp design approach is discussed, which facilitates automation in the context of an integrated fixture design methodology.Clamp design approaches have been the focus of several research efforts. The work of Chou 1 focused on the twin criteria of workpiece stability and total restraint requirement. The use of artificial intelligence (AI) approaches as well as expert system applications in fixture design has been widely reported 2,3. Part geometry information from a CAD model has also been used to drive the fixture design task. Bidanda 4 described a rule-based expert system to identify the locating and 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 Enterprise Engineering Lab (VEEL), Industrial Engineering Department, New Mexico State University, Las Cruces, NM 88003, USA. E-mail: functions. Other researchers (e.g. DeVor et al. 5,6) have analysed the cutting forces and built mechanistic models for drilling, and other metal cutting processes. Kang et al. 2 defined assembly constraints to model spatial relationships between modular fixture elements. Several researchers have employed modular fixturing principles to generate fixture designs 2,711. Other fixture design efforts have been reported in 1,3,9,1223. An extensive review of fixture design related work can be found in 21,24.In Section 2, the various steps in the overall approach to automate the clamping design task are outlined. Section 3 describes 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 workpiece is 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 is described. Clamping is usually carried out to hold the part in a desired position and to resist the effects of cutting forces. Clamping and locating problems in fixture design are highly related. Often, the clamping and locating can be accomplished by the same mechanism. However, failure to understand that these two tasks are separate aspects of fixture design may lead to infeasible fixture designs. Human process planners generally resolve the locating problem first. The approach developed can work in conjunction with a locator design strategy. However, the overall locator and support design approach is beyond the scope of this paper.CAD models of the part design (for which the clamp design has to be developed), the tolerance specifications, process sequence, locator points and design, among other factors, are the inputs to the clamp design approach. The purpose of clamping is to hold the parts against locators and supports. The guiding theme used is to try not to resist the cutting or machining forces involved during a machining operation. Rather, the clamps should be positioned such that the cutting forces are in the direction that will assist in holding the part securely during a specific machining operation. By directingA Clamping Design Approach789the cutting forces towards the locators, the part (or workpiece) is forced against solid, fixed locating points and so cannot move away from the locators.The clamp design approach discussed here must be viewed in the context of the overall fixture design approach. Prior to 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 and determination, the locator/support design and clamp design can be carried out. The clamp design approach described in this paper is discussed based on the assumption that locator/support design attributes have been determined earlier (this includes determination of appropriate locator and support faces on a workpiece as well as identification of locator and support fixturing elements such as V-blocks, base plates, locating pins, etc).2.1 Inputs to Clamp DesignThe inputs include the winged-edge model of the given product design, the tolerance information, the extracted features, the process sequence and the machining directions for each of the associated features in the given part design, the location faces and locator devices, and the machining forces for the various processes required to produce each corresponding feature.2.2 Clamp Design StrategyThe main steps in the automation of the clamping design task are summarised in Fig. 1. An overview of these steps is as follows:Step 1. Consider the set-up SUi in the set-up configuration list along with the associated process I feature entries.Step 2. Identify the direction and type of clamping. The inputs required are the machining direction vectors mdv1,mdv2,. . .,mdvn and identified normal vectors of support face nvs. If the machining directions are downward (which correspond to the direction vector 0, 0, -1), and the normal vector of the support face is parallel to the machining direction, then the direction of clamping is parallel to the downward machining direction 0, 0, -1. If sideways clamping is required, and if there are no feasible regions at which to position a clamp for downward clamping, then a side-clamp direction is obtained as follows. Let sv and tv be the normal vectors of the secondary (sv) and tertiary (tv) locating faces. Then, the direction of clamping used by a side-clamping mechanism such as a v- block should be parallel to both these normal vectors, i.e. the normal vectors of the each of the v-surfaces in the v-block will be parallel to sv and tv, respectively. The side clamping face should be a pair of faces parallel to the faces sv and tv, respectively.Step 3. Determine the highest machining force from the mach- ining forces list (for each feature) MFi (i = 1, . . .,n). This will be the effective force FE that must be balanced while designing the clamp for this set-up SUi.Step 4. Using the value of the calculated highest machining force 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 can be used as a clamping mechanism). The approach for this task is 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 clamping face is determined in an automated manner as explained in Section 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 clamps referred to as strap clamps. A strap clamp is based on the same principle as that of the lever (see Fig. 2). In this section, the automated design of a strap clamp is described. The clamping force required is related to the size of the screw or a threaded device that holds the clamp in place. The clamping force should balance the machining force to hold the workpiece in position. Let the clamping force be W and the screw diameter be d. The dimensions of the various screw sizes for various clamping forces can be determined in the following manner. Initially, the ultimate tensile strength (UTS) of the material of the clamp (depending on availability) can be retrieved from a data library. Various materials have different tensile strengths. The selection of the clamp material can also be performed directly using heuristic rules. For example, if the part material is mild steel, then the clamp material can be lowFig. 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 4 or 5). The root area A1 of the screw (for a clamp such as a screw clamp) can then be determined: Clamping force required/Design Stress DS. Subsequently, the full area FA of the bolt cross-section can be computed as equal to A1/(65%) (since the root area of the screw where shearing can occur is approximately 65% of the total area of the bolt). The diameter of the screw d can then be determined by equating FA to (3.14 d2/4). Another equation which can be used involves relating the width B, height H and span L of the clamp to the screw diameter d (B, H, and L can be computed for various values of d): d2 = 4/3 BH2/L.4. The Determination of the Clamping FaceThe required inputs to determine the clamping region include the 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 potential clamping face PCF as shown in Fig. 3. The crucial criterion to be satisfied is that the clamping surface should not overlap or intersect with the features on that face, as shown in Fig. 4. The clamping surface area, which is in contact with the workpiece surface (or PCF) is a 2D profile consisting of line segments (see Fig. 6). By using line segment intersection tests, it can be determined whether the potential clamping area of contact 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 and tertiary locator faces (lf1 and lf2) and at the farthest distance from lf1 and tcj, respectively. This is performed as shown below:(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 faces tci 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 faces but not adjacent to the additional locator faces. It is preferable to select a clamp face that does not have to share the adjacent perpendicular face with a locator. This step can be automated as shown below:(a) Consider each face tci in list TCF and obtain correspond- ing faces fci that are adjacent and perpendicular to each tci. 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 availability of potential clamping faces, as described below.Case (a). If there are no entries in list NTCF, then use the faces in list TCF and proceed to step 4. If any faces were found that were perpendicular to the secondary and tertiary location faces lf1 and lf2, such faces are the next feasible choices to be used for clamping.In this case, the only remaining choice is to re-examine the faces in list NTCF.Case (b). If the number of entries in list NTCF is 1, the feasible clamping face is fci. The normal vector of the corresponding adjacent, perpendicular face tci is the axis of clamping.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 be positioned along the centre of the face tci. The candidate geometrical positions of the clamp can be determined using part geometry and topological information, which is described in the next section.Fig. 5. Determination of the clamp profile dimensions.5. Determination of the Clamping Points on a Clamping FaceAfter the clamp face has been determined, the actual clamping positions on that face must be determined. The inputs are the clamp profile dimensions, clamp directions x, y, z, and poten- tial clamping face CF. The clamp profile dimensions are obtained (as in case (g) using CF geometry as follows.The first step is to determine a box size, which is tested to determine whether it contains any features inside it. Profile intersection tests can also be performed using the method described earlier. If the intersection test returns a negative result, then no feature intersects with the clamp box profile, as shown in Fig. 4. If the intersection test returns a positive result, the following steps can be performed:1. Divide the clamp box profile into smaller rectangular strips of size (1 w) (Figs 5 and 6).2. Perform the intersection tests with the feature profiles of features 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 one candidate rectangle for clamping, the rectangle profile that is toward the mid-point of the CF face along the clamping axis is the clamp profile (and clamp points).If no profile Pi can be found that does not intersect with the feature profiles, clamp width can be reduced by half and the number of clamps increased to two on that face. Using these modified clamp dimensions, perform the feature intersection test described earlier. If this test also fails, then the side face adjacent to the PCF can be used as the clamping surface to perform side clamping. The side face then becomes the PCF and the feature intersection test can be repeated.5.1 The Intersection of Profiles TestThe required inputs include the 2D profile P1 another 2D profile P2. The intersection of profiles can be determined in an automated manner using the following approach. Each input profile Pi consists of a closed loop of line segments Lij. The steps in this profile test are as follows:(T1) Consider a line segment L(i,1) in P1 and another line segment L(2, j) in P2.(T2) For inputs L(i,1) and L(2, j), the intersection of edges can be employed. If the edge intersection test returns a positive value, then the feature profile intersects with the candidate or potential clamp profile under evaluation. If it returns a negative value, 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 or segments L12, L13,. . .,L1n in profile P1.If the feature profiles overlap the clamping profiles, the line intersection tests will determine that occurrence. The inter- section of edges test can be performed automatically to detect whether two edges intersect with each other. The inputs required 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 substituting x3 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 the signs of r3 and r4 are the same, (which indicate r1 and r2 lie 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, and the signs of both r1 and r2 are the same , then r1, r2 lie onFig. 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 completes the test.Consider the same sample part shown in Fig. 7. The features to be produced are a step and hole. Initially, the locator design is completed. The support locator (or primary locator) is a base plate (placed against face f4) and the secondary and tertiary locators are placed against faces f6 and f5 (which correspond to the locator faces lf1 and lf2 discussed in Section 4). An ancillary locator is also used, which is a v-block (positioned against the ancillary faces f3 and f5), shown in Fig. 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 are parallel and at the farthest distance from lf1 and lf2) are face f3 and f5. There are no faces which are parallel to the locator faces but not adjacent to them. Using the priority rules in such cases (as discussed in step 3 of Section 4), the remaining candidate face is face f2. The clamp direction is downward; the v-block radial locator and other locators provide the required location with the clamp holding the workpiece down- ward against the baseplate.The position of the clamp is determined based on the steps described in Section 5. As there are no feaures occurring on face f2, there is no need for feature intersection tests to determine collision-free clamping. The position of the clamp should be away from the v-locator (which is positioned along the ancillary location faces) as the clamping face is adjacent to the ancillary location faces (this ensures better access for quick clamping). The final location and clamping design is shown in Fig. 8.The method discussed in this paper compares favourably with the other clamp design methods discussed in the literature. The uniqueness of the discussed approach is the systematic identification of the clamping faces based on part geometry, topology, and the occurrence of features to be machined. While other approaches have not exploited the position of the locators adequately, the proposed method uses the locators to hold the workpiece during machining against the primary, secondary, and tertiary locators. Another advantage of this approach is the determination of candidate feasible locations on clamp faces using the detection of profile intersections test (described earlier), 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 context of a fixture design methodology was discussed. The locator design, the part design specifications, and other inputs are considered 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 approach to automatic configuration of machining fixtures: analysis and synthesis”, Transactions ASME, Journal of Engineering for Indus- try, 111(4), pp. 299306, 1989.2. Y. Kang, Y. Rong and M. Sun, “Constraint based modular fixture assembly modelling and automated design”, Proceedings of the ASME Manufacturing Science and Engineering Division, 8, pp. 901908, 1998.3. M. Mani and W. R. D. Wilson, “Automated design of workholding fixtures using kinematic constraint synthesis”, 16th NAMRC, pp. 437444, 1988.4. B. Bidanda and P. H. Cohen, “Development of a computer aided fixture selection system for concentric rotational parts,” Advances in Integrated Design and Manufacturing, Proceedings 1990 ASME Winter Annual Meeting, San Francisco, CA, vol. 231, pp. 151 162, 1990.5. R. E. DeVor, V. Chandrasekharan and S. G. Kapoor, “Mechanistic model to predict the cutting force system for arbitrary drill point geometry”, Transactions ASME Journal of Manufacturing Science and Engineering, 120, pp. 563570, 1998.6. R. E. DeVor, S. G. Kapoor and W. J. Endres, “A dual based approach to the prediction of machining forces for metal cutting processes: Part II, Model validation and interpretation”, Trans- actions Journal of Engineering for ASME Industry, 117, pp. 534 541, 1995.7. M. V. Gandhi and B. S. Thompson, “Automated design of modular
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