中英文翻译几何在机械设计中的作用

本科毕业论文（设计）翻译

题目新型超声波洗碗机

学院制造科学与工程学院

专业机械设计及其自动化

学生姓名

学号年级08 指导教师蔡鹏

教务处制表

二O一二年五月二十八日

On the Role of Geometry in Mechanical Design

Vadim Shapiro Herb Voelcker

The Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA

A complete design usually specifies a mechanical system in terms of component parts and assembly relationships. Each part has a fully defined nominal or ideal form and well defined material properties. Tolerances are used to permit variations in the form and properties of the components, and are used also to permit variations in the assembly relationships. Thus the geometry and material properties of the system and all of its pieces are fully defined (at least in principle). Henceforth we shall focus on geometry and, for reasons that will become evident, will not deal with materials despite their obvious importance.

Mechanical systems specified in the manner just described meet functional specifications that appeared initially as design goals. The process of design can be thought of as "generating the geometry "the breakdown into components with coarsely specified geometry, and then the detailed specification of the component forms and fitting relationships. Design seems to proceed through simultaneous refinement of geometry and function [I]. An important line of design research seeks scientific models for this refinement process and systematic procedures for improving and perhaps automating it.

At present we have tools for dealing with two widely separated stages of the refinement process.

For single parts, function is usually specified through loads on pieces of surface (e.g.

a force distribution over a support surface, a flow rate through an orifice, a radiation pattern over a cooling fin); specification of the solid material that pro-vides a carrier for the pieces of surface may be viewed as a constrained shape optimization process. At the higher level of "unit functionality," where one deals with springs, motors, gear boxes, heat exchangers, and the like, geometry usually is abstracted into real numbers if acknowledged at all, and function is cast in terms of ordinary differential or algebraic equations (for heat flow, motor torque as a function of field current, and so forth).Systems of such equations describe the composite functionalism of networks of functional units. There is a big gap between these "islands of understanding," and intermediate stages of abstraction are needed which acknowledge the partial geometry and spatial arrangement topology of subassemblies. Broadly speaking, geometry is faring badly in contemporary design

research; many investigators either "sweep it under the carpet" ordeal with it syntactically, e.g. through "features" defined in ad hoc ways. Clearly we need more systematic ways to address the relationship between geometry and function, and we suggest below some initial steps toward this goal.

Energy Exchange as a Mechanism for Modeling Mechanical Function Mechanical artifacts interact with their environments through spatially distributed energy ex-changes, and we argue below that mechanical functionalism can be modeled in terms of these exchanges. The initial cast of the argument draws heavily on seminal work by Henry Paynter [2].We shall regard mechanical artifacts as systems that range from single solids or fluid streams, which usually are the lowest level of natural system that exhibit important properties of mechanics, to complex assemblies of solids and streams. A closed boundary, which may be physical or conceptual, is a distinguishing characteristic of a system: the sys-tem lies within (and partially in) the boundary, the environment lies outside, and interaction occurs through the boundary. We distinguish the following:

S : the physical system under discussion;

8S : the boundary of S;

V : a spatial region containing S whose complement isthe environment;

8 V : the boundary of V.

S may coincide with V, and 8S and 8 V are closed surfaces (usually 2-mainfolds) in E 3. We distinguish S from V because S may be partially or wholly un-known (recall that this note is about design) but bound able by a known V. The principle of continuity of energy applies tall levels of system abstraction. If no energy is generated by the system, then

The surface integral on the left describes the total energy flux (instantaneous power) through the boundary; P is a generalized Poynting vector describing the instantaneous rate at which energy is transported per unit area, and n is the normal at a point in the boundary 8 V. On the right, Oe/Ot is the(volumetric) density of energy stored in the system, and g is the rate of energy loss or dissipation. A system interacts with its environment by ex-changing energy through its physical boundary: for example, by radiating energy stored in the system over a portion of its area, or by providing support to an external mating part and thereby inducing storage of deformation energy in the system. The sub-sets of the physical boundary over which such ex-changes occur will be called (following Paynter) energy ports. If s~ is the physical boundary subset ('piece of surface') associated with the it u port, then

Thus the total energy flux through the boundary is as um of signed fluxes through the ports. We note that a boundary subset si may belong to several ports, and that body forces, such as those induced by gravitational and magnetic fields, may be accommodated by taking ~S as the associated port.

Geometrical and Functional Refinement in the Limit

The left side of Eq. (2a) specifies energy exchanges through the system's ports and requires that the flux vector(s) and port geometries be known. The terms on the right cover internal energy (re)distribution and/or dissipation. The physical effects implied by these terms depend on the energy regime(s) and the geometry of the system; there may be rigid body motion, elastic or plastic deformation, temperature redistribution, and so forth. Mathematical evaluation requires the solution of 3-D boundary- and/or initial-value problems. Very marked simplifications ensue if one assumes that 1) the ports are spatially localized and idealized so that the integrals on the left of Eq. (2a)may be evaluated individually to yield terms Pi, and2) internal energy storage and dissipation are similarly localized in disjoint discrete regions, thereby permitting the right-hand integrals to be decomposed into sums of local integrals which may be evaluated individually. With these assumptions, Eq. (2a) may be rewritten

where Pi is the power through the discrete port, E is the instantaneous energy stored in the discrete region, and Gk is the dissipation rate in the k discrete region.

A limiting form of this refinement(in Paynter's terminology--reticulation) is a "Dirac-delta limit" wherein the ports shrink to spots of zero area and the volumetric regions shrink to point masses, idealized resistors, and the like. Equation (3) is the basis for Paynter's energy bond diagrams, or bond graphs. It describes a sys-tem that may transfer, transform, store, and dissipate energy through elements whose geometry has been refined into a few real numbers--the spatial l positions of the discrete ports and lumped regions(which generally are not carried in bond-graph representations), and integral characterizations of the

discrete ports and regions (for example the" value," in kilograms, of a point mass). This higher view enables one to analyze the dynamics of the idealized (discreet) system, but one can deduce little about the geometry of feasible distributed (i.e., real) systems from such analyses; essentially all geometry must be induced. Apparently we have gone too far, i.e., have thrown away too much geometry.

Fig. (1) Design of simple bracket

Toward an Appropriate Role for Geometry We would like to step back from the limiting refinement just discussed, where all notions of form have been lost, and includes in the problem some continuous geometry--but not the full-blown field problem covered by Eq. (I) unless this is unavoidable. We shall suggest below three principles governing the interaction of form and function that we believe will yield geometrically well defined (but not necessarily optimum) designs. A simple but common example drawn from practice--design of a bracket—will motivate the discussion (Fig. 1).

The design begins with three holes of known diameter and configuration that are to be carried by an unknown solid (Fig. la); these mate with other parts (two screws and a pivot pin). Bosses are created to contain the holes (Fig. lb) because of concern about interference with other components passing between the holes. Finally the holes and bosses are bound together into a single part as in Figs. lc and ld, with the final shape being governed by criteria for clearance, strength, weight, and aesthetic and manufacturing simplicity. Two simple but important inferences may be drawn from the example. Firstly, the initial holes(plus some implied constraint surfaces in the third dimension) are the bracket's energy ports; they are fully specified geometrically and specify by implication what the bracket is to do--maintain the

relative position of ports whose geometry admits rotational motion. In principle the associated energy regimes(force, torque: elasticity) can be fully specified as well, but in practice they are often only implied or "understood." Secondly, the remaining geometry is discretionary but constrained by requirements that the holes be bound into a connected solid, that the solid not interfere with other components, and so forth. We note that, at the single-component level of the bracket, shape optimization usually does require solution of the full 3-D field problem covered by Eq. (2a).

Fig (2) position-fixing of the character bracket

From this example and others we induce: Principle 1. A system's "function" is determined by its energy ports, which are generally subsets of its physical boundary, and the energy regimes operating on those ports; both should be fully defined. The remaining geometry of the system is discretionary provided that 1) it admits at least one physical realization of the system that satisfies the port specifications, and 2) other external constraints, e.g. on overall size, are met. Principle 2. Energy exchanges within a system al-ways may be represented independently of geometry, e.g. via bond graphs. Figure 2 shows the position-fixing capabilities of the bracket represented (non uniquely) by ideal springs attached to the locally rigid ports. This representation of the bracket's partial functionalism assumes ideally elastic behavior, and this assumption should be checked, e.g. by finite-element analysis, as the bracket's final shape is being determined. Figure 3 shows a slightly more complicated sys-t e m - a n indicator that senses pressure via an orifice (port) of known geometry, and displaces a rotary indicator correspondingly. The output indicator is a port because we require that it be able

Fig(3) A pressure measure system

to do work on the environment, e.g. overcome specified restraining torques over a defined range of travel, and hence its geometry must be defined. The system also has a third support port. The system's primary function is represented internally by a pres-sure/torque transformer and a rotary spring which are shown as bond graph elements in the style of Ulrich and Searing [3], but this representation is not unique; it may be replaced with other, arbitrarily elaborate arrangements of idealized elements having the same input/output functionalism plus other paths that terminate internally. Equation (4) provides the rationale for Principle2. The essential idea is that the port flow on the left of Eq. (2a) may be handled internally (the right-hand integrals in E q. (2a)) in many ways.

If we are assured by Principle I, or simply assume, that internal solutions exist, then we may reticulate the internal geometry and deal with integral quantities as in Eq.

(3).Principle 3. Principles 1 and 2 must hold for all subsystems defined on combinatorial decompositions of a system. Principle 3 provides means for the simultaneous refinement of geometry and function. It enables complicated systems to be decomposed recursively into functional subsystems provided that one defines the ports as one proceeds. The limiting combinatorial refinement is single parts, and at this level one must solve the field problem of Eq. (2a) to obtain complete geometric specifications.

Concluding Remarks

The thoughts above are aimed at finding means to establish for geometry an appropriate formal role in a theory of mechanical design. It seems obvious to us that geometry should have such a role, but the work needed to establish it has barely begun.

Epilogue Remarks on Features

This work grew out of a several-month effort to characterize geometric features in a formal man-n e r w a n effort that largely failed. The effort was motivated by the fact that mechanical design and manufacturing are often discussed and done in terms of "features," but there are no agreed view son what features " a r e " or " d o " [4]. (Slots, fibs, webs, and shafts, are typical features; all involve geometry in one way or another.)We began with a conjecture: A geometric feature may be defined as a geometric idealization of a port for energy exchange in a defined regime. (This notion is appealing because it implies that a system's feature-set specifies all of the geometry needed to define the system's interactions with its environment; the remaining geometry is determined by constraints and optimization.) We then proceeded to show that the conjecture is formally consistent in design, manufacturing, and inspection applications. In machining, for example, geometric features maybe associated with the boundary of the removed material; the energetic process is machining itself, whose dynamics are reasonably well understood in a

macroscopic sense. Clamping features may be de-fined primarily through elastic energy storage, inspection features through the energetic exchange involved in the measurement process, etc. But a sour explanations grew increasingly contrived and our difficulties with solid and other non-surface features mounted, we began to sense that features could not be defined in any universal system other than a purely syntactic system. Currently we believe that features are simply in-formation structures that represent, often in parametric form, known solutions to local problems. While a syntactic structure can be imposed on them, their underlying semantics can vary widely and need not involve particular kinds of geometry, or indeed any geometry at all. However, if a feature is to be used properly, a feature-context must be supplied the technical conditions and criteria that led to the solution the feature represents. Given the feature-context (e.g., as domain knowledge in a de-signer's head) and appropriate reasoning power to adapt the solution to the current problem, features can be very effective; their popularity among human designers attests to this. Recent work by Duffey and Dixon [5] illustrates that features can be used in automatic design when feature-contexts and appropriate reasoning power are provided. (The handling of features by Duffey and Dixon seems ad hoc, but "ad-hockey" may be intrinsic if our current permissive view of features is correct.) Features can be dangerous when used without their contexts and appropriate reasoning power, as nonsense designs produced by certain automatic design systems illustrate. Finally, we wish to point out that the Characterization of features as " known solutions to local problems " places strong constraints on schemes for combining features to make new features. A feature combination makes sense only if it can be shown to be a valid solution to a well defined local problem. But even determining the domain of the combination problem as a function of its c o m p o n e n t do-mains may p r o v e very difficult. Acknowledgments

The work reported here was supported in part by the General Motors Corporation under its corporate fellowship program, and by the National Science Foundation under grant MIP-87-19196.

References

1. Alexander, C., Notes on the Synthesis of Form, Harvard University Press, 1964

2. Paynter, H.M., Analysis and Design of Engineering Systems, MIT Press, 1961

3. Ulrich, K.T. and Searing, W.P., "Conceptual Design: Syn-thesis of System of Components," 1987ASME Winter Annual Meeting, PED Vol. 25

4. Report of the Workshop on Features in Design and Manufacturing, February 26-28, 1988 University of California, Los Angeles

5. Duffey, M.R. and Dixon, J.R., "Automating extrusion de-sign: a case study in geometric and topological reasoning for mechanical design," Computer-Aided Design, Vol. 20, No.10, pp. 589-596, December 1988

几何在机械设计中的作用

Vadim Shapiro，Herb Voelcker*

The Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA

一个完整的设计通常指定一个机械系统的零部件和装配关系。每个部分都有一个完全定义的名义或理想的形式和定义良好的物质属性。公差是用来允许组件的形式和性质的变化，也用来允许在装配关系的变化。因此，该系统的几何形状和材料的性能和其所有的作品都完全定义（至少在原则上）。今后，我们将集中几何，将成为明显的原因，将不会处理的材料，尽管其重要性显而易见。描述的方式在指定的机械系统只是满足最初出现作为设计目标的功能规格。在设计过程中，可以被认为是“生成几何”与粗糙指定的几何体划分成组件，然后组件的形式和拟合关系的详细规范。设计似乎着手，通过几何形状和功能的同时细化。细化过程和改善，或许自动化系统的程序设计研究的一个重要防线，旨在科学模型。目前，我们有两个相距甚远的细化过程中的阶段处理工具。为单件，功能件表面上的负载（如支持表面的受力分布，通过孔板的流量，通过冷却鳍的辐射模式）规范，提供了坚实的物质通常被指定通过表面件的，承运人可以被看作是受约束的形状优化过程。[1]

对单件而言，功能件表面上的负载（如支持表面的受力分布，通过孔板的流量，通过冷却鳍的辐射模式）;固体材料的规范通常规定通过亲比德斯载体表面的碎片可以被看作是一个约束的形状优化亲过程。

在更高层次的“单位的功能，”其中一个弹簧，马达，齿轮箱，热交换器，之类的，几何的交易通常抽象的实数，如果都承认，和普通功能差分或代数方程组（热流，扭矩电机励磁电流的功能，等等）。这些方程的系统描述网络的功能单位的复合机能。之间有一个很大的差距“联合国理解岛”和抽象的中间阶段，需要承认部分的几何结构和空间安排的组件拓扑。从广义上讲，几何严重的是远在当代设计研究;许多研究者或者“扫地毯下的”磨难与语法，例如通过特别的方式定义的“功能”。显然，我们需要更系统的方法来解决几何结构和功能之间的关系，我们建议以下一些初步的步骤，为实现这一目标。

作一个能源交易机械功能建模机制

机械构件交互他们的环境中使用，通过能量空间分布前的变化，我们认为以下机械机能，可以在这些交流为蓝本。[2]的说法初始投绘制沉重的开创性的工作，由亨利·潘德。我们应视为系统的机械构件，范围从单一的固体或液体流，这通常是自然系统的最低水平，表现出力学的重要属性，固体和溪流的复杂组件。一个封闭的边界，可能是物理或概念，ISA系统的显着特征：系统的边界范围内（部分），在于外部环境，并通过边界发生互动。我们区分如下：S：所讨论的物理系统;

8S：S的边界;

V：含S环境的补充是一个空间区域;

8 V：VS的边界

可能与V不谋而合，8S和8 V的表面（通常主要褶皱2）在E3。我们区分从V因为可能是部分或全部联合国著名的（记得，这说明设计），但必然能够通过一个已知的五能源的连续性的原则适用于高层次的系统抽象。如果没有能量，然后由系统生成。

在不可分割的表面上，介绍了能量通量（瞬时功率）通过边界，P是一个广义的坡印廷矢量划线在能源运输每单位面积，和n的瞬时速度是在8V，在边界问题上的权利，OE正常/ OT是能源（体积）密度在系统中存储，g是能量损耗或损耗率。一个系统的相互作用与变化前通过其物理边界的能源环境：例如，通过辐射能量储存在系统超过其面积的部分，或提供支持托安对外交配的一部分，从而诱发变形能量存储年龄系统。超过前变化发生的物理边界的子集将被称为（以下潘德）能源港口。如果是物理边界的一个子集（“面片”）国际电联端口相关，然后

因此，通过边界的总能量通量的通过端口签署的通量ASUM。我们注意到综合类边界的一个子集SI可能属于多个港口，该机构的力量，如引力和磁场诱导的，可以由小号关联的端口提供获知

在限制式的几何结构和功能的细化。

左侧（2A）通过系统的端口指定的能量交换，并要求被称为磁通矢量（S）和端口几何。右盖板内部能量（重新）分配和/或耗散的条款。这些条款所隐含的物理效应，取决于能源制度（S）和系统的几何形状;有可能是刚体运动，弹性或塑性变形，温度再分配，依此类推。数学评估需要的3-D的边界和/或初始值问题的解决方案。非常明显的简化，随之而来，如果之一，仅从1）端口空间本地化和理想化，所以上式左边的积分。（2A）可单独评估，以产量计算PI，and2）内部能量储存和消耗同样定位在不相交的离散地区，允许右手积分可单独评估当地的积分款项分解构成。与这些假设式。（2A）可能被改写

其中Pi是权力通过IH分立端口，EJ是瞬时能量储存在第j个离散地区，GK 是在第k个离散地区的耗散率。这种细化的限制形式（或离散，或- 在潘德的术语- 网状）是“狄拉克三角洲极限”，其中的端口缩小到零面积的斑点和TRIC 地区的体积缩小点群众，理想化电阻，和喜欢。方程（3）潘德的能源债券的图表，键合图的基础上。它描述了系统温度，可转让，转换，存储，并通过精成几个实数的几何元素被检定的能源- 耗散，颈部离散港口和集中的地区（一般不进行债券的空间位置图表示）和离散港口和地区（例如“价值”，以千克为一个质点，）组成的刻画。较高的视图使一个理想化的（离散）系统的动力学分析，几何可行的分布式系统（即实际）从这样的分析，但可以推断小，基本上所有的几何结构必须引起。显然，我们已经走得太远，即，已经丢掉了太多的几何图形。

图1 简易支架的设计

走向几何适当的角色，我们想退一步限制完善的，只是讨论，所有形式的疑问和观念的丢失，并在问题，包括一些连续的几何- 而不是全面爆发式所涵盖的领域的问题。除非这是不可避免的。我们将提出以下三个互动的形式和功能，我们相信这将产生几何定义（但不一定是最佳的）设计的原则。从实践中得出- 支架的设计- 一个简单而常见的例子将激励的讨论（图1）设计开始与著名DI-直径三洞和配置是由一个未知的固体进行（图。LA）;这些队友与其他部分（两个螺钉和枢轴销）。老板是创建包含孔（图磅），因为关注与孔之间的传递其他组件的干扰。最后孔和老板联系在一起，作为在图的一部分。LC和LD，最终的形状与间隙，强度，重量和审美和制造简单的标准管辖。从这个例子可以得出两个简

单但重要的推论。首先，初始孔（加上一些隐含在第三个层面的约束表面）括号内的能源港口;它们完全指定几何，并指定由支架是做什么的意义- 维护港口的相对位置，其几何承认旋转运动。相关的能源制度（力，扭矩：弹性），原则上可以完全指定为好，但在实践中，他们往往只暗示或“理解。”其次，余下的几何是全权的，但要求限制孔将连接坚实的约束

图2 支架位置固定的特点

固体不干扰其他组件，等等。我们注意到，在支架上的单组分，形状优化通常需要全覆盖式3-D场问题的解决方案。（2A），我们从这个例子和其他诱导：原则1。系统的“功能”是由一般亚群挡住物理边界，其能源港口，能源制度，对这些端口进行操作，同时应充分界定。该系统的其余几何酌情元提供

1）承认至少有一个系统，满足港口规范，应征者具备的物理实现.

2）其他外部约束，如整体规模上，都得到满足。原则2。可派代表在一个系统内能量的方式交流，独立的几何结构尝试，例如：通过键合图图2显示了代表固定位置的能力国税发支架连接到本地的刚性端口的理想弹簧（非唯一）。这种支架的部分机能，仅从理想的弹性行为，这种假设的代表权应进行检查，如有限元分析，作为支架的最终形状被确定。图3显示了一个稍微复杂的系统的一个指标，通过已知的几何口（端口），取代旋转指示器相应的感官压力。输出指示灯是一个港口，因为我们需要它能够

图3 压力测量系统

做对环境的工作，例如克服制约了旅游的定义范围的扭矩指定的，因此必须定义其几何。该系统还具有第三个支持端口。该系统的主要功能是代表国内1压力/扭矩变压器和1旋转弹簧撰稿显示乌尔里希的风格债券图形元素和见环[3]，但

这种表示不独特，它可能会被其他，随意更换甲肝相同的输入/输出机能，加上国内其他路径终止理想化元素的精心安排。方程（4）提供的理由为原则2。基本思想是港口流动式左。（2A）可处理包括内部（右边积分式（2A））在许多方面。如果我们原则上是放心我，或简单地假设，即内部解决方案存在，那么我们可能会活动的数量网纹式的内部几何和处理。（3）原则3。原则1和2必须持

有组合分解系统中定义的所有子系统。原则3提供的几何形状和功能的同时细化的手段。它使复杂的系统分解成递归功能子系统提供的罚款作为一个所得的端口。组合细化的限制是单件，并在这个水平，就必须解决的EQ域的问题。（2A），以获得完整的几何规格。

结束语

上述思想的目的是寻找手段几何建立一个适当的正式角色INA机械设计理论。这似乎是显而易见的几何，应该有这样的作用，但需要建立它的工作才刚刚开始。

特点后记备注

这项工作持续了数月的努力，表征几何特征，在一个正式的方式，基本上未能努力。事实上，机械设计努力的动机和制造经常讨论，并在完成“功能，”但也有不同意的观点儿子有什么特点“是”或“做”[4]。（槽，避免信口开河，网，并轴，是典型的特点;所有涉及这样或那样的几何形状。）

我们开始了一个猜想：一个几何特征可以作为定义政权的能量交换端口的几何理想化定义。（这种观点是有吸引力，因为它意味着该系统的功能，集指定所有需要定义与环境系统的相互作用的几何;。，其余的几何形状取决于约束和优化），我们再进行的，猜想是正式在设计，制造，检查应用程序一致。例如，在加工，几何特征也许与拆下的材料边界;充满活力的过程是加工本身，其动态合理以及在宏观意义上的理解。夹紧功能，可去罚款，主要是通过弹性储能，在测量过程中所涉及的充满活力的交流功能，通过检查等，但酸的解释越来越做作和安装我们的困难与固体和其他非表面特征，我们就开始感，不能被定义在一个纯粹的语法系统以外的任何通用系统的功能。

目前，我们相信，特点是简单中形成的结构，往往在第十进制的形式，代表，被称为解决当地问题。虽然语法结构可以强加给他们的，其基本语义可以有很大的不同，需要不涉及特定种类的几何形状，或任何几何。但是，如果要正确使用的功能，一个功能上下文必须提供的技术条件和标准，导致解决方案的功能代表。鉴于功能的上下文（例如，作为一个去签名者的头域知识）和相应的推理能力，以适应当前的问题的解决，功能可以非常有效，他们胡男子设计师之间的人气证明了这一点。

Duffey和Dixson[5]最近的工作表明，功能可以在自动设计功能，环境和适当的推理能力提供时使用。（Duffey and Dixson的处理功能似乎特设但“ad-hocery”可能是内在的，如果我们目前的许可功能的看法是正确的。）功能可能是危险的，如果没有他们的环境和适当的推理能力，废话设计产生某些自动设计系统的说明。

最后，我们想指出，为“地方问题的已知解决方案”的功能特性会将计划的

强有力的约束相结合的功能，使新的功能。一个功能相结合，使感，只有当它可以被证明是一个有效的解决方案，以一个定义良好的本地问题。但即使确定的组合，作为一个组成部分，其功能做水管可能被证明是非常困难的问题域。

致谢。

这里报道的工作是支持的，由通用汽车公司根据其公司的奖学金计划，并授予国家科学基金会下的一部分MIP-87-19196。

References：

1. Alexander, C., Notes on the Synthesis of Form, Harvard University Press, 1964

2. Paynter, H.M., Analysis and Design of Engineering Systems, MIT Press, 1961

3. Ulrich, K.T. and Seering, W.P., "Conceptual Design: Synthesis of System of Components," 1987ASME Winter Annual Meeting, PED Vol. 25

4. Report of the Workshop on Features in Design and Manufacturing, February 26-28, 1988 University of California, Los Angeles

5. Duffey, M.R. and Dixon, J.R., "Automating extrusion de-sign: a case study in geometric and topological reasoning for mechanical design," Computer-Aided Design, Vol. 20, No.10, pp. 589-596, December 1988

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