拖拉机Ⅱ-Ⅲ档倒挡拨叉工艺及钻φ5孔夹具设计【版本2】参考素材
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科技译文科技译文科技译文AUTOMATIC FIXTURE SYNTHESIS IN 3DKamen PenevProgrammable Automation LaboratoryComputer Science Department and Institute for Robotics and Intelligent SystemsUniversity of Southern CaliforniaLos Angeles, CA 90089-0781Aristides A. G. RequichaProgrammable Automation LaboratoryComputer Science Department and Institute for Robotics and Intelligent SystemsUniversity of Southern CaliforniaLos Angeles, CA 90089-0781ABSTRACTA 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. INTRODUCTIONA 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 3DFollowing 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 placementIn 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.baFigure 2: From contact point configuration to fixture layout designIn 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 INPUTThe 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 BOUNDARYThe 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 FIELDThe 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: CCmziki1After 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：PPCd m ndnnm12110,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 meshAssuming 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 49 166 166 166 49 49Figure 4: Potential field generated by three charged nodesThe 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:P m nm n(,)(,)1142Here 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 EPOCHSEach 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 TESTIn 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: sswiCi01The 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. DISCUSSIONThe 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 AnalysisVarious 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 surfacesmachined surfacessurfaces with “good” orientationareas with good accessibilityareas that need additional support to prevent deflection and deformationRepulsion zones can represent:inaccessible areasforbidden areas due to tool accessibility requirementssurfaces with poor orientationcast surfacessensitive 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 CompletionAn 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 engine7.3 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 EfficiencyThe 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 the boundary provide a sufficient basis for fixturability of any solid object. 科技译文自动夹具在三维中的合成自动夹具在三维中的合成Kamen penev可编程自动化实验室计算机科学系和研究所，机器人与智能系统南加州大学洛杉矶，加州 90089-0781 Aristides A. G. Requicha可编程自动化实验室计算机科学系和研究所，机器人与智能系统南加州大学洛杉矶，加州 90089-0781摘要夹具是一个安排在装夹模块中的位置，并举行工件在一个以制造业为主的运作。我们在这项工作中,考虑固定装置与无摩擦点接触，并给出了一个方法，为安置的接触点上的非棱柱体三维工件 。它是一个非确定性，势场算法的接触点安置。该方法提供了一个基本框架，为整合异构高层次装夹代理商通过一个界面基于区的吸引力和斥力就工件边界。该算法可能会产生多余的固定装置，并能增加部分的解决办法，以形成完整的封闭装置。 1. 导言夹具是一个安排的装夹模块中的位置，并举行工件在一个以制造业为主的操作，如加工，装配和检验。装夹是最重要的，以工业制造，并构成的一个重要部分，所有的制造成本。因此，夹具设计自动化是非常重要的。夹具设计涉及多种因素，例如，克制，决定性的位置，装载和工具无障碍环境。高效的算法处理整个一系列的装夹问题，为全面域工件尚不存在。最近， brost 和彼得斯出版了一种算法 brost 彼得斯 1996 延伸早前经典的工作 brost 和戈德堡 brost 戈德堡， 1994 ，以三维域。这种算法，但需要纵向和横向平面构成相当大一部分的工件边界。它产生的所有可能的固定装置，然后在利率，他们因此对某些衡量标准。这是在计算上昂贵的。 Wagner 等提出了一种算法，使用 7 个模块的 Struts 安装在一个盒子里，以夹具多面体 Wagner 等， 1995 年 。这个算法是不全面的，在这个意义上讲，它并不能有效地处理某些情况下，例如一个立方体的脸平行包装盒。它也经历着从高计算复杂度。 wallack 和精明提出另一种方法，并有列举与汇率的味道 wallack Canny， 1996年 。它可以夹具棱柱工件与平面和圆柱垂直表面。庞塞提出了一种算法，利用曲率的影响，计算出固定装置与四指为多面体零件庞塞 96 。在数量减少的接触应提供更好的复杂算法，但质量的生产设备，似乎不亚于那些利用更多的接触，并提供古典形式封闭。 在这篇文章中我们提出了一种新的潜在场算法，有效地生产优质夹具设计。我们的算法工程任意工件 ，并提供便捷的普遍手段，代表不同的装夹要求。这种算法是一种直接泛化的二维势场装夹算法 penev 和 requicha penev requicha 1996 。我们认为，固定装置与无摩擦点接触。它已证明七名接触是必要的。 somoff ， 1900 ，并有足够的 markenscoff 等人， 1990 年固定任何工件在三维继至少承诺的策略，过程夹具合成可分为三个阶段-装夹任务分析，接触点安置以及夹具布局设计。在装夹任务分析阶段工件几何和制造过程中分析，以确定各种参数的装夹问题，如切削力，交通不便或禁止的领域，并找出特点，可用于申请装夹装置，例如机械平面，横向和纵向表面，对平行表面，对垂直于表面，等等。图 1 ：接触点安置在接触点安置阶段的一些联络点，是摆在工件边界（图 1 ） ，因此由此产生的配置接触满足确定的限制因素，在分析阶段，以及一些运动学要求必须得到满足，任何夹具如完全克制。图 2 ：从接触点配置，以夹具布局设计在布局设计阶段水塔的装夹元件是建立并置于周围工件等，以接触的部分，在点位置计算，在接触点安置阶段。举例来说，一个接触点上，横向工件表面（图甲） b a 科技译文，可导致以实例化的额外开销钳说，接触了工件在那个特定点（图 2B ）条。这是一个以设计为功能的问题，制约了一套可装夹单元及其参数。这实现了套联络点的功能规格及夹具布局是一个配置的部件。 在本研究中，我们的重点联系点安置，并把它纳入其中部分和任务的分析。安排的接触点必须满足某些运动学条件，以一个基础，有一个良好的夹具。特别是，它必须提供的封闭形式，确定位置，夹紧稳定， 脱离能力和装载Asada & By 。该算法采用离散化的工件边界，类似的网格所使用的有限元分析。但是，不同于有限元分析，我们注意的是，对网格节点上，而不是放在网格元素。离散选择为以下几个原因：首先，我们可以处理工件任意几何，只要把部分的边界是一家集表面光滑，而我们知道如何主题词。这项规定是满意的所有表面用在现代 CAD 系统。其次，离散化是必要的，以避免昂贵的计算测曲线。第三，离散应该不会大大影响结果，只要有多少离散候选地点就边界要远远大于人数表面上。在我国实施离散边界构成的几百点。实验证据表明，这是不够现实的工件。 我们引进一个潜在场对工件边界界定区的吸引与排斥，我们称之为个 P -区。接触是仿照由于带电粒子的这一举动对边界驱动这个潜在的领域。接触也受到相互排斥的基础上，之间的距离每两个接触，在扳手向量空间。该算法执行了一系列的模拟时代。每一个划时代的开始，以随机配置，收益是通过一定数量的步骤，向低势能和结束一场考验运动学条件（形成封闭） 。该算法终止时，一个划时代的产生令人满意的配置。 传播接触点上的边界，我们模拟斥力之间相互对他们。强度斥力之间的两个接触点，取决于它们之间的距离及其相应的扳手在扳手向量空间。我们的模拟收益，在有限的几个步骤，或直至平衡是达成共识。由此产生的就业，应该有很好的机会，导致一个好的夹具。这种随机方法假定一套正元组的联系点（对 N 大于 3 ）表示，满足运动学要求，有措施，都大于零，是比较大。这就是说，解空间非常大。虽然我们尚未能证明这一假设的数学，我们的实验已经证实了它。此外，这项措施增加多少接触点，例如，这是比较容易找到一个封闭的形式安排多于 8 分之 7。 概念斥力是必不可少的方法，因为这可以容易容纳其他因素。我们可以把更多的斥力点就工件边界，以代表故宫地区。我们还可以介绍中心的吸引力。这些对应的地方被推荐人的分析阶段可取配售联系点，例如，基准面表面。因此，我们提出一个势场为代表一致异构装夹信息。地区斥力对应地区的积极潜力。负电位，是与魅力。零电位对应于中立地区。初始随机抽选的联系点，被视为微粒，正在吸引或击退一个势场，其中包括成对斥力。目标体系的联系点是为了最大限度地减少其总势能。2. 输入输入我们的算法包括 CAD 模型的工件边界，以及一套坚实的 P -区。每个人 P -区界定一个潜在场的影响区域与非零收费。三离散工件边界，第一步，我们的做法是把离散边界的工件 ，因而创造候选人接触点的位置，我们称之为节点。离散化是做了引用标准工作面嵌入在几何造型。离散是储存在一个面向图形数据结构。每个节点的图形对应的一个节点上的网格。边缘的图形对应边的网格连接相邻节点。在每个节点螺丝代表联系点，是计算和储存。螺丝钉是一个简洁和方便的代表性表面正常位置的节点。它是用来在所有运动测试基于螺旋理论。 3. 离散工件边界第一步，我们的做法是把离散边界的工件 ，因而创造候选人接触点的位置，我们称之为节点。离散化，是做了，引用标准表面嵌入在几何造型，我们使用。离散是储存在一个面向图形数据结构。每个节点的图形对应的一个节点上的网格。边缘的图形对应边的网格连接相邻节点。在每个节点螺丝代表联系点，是计算和储存。螺丝钉是一个简洁和方便的代表性表面正常位置的节点。它是用来在所有运动测试基于螺旋理论。4. 计算势场联系点，在我们的算法是受联合行动，由两部分组成，形成了潜在的领域。背景势场是其中的组成部分。这是产生由 P 区和不依赖于地理位置的联系点。背景势场的计算方法是只计算一次，在一开始的算法。另一部分是动态的和，这是由于该斥力之间的接触。动态部分是计算机在每一个划时代的。 计算的背景势场的收益如下：首先，我们找到所有的节点所在内的 P -区。我们履行会员分类每个节点对每个人 P -区 tilove 1980 年 。如果节点内一定的 P -区，负责为 P 区，有助于节点的电荷。贡献，可以是正面的还是负面的，这取决于该标志区的电荷。经过这个程序的节点进行分类外，所有的 P -区仍具有零收费。如果一个节点米制内的 P -区 Z1 的， z2 的.专用料 ZK 其负责厘米等于一笔收费的那些人 P -区：CCmziki1之后，负责该节点内的 P -特区，是我们评价我们开始通过计算潜在的所有节点。我们界定的潜在处于被控节点，初步等于它的电荷时=厘米。每个被控节点 m 的范围内负责厘米，我们演出广度优先遍历其邻居更新他们的潜力根据公式科技译文PPCd m ndnnm12110,这里 D 类（ m ， n ）的是它们之间的距离节点米（带电节点）和 N ， d0 是一个不断的所谓距离的影响力。它们之间的距离两个节点定义为边数上的最
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