Design and Analysis of Integrated Manufacturing Systems (1988)

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MODELING IN THE DESIGN PROCESS HERBERT B. VOELCKER ABSTRACT This paper summarizes the evolution of modeling technology and provides a status report on the newest technology—solid modeling. It discusses two (of many) issues that indicate how little we really know about design and about the interplay between design and manufacturing, and it closes with the following assessment: Contem- porary modeling systems are most useful for refining and documenting nearly finished designs and for driving a growing array of computer-aided manufacturing modules; they provide little help in the early, conceptual stages of design. Thus, we have, in essence, a growing technological imbalance, with manufacturing striding ahead of design in terms of scientific understanding and automation. The appendix explores the current situation by tracing some of the history of design and manufacturing. INTRODUCTION Design is the first major step in a prod- uct's life cycle, and design is often the main determinant of a product's manufacturabil- ity, salability, serviceability, and longevity. The quality of design in individual compa- nies, specific industries, and whole nations is influenced by many factors, with the tools that are available to designers being among the most important. This paper focuses on modeling tools for discrete-goods design (loosely defined as mechanical design). These tools have evolved rapidly, but they still have major deficiencies, and design it- self is poorly understood in a scientific sense. Figure 1 shows an idealized product cy- cle. Sales and marketing define a new or revised product in terms of functional re- quirements, price or volume trade-offs, and other similar parameters. Design and engi- neering convert the set of perceived needs 167 and market constraints into complete spec- ifications a design for a deliverable product. Manufacturing planners then pro- duce specifications for the product's manu- facture (typically process and inspection plans, numerical control tNC] programs, and the like), and these are executed to pro- duce a product that is then marketed. Design is often the pivotal operation in the product cycle because it establishes a match (a compromise) between the initial marketing goals and a product's "deliver- able functionality," economic producibility, maintainability, and longevity. Clearly, the design capabilities of individual companies and whole nations are strong determinants of their long-term viability in a competitive world. Although the companies' and nations' de- sign capabilities are influenced by a host of commercial, cultural, and historical fac- tors, the primary intrinsic determinants are

168 sales {Customers} _ , ~ and \tarketin~ FIGURE 1 An idealized product cycle. the skills of the designers and the tools and methods that they use. The principal focus in this paper is on tools specifically, mod- eling tools—because these are understood well enough to admit technical assessment and forecasting. Although design methods and designers' skills are at least as impor- tant as tools, they are poorly understood and are covered only briefly and somewhat obliquely. Further, the paper focuses on modeling tools for discrete-goods design (loosely, me- chanical design—the term used hereafter for brevity) because mechanical design is both pervasive and ill-understood in a sci- entific sense. Nonmechanical design do- mains, such as digital electronics, chemical processes, and soft goods (e.g., apparel), pose unique and interesting problems, but each is smaller than the mechanical aggre- gate, and at least the first two are more advanced than mechanical design in terms of scientific understanding and automa- tion. Computer-aided design (CAD) and com- puter-aided manufacturing (CAM) systems have proliferated in the mechanical indus- tries over the past two decades, and within each lies a modeling system of some kind. Although the early progress in CAD and CAM was paced mainly by advances in computing and graphics technology, prog- ress in the past decade has been paced HERBERT B. VOELCKER FunctIonal [ design ,~ Design Specification ~ and ~ (for a product) ~EnaInQnrina' | Product |) ~ >` , ~ I Manufacturing plans, programs ·j ~ Product1 t~ Manufacturln7~ drawings, specs, data ~ | Products J \ / __ _ Manufactu:\ ~ Planning>) mainly by advances in modeling and in un- derstanding of how to use models. This paper surveys the evolution and cur- rent status of mechanically oriented com- puter modeling and discusses two (of many) issues that indicate how little we know about design and about the interplay be- tween design and manufacturing. It con- cludes that modern CAD/CAM systems are best suited to the final "tuning" and "de- tailing" of parts and products and as sources of data for increasingly automated manu- facturing processes; they provide little help in the early, conceptual phases of design. The appendix traces some of the history of design and manufacturing in an effort to understand why manufacturing is ahead of design in terms of scientific understanding and automation. MECHANICALLY ORIENTED MODELING SYSTEMS1 Contemporary modeling systems are concerned primarily with geometry. They 1The section dealing with mechanically oriented modeling systems is based in part on updated material from two papers written by A. A. G. Requicha and the author about 5 years ago (Requicha and Voelcker, 1982, 1983). These papers provide more than 150 ref- erences, most of which are still pertinent. Wolfe et al. (1987) provide a view from within the context of a single modeling.system, namely, IBM's internal-use GDP modeler. .

MODELING IN THE DESIGN PROCESS provide means for defining the shapes of components and sometimes allowable shape variations (tolerances), for positioning com- ponent representations to define assemblies, for calculating properties (appearance, mass, etc.), and when linked to CAM modules for generating manufacturing- process data such as NC programs. One can discuss these systems in terms of the generic geometry system shown in Fig- ure 2. Representations (models) of objects are built from definitional data supplied by users, and procedures are evoked by user commands to compute properties and do other useful work. The users may be hu- mans, as is almost universally the case in design, or programs increasingly the norm in manufacturing applications, where mod- eling systems are used as utilities by pro- g~ams that simulate the motion of robots, check the correctness of NC programs, and so forth. The effectiveness of systems of the type shown in Figure 2 is set mainly by the intrinsic power of the internal representa- tion schemes what can be represented, and with what fidelity and by the proce- dures that can be deployed to calculate use- ful results. Nearly all of the pre-1980 sys- tems carried ambiguous representations that required human interpretation to be useful, whereas the new-generation solid modeling systems carry unambiguous representations GEOMETRIC MODELING SYSTEM Deflnitlons of ObJect Geometry ~ Commands : 169 that permit many calculations to be auto- maten, at least In principle. The Evolution of Computer Modeling Figure 3 summarizes the evolution of modeling technology. The early roots can be traced to the 1950s, when computer graphics was invented, the first program- ming languages were devised for the then- new NC machine tools, and some compu- tationally useful segments of projective ge- ometry became popular in pockets of the engineering community. This early work nurtured the four largely independent streams shown in Figure 3, which are only now beginning to merge. Airframes The wireframe stream supplied nearly all commercial CAD and CAM systems until the advent of commercial solid modeling. These systems appeared first as simple two- dimensional programs for designing printed circuit boards and digitizing mechanical drawings, one view at a time. In the 1970s the systems' modeling entities two-dimen- sional lines and arcs were generalized to represent segments of three-dimensional space curves that could be linked to repre- sent the edges of solids (hence the name i Rae _~ 1 Geometric ~53 ~ Models (Representations) J: J ~~J | Command ,\ J ~ !-~ - . 1 I Procedure; - l 14 ~ Procedure ~ ~;~ FIGURE 2 A generic geometric modeling system. ~ > Results

170 1955 -1 964 +1 1965. ·1972 1 It 1 1 1973- ·1978 ~ 1 !1 It 1 1979 - 1984 2-D Systems based on drafting principles; early NC from graphic data bases 3-D Systems; better NC; more convenlence~s Bounded surfaces; better analysis packages; color; more conveniences 1 - HOMOGENEOUS- INTERACTIVE COORDINATE COMPUTER GRAPHICS (PROJECTIVE) "INVENTED" GEOMETRY ~ ,~ <~ Polygonal Schemes I 1 1 Early hidden-line and visible-surface algorithms for polygonal faces; simulators Better algorlU'ms; polyhedral smoothing; faster simulators; 3-D animation Special C-hardware Improved dlaplays; animation languages 1 ll I B-spilne subdivision I algorithms \ I ~ \ 1985-1995: A NARROWER SPECTRUM OF MORE POWERFUL SYSTEMS FIGURE 3 Evolution of mechanically oriented modeling technologies. "wireframe"). Wireframe representations of solids can be projected computationally to generate multiple-view orthographic, iso- metric, and perspective drawings that, with human cuing to control visibility, mimic manually produced drawings. Figure 4 demonstrates two serious defi- ciencies of wireframes: They may be am- biguous, and they may represent invalid FUGUE 4 Deficiencies of wireframes: ambi~i~ (left) and invalidity (right). HERBERT B. VOELCKER NC PROGRAMMING LANGUAGES Solid Modeling Sculptured Surfaces I 1 Aero, auto, marine lofting; I Ad hoc experiments using | parametric polynominal and I diverse approaches 1 1 1 I Experimental boundary- | CSG, and sweep-based aces I systems demonstrated; thooreUcal foundations I emerge j Development of Industrlal prototypes; early production ver~lons ("impossible") solids. Specifically, three dis- tinct solids exhibit the edges displayed in perspective on the left in Figure 4, whereas no solid can have the edges implied in the right-hand illustration. In principle both conditions can be detected automatically, but detection is computationally expensive and automatic repair is impossible. Thus, wirefra~nes cannot be used as primary rep-

MODELING IN THE DESIGN PROCESS resentations in automated systems. Never- theless, wireframe modeling systems proved useful in the largely unautomated 1970s be- cause they offered essentially paperless drafting as well as electronic data manage- ment for handling revisions. They continue to be useful today for somewhat different reasons, as will be noted later. Solid Modeling Solid modeling is distinguished by the use of valid and unambiguous representations of solids. It is the newest mechanical mod- eling technology and almost certainly will replace wireframe technology as various system problems (noted later) are resolved. Figure 5 shows the two schemes that are used most frequently: boundary represen- tations (b-reps), in which solids are repre- sented by sets of faces that enclose them completely, and constructive solid geome- try (CSG), in which solids are represented as Boolean combinations (unions, differ- ences, and intersections) of simple primitive solids. Four other unambiguous schemes for representing solids are known and used, of- 1 1~71 Solid A Constructive Representation 171 ten in conjunction with boundary or CSG schemes, for certain kinds of applications: · Spatial Enumeration. A solid is repre- sented (usually approximated) as a union of quasi-disjoint box-shaped cells "filled with matter." The cells may be of uniform size or of varying sizes if generated by recursive binary spatial subdivision. Enumerations of the latter type may be organized as logical trees, called quadtrees in two dimensions and octrees in three dimensions. · Cell Decompositions. A solid is again represented as a union of quasi-disjoint cells, but now each cell may have a distinc- tive shape, provided that it is homeo- morphic to a sphere. Triangulations are the simplest form of cell decomposition, and finite-element meshes are the most widely used engineering embodiment. · Sweeping. A solid is represented as the spatial region traversed ("swept-out") by ei- ther an area or a solid moving on a spatial trajectory. Although sweeping is central to modeling motional processes such as ma- chining and robotic assembly, there are many open mathematical and computa- tional questions surrounding it. :_~: a////////: A Boundary Representation FIGURE 5 Solid modeling examples: constructive solid geometry and boundary representations.

172 · Primitive Instancing. This is a formal- ization of the family-of-parts concept. A solid is represented as a particular mem- ber of a family- say, the family of single- diameter round shafts with oil grooves by supplying appropriate numerical pa- rameters to a family-specific collection of formulas for displaying members of the family, calculating their mass properties, and so forth. The roots of solid modeling can be traced to a few experimental systems built in the early 1960s that largely failed. The first suc- cessful experimental systems appeared in the early 1970s, mainly in European, Japanese, and American universities. Formal theories of solid modeling began to appear a few years later. In the late 1970s a second gen- eration of experimental systems appeared. These seeded a first generation of vendor- supplied industrial solid modeling systems that appeared in the early 1980s. Polygonal Schemes The polygonal-scheme stream in Figure 3 could be retitled "graphic rendering" in that the goal is to provide visual effects. These effects range from real-time imagery for flight simulators, through commercial animation (as used in television, for exam- ple), to research in visual perception. This stream draws its title from the representa- tion scheme that is common to all such ap- plications collections of polygons that ap- proximate the boundaries of the objects being displayed. Extensive research has fo- cused on developing fast algorithms and special computer hardware for generating displays from polygon lists, and some of this technology has been incorporated recently in industrial solid modeling systems to build approximate boundary representations. Sculptured Surfaces The sculptured-surfaces stream has the oldest roots, which lie in the mathematics HERBERT B. VOELCKER of curves and surfaces. The first design ap- plications appeared in the l9SOs and 1960s, when Coons (1967), Bezier (1972), and a few other pioneers sought to replace the lofting and clay modeling techniques used in the aeronautical, marine, and automo- tive industries with computerized descrip- tions of doubly curved surfaces. Subse- quently, there has been almost continuous development of mathematical bases and computer techniques for representing curves and surfaces, but until about 1980 little at- tention was paid to algorithms for process- ing surfaces: for example, computing curves of intersection or testing closedness to deter- mine whether a surface may qualify as the boundary of a solid. Contemporary Modeling Systems Wireframe systems are at, or close to, the practical limits of their potential. They are still being installed in significant numbers because large collections of semiautomatic application codes are available for wire- frame systems, there are large numbers of trained users in industry, many thousands of parts have been defined through wire- frame systems, and a new generation of PC- based systems makes wireframe technology accessible to small firms. Polygonal systems have never played a major role in industrial modeling. Sculptured-surface systems tend to be proprietary within each major orga- nization (e.g., airframe company) and are regarded as special-purpose systems rather than general mechanical modelers. Thus, the future lies with solid modeling, but, for reasons noted later, this modeling system is not yet ready to take over all of the model- ing now done through wireframe and sculptured-surface systems. System Organization and Geometric Coverage The 1970s solid modelers fell into one of the two families shown in Figure 6. They

MODELING IN THE DESIGN PROCESS 1 i ~ 1 J I rip ~ | I Reps I ~ ~ I .' I_lConvertl_ ~ ~ CSG I `` | ~ Sweep | — 1 .____, (a) B-Reps To AppilcaUon Programs | Graphics _ I Mas~props 1 : 1 1 ~1 ~ 1 B-Rep~ A) FIGURE 6 The single- and dual-representation architectures characteristic of the 1970s. either had a single primary representation scheme, usually of boundary type, or dual (CSG, boundary) schemes, with the dual representation being computed from the boundary representation. Nearly all of the 1970s systems were quadric-surface mod- elers; that is, they could describe only ob- jects bounded by first- and second-order surfaces in practice, planar, cylindrical, spherical, and conical surfaces (the so-called natural quadrics). As we shall see later, the natural quadrics cover almost all unsculp- tured, functional mechanical parts. The emergence of commercial solid mod- elers in the 1980s brought greater orga- nizational variety. Figure 7 shows the trends: multiple representations,2 some rep- resentations (at least one) being exact and the others approximate; auxiliary represen- tations for several purposes, such as to speed up important algorithms and to carry at- tribute data; and a collection of geometric utilities available for use within the mod- eler and also by external applications. Thus, for example, many systems now compute planar approximations to curved surfaces using technology developed in the polygo- 2An unambiguous representation is guaranteed to contain, in principle, enough information to allow any computable geometric property of the repre- sented solid to be calculated automatically. This means that, in principle, a modeling system need contain only a single unambiguous representation scheme. In practice, however, no single scheme can support a range of applications efficiently, and hence the inter- est in multiple representations. 173 To AppilcaUon Programs Graphics Massprops. . nal stream (see Figure 3), and some systems maintain octree approximations. Represen- tation-conversion algorithms are the "glue" that holds such systems together, and the maintenance of consistency over the whole set of representations when any one repre- sentation is edited (to install an engineering change, say) is a major system-design chal- lenge. An important current goal in solid mod- eling is installing "exact" sculptured-surface facilities to replace the planar-approxima- tion methods used in some systems. This is proving to be considerably more difficult than expected, with the calculations needed to implement Boolean operations posing the main problems. Boolean operations are es- sential for many purposes, such as modeling material removal and detecting collisions Input dotinitlon ; Stored or , volatile I i,/ 1 ~ | Object Rep 1 l ~ | ExacUapprox. ~ AUX _ REP 1 ~~ _ AUX REP 2 1 ' 1 ~ | ExacUapprox. I I Externally accessible 1 | procedures j ~ TO APPLICATIONS FIGURE 7 Generalized modeling system archi- tecture.

174 between moving bodies and interference in assemblies, and as conveniences in defining parts; Boolean implementations, however, are mathematically delicate and computa- tionally intensive. Applwat~ons Solid modeling has the potential to sup- port the automation of almost all conven- tional technical tasks done in industry, from detailed strength analyses through graphic rendering to the automatic planning of ma- chining and assembly operations and the programming of tools to do the work. We say this with confidence because we have mathematical proof that our representa- tions of parts, fixtures, etc., are "informa- tionally complete." This proof, however, is an existence proof; it tells what is possible without telling how to accomplish it. The fact that relatively few tasks are automated today is due primarily to our lack of scien- tific understanding of the tasks; succinctly, we have inadequate mathematical task and process models, and without these we can- not write reliable applications codes. A brief applications status report follows. We wrote almost 5 years ago (Requicha and Voelcker, 1983, 29-30) "only three ma- HERBER T B. VOELCKER jor applications graphics, mass properties [volume, centroid, inertia tensor], and static interference checking are understood well enough to be handled automatically in most systems.... Modelers that can support only [these applications] are difficult to justify in most industrial installations, and thus ven- dors are using existing packages to provide numerical control and other services while awaiting more advanced modules that can exploit the power of solid modeling." There has been little overt change in the interven- ing years, and thus Figure 8, taken from the 1983 reference, depicts the current situ- ation reasonably accurately: a few appli- cations are handled automatically from the solid modeler, and the others through human-interactive programs devised mainly for wireframe modelers. The requi- site wireframe representations are easy to derive automatically and download from the solid modeler; uploading from a wire- frame modeler to a solid modeler requires considerable human assistance. Although there has been little overt change in the automation of applications over the past several years, applications re- search has progressed steadily, and one can expect a few of the dashed lines in Figure 8 to become solid by 1990, with most of the i Solid modellag system ~ ~--~___ ~ programs {: ==_ _ Commercial wireirame system /= Human \ programs ~ Assistant `_ _~ Graphics Mass Static Flnite-Element Manufacturing Properties Interference Meshes Plans NC Code FIGURE 8 A contemporary, and probably temporary, marriage of convenience. Other

MODELING IN THE DESIGN PROCESS . ' :~ ~ , . __ ~ f . ._ ~ . . ~ ~ K ~3 (a) (b) FIGURE 9 Two-dimensional finite-element meshes: (c) automatically refined version of mesh. Others (including several not shown) follow- ing before the end of the century. Two ex- amples of current research will be dis- cussed, together with summary comments on other applications. · Automatic finite-element analysts. Au- tomatic finite-element mesh generation has been under study since the late 1970s, and industrially viable automatic mesh genera- tors can be expected by 1990. There are several approaches to the problem, with one of the most promising being a two-stage process using quadtree or octree enumera- tion to mesh the interior of a solid, followed by boundary traversal to extend the interior mesh to the surface of the part (Kela et al., 1986, Kela, 1987~. Figure 9a shows such a mesh in two dimensions, with the interior quadtree structure of graded blocks clearly [~'': Oblect Detinitlon T~ = \ . . , , , , , ~ it, 175 _ ~ 1 7 Ed - (c) (a) mesh in two dimensions; (b) loaded mesh; visible. One could stop at this point and submit the mesh to a standard analysis pro- gram such as NASTRAN; however, there is much to be gained by treating mesh gener- ation and mesh analysis as coupled prob- lems. This is accomplished by including a correction loop, as shown in Figure 10. Thus, errors associated with the analysis, such as high stress gradients, can be used to guide local refinement of the mesh and sub- sequent incremental reanalysis. Figure 9b shows the loaded mesh (the left face is fixed and the hole carries a downward force), with error indicators written in each ele- ment. Figure 9c shows an automatically re- fined version of the mesh. The solid modeler shown in Figure 10 supplies part geometry and, through an at- tribute facility, loading and boundary con- ditions. The modeler also generates the AttrlbLlta n~fInitir~n 1 Solid modeling system with attribute facilltles | | Refinement . I ~~ FIGURE JO An automatic finite-element analysis system.

176 1~1 me, ~ Current Updated Workpiece Cutter Workpiece Swept Region FIGURE 11 The basis of machining simulation. quadtree or octree approximations used in the meshing procedure, plus other aids for managing the process. A two-dimensional version of the system shown in Figure 1O is running (Kela, 1987), and an experimental three-dimensional version can be expected in 1 to 2 years. · NC machining. Figure 11 shows the essence of machining simulation, which is easy to do given a solid modeler with ap- propriate geometric power. The driving re- lation is Wi = Win—Vi, where Wi is the workplace after (simulated) execution of the ith NC command, Vi is the spatial region swept by the cutter on the ith command, and "-" is the (regularized) set-difference operator. Thus, a simple simulator reads an NC program block by block and displays the workplace after each command; a per- son watches the displays and tries to spot problems (collisions, invasive machining, etc.~. Machining simulators of this form can be expected soon for industrial applica- tions. HERBERT B. VOELCKER Automatic NC-program verifications seeks to do two things: detect problems without recourse to human observers, and determine automatically whether the final machined part WF is identical to the de- sired part P (Sungurtekin and Voelcker, 1986~. The latter goal-attainment test (WF = P?) is easy to do in a solid modeler in Drincinle. but there are computational subtleties. Automatic problem detection is done by applying two different kinds of tests at each stage of a simulation. Spatial prob- lems are detected by various intersection tests, with PnVi = 0? (does the current cutter-swept region Vi intersect the desired part P?) being the test for invasive machin- ing. Figure 12 shows output from a verifier when a cutter executing a positioning (rapid) motion collides with the workplace and fixture. The detection of "technologi- cal" problems, such as cutter breakage or 3The terminology in the field is not standardized. Some authors use "verification" to denote what we have called "simulation."

MODELING IN THE DESIGN PROCESS violation of tolerance constraints, mainly requires force calculations that are done in- directly. For example, Ri = Wi- 1 n vi is the "solid" actually removed (made into chips) by the ith command, and the volume of R can be calculated automatically by a mod- eler's mass-property module. From this and the known cutting conditions, such as path length, and feed rate, an average material removal rate can be calculated. From the removal rate and other data it is possible to estimate the average forces on the cutter and hence predict its deflection, breakage, and so forth. Methods for estimating peak forces through higher moments of Ri are under study. Although at least one NC verifier pro- gram should be ready for industrial tests in a year or so, automatic NC program gen- erators are farther away. High-level ma- chining programming languages coupled to GO- RAPID ***** ERROR: COLLISION WITH THE WORKPIECE ***** ERROR: COLLISION WITH THE FIXTURE A_ _: 177 solid modelers should appear by 1990 (Chan and Voelcker, 1986~. These programs prob- ably will be followed sometime in the l990s by automatic process planners with outputs of programs in high-level machining pro- gramming languages. · Other appl?~at~ons. Industrial robotics clearly offer fertile ground for model-based automation, with off-line manual and au- tomatic programming being prime targets. The situation here is similar to that in ma- chining: Graphic simulators are essentially available and automatic program verifiers and high-level languages should be in use by about 1990, but automatic planning and programming lie farther away. Another fertile problem area is simulating material flow in dies, as in injection molding and forging, and progressing from simulation to computer-aided and computer-automated FIGURE 12 Automatic detection of collisions in an NC program . ^. verifier.

178 die design. This work has a high payoff potential but low public visibility, because the underlying physical processes are com- plicated (Dawson, 1986~. Solid-modeling- based flow simulators are already in use in a few companies (Wang et al., 1986~. Although it does not exhaust the list of applications, the foregoing survey should convey a sense of the current state of the art. Some issues close to part and product design are discussed later. User Interfaces Early CAD/CAM systems were designed to be electronic drafting boards. T square, compass, and triangle were replaced with pointing devices (cursor, light pen, etc.) and command menus whereby users could cre- ate lines, circles, arcs, free-form curves, icons (e.g., arrows), and text. Users could establish relations between elements of a drawing, for example, making one element parallel, perpendicular, or tangent to an- other and could copy, rotate, translate, save, and delete entities. These drafting in- terfaces came to be highly engineered, con- venient, and fast as computer-graphic tech- nology advanced, but they enforced almost no model-based discipline on the user. These systems could be used to draw any- thing, because there were no underlying mathematical models of any object of higher order than curves. When wireframe systems appeared, drafting interfaces generally were ex- tended, rather than redesigned, to exploit the mathematical rules governing wire- frame structures. Thus, users continued to work mainly in orthographic views, with some behind-the-scenes view-linking, and they retained much of the draftsman's credo that one drafts to communicate shape to humans rather than to define mathemati- cally correct models of solids. The advent of solid modeling forced se- rious thought to be given to the design of user interfaces, beginning about 1980, for HERBER T B. VOELCKER several reasons. First, many solid modelers emerged from the research laboratories with command language interfaces rather than graphic interfaces, thus, there was in- terface design to do, since engineers often resist "programming" and insist on graph- ics. Second, solid geometry is usually cre- ated in chunks whole blocks and cylin- ders rather than through lower-order lines and arcs. Thus, the highly engineered drafting interfaces became largely irrele- vant. Finally, solid modeling requires three- dimensional thinking and visualization skills; thus, three-dimensional displays (per- spective line drawings and shaded images) are almost essential, because defining enti- ties in three dimensions is more difficult than in two dimensions, and working through two-dimensional views is often not the best approach. Most contemporary solid modelers have "first-generation" solid-oriented graphic in- terfaces.4 These are, in essence, graphic versions of simple command languages that permit primitive solids to be instantiated from menus, positioned through rigid mo- tions and coordinate-system declarations, and combined through Boolean operations. Figure 13 shows some of the menus and displays in a typical system (McDonnell Douglas's UNISOLIDS=~. Many systems also provide means for "extruding" and "swinging" closed planar contours into translationally or rotationally symmetric solids, and the newest interfaces (e.g., ver- sion 4.0 of UNISOLIDS™) offer simple "features" such as countersunk holes and various kinds of slots and pockets as defini- tional primitives. Few contemporary mod- elers offer relational facilities that would, for example, allow a user to "Put face A of solid B against face C of solid D," and none, insofar as the author knows, supports con- 4A few systems, e.g., MEDUSA™, were designed from the outset with drafting-like input facilities in mind, but these required internal compromises that may limit the systems' longevity.

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180 strained design, wherein critical parame- ters of parts are found automatically by solving systems of equations. The appear- ance of such facilities will mark the transi- tion into second-generation interfaces. Thus far we have focused on graphic in- terfaces for human users, but, as we noted earlier, automata (programs for automatic finite-element analysis, machining simula- tion, and so forth) also use modeling sys- tems; indeed, programs are likely to be the major users within a decade. Formal lan- guages are the appropriate interfaces for automata and also for humans who wish to design parametrically. Languages are be- coming highly developed for modelers with CSG input facilities (because representa- tional validity is easy to guarantee in CSG). The following provides a simple example wherein a generic shelf is defined as an as- sembly of a board (a solid-block primitive) and two brackets defined separately as ge- nerics:5 GENERIC SHELF (SHELFPART); PARAM LEN {New length value for bracket}; PAR AM T New thickness value for bracket); LEN = 6; T = 0.5; BOARD = BLO(X=24, Y =0.7S Z=8~; BRACKET1 = BRACKET(L=LEN, T=T) AT MOVX=3; BRACKET2 = BRACKET(L=LEN, T=T) AT MOVX=20; SHELFPART = BOARD ASB BRACKET1 ASB BRACKET2. Note that some parameter values in this definition are fixed whereas others are vari- ables with default values. This language allows algebraic and trigonometric expres- sions and conditional statements but not re- — 7 cursion or iteration. In summary, two quite different modeler 5"Generic" is PADL (Part and Assembly Descrip- tion Language) jargon for an archived parametric definition (Hartquist and Marisa, 1985~. HERBERT B. VOELCKER interfaces are available. Definitional lan- guages offer much of the abstractive power of programming languages naming, scop- ing, conditionals, and so forth- and are the natural input media for automata, but they do not exploit humans' visualization skills. Interactive graphic interfaces are powerful aids to human spatial reasoning but lack abstractive power. (It is difficult, for ex- ample, to do parametric design through a graphic interface.) A new medium combin- ing the strengths of graphics and defini- tional languages is needed, but no serious candidates are on the horizon. Current Limitations and Research Frontiers Computer modeling and its applications in the mechanical industries have bur- geoned in the past 20 years. We have come a long way, but we still have a long way to go. The major current limitations of mod- eling and applications technology are sum- marized next, and the state of pertinent re- search is discussed. Solid Modeling In the following we assume that solid modeling will become the dominant me- dium for describing parts and products (and stock, fixtures, etc.) in the mechanical in- dustries and that it will subsume useful techniques from the other streams shown in Figure 3. Theory Current theory, most of which is less than a decade old, can be thought of as having three components: an existential (representation-free) theory of solids as point-sets or spatially embeddable topolog- ical polyhedra,6 a companion theory of rep- 6There are two competing existential theories, one based on "resets" (compact, regular, semianalytic sets in E3) and Qne based on manifolds. The differ- ences, and their practical implications, are too subtle to delineate here.

MODELING IN THE DESIGN PROCESS resentation (the six unambiguous schemes summarized earlier), and a growing collec- tion of functions and algorithms that are central to building and maintaining repre- sentations and to converting between repre- sentations. This body of theory covers the nominal or ideal-form geometry of rigid solids, and the qualifiers "ideal-form" and "rigid" mark the main limitations: · The ideal-form restriction limits se- verely the ability to handle tolerancing- i.e., allowable variations in form, position, and relation (to other entities). The issues here are complex and subtle (Requicha, 1984~. Although many applications can be automated without a satisfactory theory and a technology of tolerancing, others automatic planning of machining, auto- matic die design, automatic tolerance as- signment in assembly design, and a few others probably cannot. A growing vol- ume of research is focused on tolerancing. · The rigidity restriction can be dis- cussed for present purposes in terms of ob- jects that are nominally rigid and objects that are not. Linear deformations of nomi- nally rigid solids for example, elastic strain and thermal expansion can be han- dled relatively easily by finite-element methods. Mass-preserving plastic deforma- tion, as in forging and extrusion, can be handled similarly if the constitutive re- lations are known. Certain non-mass- preserving deformations, notably machin- ing, can be handled easily by different methods, as indicated earlier. The really open issues lie with objects that are not nominally rigid. These include nominally elastic objects (e.g., snap fasteners), flexible objects (e.g., electric-cable harnesses), and limp objects (e.g., upholstery and padding materials). No systematic means, much less unified means, exist for modeling such ob- jects, and thus far little research has been focused on them. der the nominal-form and rigidity restric- tions just cited. Their industrial usefulness is limited by the following additional fac- tors (as well as other factors associated with applications, which are discussed sepa- rately). Adequately robust systems have limited geometric domains—typically objects bounded by the natural quadric surfaces. As noted earlier, efforts to incorporate sculptured surfaces are encountering prob- lems, but given the talent being focused on domain extensions these problems are likely to be solved in one way or another in the next several years. All systems, except for a few optimized for special applications, are slow because solid modeling is computationally inten- sive. This problem is also attracting talent and resources and in the next several years will be ameliorated (it will never be solved to the full satisfaction of users) by better algorithms and massive computing power initially supercomputers for critical appli- cations and, within 5 years, board-level hardware accelerators optimized for solid modeling (Goldfeather and Fuchs, 1986; Kedem and Ellis, 1984~. All systems, except for a few optimized for special applications, seem to be subject to a complexity barrier that limits their ef- fective domains to objects representable by about 103 or fewer representational primi- tives (faces, primitive solids, etc. 3 .7 This limit was acceptable 5 years ago with com- puters capable of only about 1 million in- ferences per second. But computers 10 times faster and 10 times larger (i.e., 10 times more on-line storage) are becoming avail- able, and users would like to handle objects 10 times larger now and objects 100 times larger 5 to 10 years hence. Current model- ing software probably will not support such 7By way of contrast, automobile engine blocks require 0~04) representational primitives and whole- engine assemblies require 04~05~. Current systems can handle such objects in principle, but in practice the System Technology. Contemporary In- costs, delays, and technical difficulties of doing so are dustrial solid modeling systems operate un- almost always unacceptable.

182 growth because it treats all aspects of a def- inition as equally important, from the smallest hole to the largest macrofeature. Humans cope with complexity through ab- straction and "dynamic hierarchies," which enable them to ignore two kinds of infor- mation that which is irrelevant and that which is too detailed. Modeling software must be endowed with similar faculties, and research toward this end is in progress.8 Applications of Solid Modeling in Manufacturing Five years ago manufacturing-process automation was concentrated at the effec- HERBER T B. VOELCKER Applwat?ons of Solid Modeling in Design The status of modeling in design, which is the subject of this paper, is a slippery topic, in part because "design" is both a noun and a verb. We shall approach the subject cautiously, proceeding from the ev- ident to the conjectural. ~ ~ ~ ~ T ~ '' Design Definition. In current indus- trial practice, a finished design (noun) for a product is defined by four coupled bodies of information: 1. Ideal-form (shape) specifications for the component parts 2. Associated variational specifications tors (e.g., at the machine tools), and the ~tolerances' requisite upstream support in the form of (Note that these first two Items taken to- gether are equivalent to "detail drawings.") 3. Component-combination specifica- tions ("assembly drawings") 4. Material and finish specifications Performance specifications rank as collat- eral information or as part of the design- process documentation; they cannot be part of the design definition unless consistency with the four components can be guaran- teed, in which case performance specifica- tions are redundant (because they are de- rivable from the design definition, at least in principle). Note also that manufactur- ing- and assembly-process specifications are not included in the design definition a matter we shall discuss later. manual process planning, machine-tool and robot programming, etc., was expensive unless production runs were long. Today, model-based automation of some of the up- stream activities is imminent, as discussed earlier, and almost complete "vertical au- tomation" of some important manufactur- ing processes seems attainable before the end of the century. The key to "vertical" manufacturing-process automation seems to lie in finding effective computational mod- els for processes (machining, forging, dex- trous assembly, etc.~. A century of classical research on processes, when coupled to new solid-modeling and analytical tools, pro- vides a strong springboard into a new world of computational process planning and process control. Thus, modern manufactur- ing research is growing steadily in both breadth and depth, and dramatic progress seems likely in some areas.9 The underlying problem is that solid modeling algorithms run in polynomial rather than linear time, and thus a tenfold expansion of a model may require a fiftyfold expansion of computing power to maintain a given level of performance. One way to avoid this is to treat only the "currently relevant" portions of the larger model. 9We note for completeness that automatic oper- ation of manufacturing systems—machining cells, Contemporary object modeling theory and technology can handle items 1, 3, and probably 4, at least in principle (i.e., sub- ject to the geometric coverage, complexity, etc., limits already noted.~. Item 2 toler- ances is a problem area, as noted earlier. CIM complexes, whole factories—involves different lines of research into different types of problems (scheduling, line balancing, etc.) using different mod- els (probabilistic discrete-event models, rather than mainly deterministic Euclidean and Newtonian mod- els). This is the province of industrial engineering and operations research.

MODELING IN THE DESIGN PROCESS Design Validation. Physical testing pro- vides the ultimate validation for a design by ensuring that the product is, for example, strong enough or not too heavy to meet its performance specifications. But physical testing is expensive and time-consuming, and therefore computational analyses are being substituted as confidence in modern analytical methods grows. Contemporary modeling systems already support auto- matic mass-property calculation and soon will support automatic finite-element and more specialized kinematic and kinetic analysis procedures. Thus, computational design validation is in relatively good shape because few of the pertinent analytical pro- cedures require tolerancing information. Optimization of Parametric Designs. As a design approaches completion, a stage is reached where the design is explicitly or implicitly parametric. That is, ranges for a small number of key parameters are known, and one seeks values for these pa- rameters that optimize the design under metric criteria. (A typical problem is mini- mizing the weight of a critical component under strength constraints, with certain shape parameters fixed and others vari- able.) Here again the analytical procedures supported by modern parametric object modelers are adequate, at least in principle, if coupled to optimization software (gradi- ent-driven hill-climbing algorithms, linear- program solvers, and the like). Support of Conceptual and Prepara- metr?r Design. Some issues that arise can be posed through the simple example shown in Figure 14. A designer begins the design of a simple component with three holes of known diameter and configuration (Figure 14a); these mate with features of other parts. The designer then creates some bosses to contain the holes (Figure 14b) because of concern about interference with other com- ponents passing between the holes. Finally, the holes and bosses are bound together into 183 __ (`O,' o (a) fit i, (c) _ .% ION _ ~ ( _ ~ (b) (d) FIGURE 14 Design of a simple component. a single part as in Figures 14c and 14d, with the final shape being governed by criteria for clearance, strength, weight, and sim- plicity. The process described is easy to do in an electronic drafting system or in most wire- frame modelers, but of course little can be calculated along the way because such sys- tems are mainly display engines. The pro- cess is not easy to do, as described, in many contemporary solid modelers; one must "trick" these systems for example, by de- fining the holes as an assembly of solid cyl- inders that will be "subtracted" later, when the encompassing solid has been defined. The situation gets worse when one tries to do preliminary assembly design in a solid modeler. Broadly, most current modelers require that all entities be valid attributes of well-defined solids, and, if properties are to be calculated or displays generated, all parametric variables must be assigned values. In summary, it is fair to say that contem- porary solid modelers are suitable for doc- umenting (creating definitions of) finished designs and for supporting the calculations

184 needed for design validation and paramet- ric optimization of nearly finished designs. Current systems provide little help during (and indeed may hinder) the conceptual and preparametric stages of design (as done by humans). There is a growing body of research, much of it based on artificial in- telligence, aimed at this problem. This is not the end of the story about modeling in design, however, because thus far we have addressed only the modeling of objects. By taking a broader view, we shall see that other types of modeling are equally important. A Broader View of Modeling In Design and Manufacturing J. R. Rinderle (1986, 1987) has suggested a triad of function, form, and fabrication as a mechanism for discussing the design and manufacture of mechanical products. The following paraphrases seem to capture Rinderle's notions: · Form refers to the product as a physical artifact (typically an assembly of sub- artifacts3 having shape and various shape- and material-determined motional, ther- mal, and other characteristics. · Function refers to what the product is Function Functional | Speclflcations | (?) HERBER T B. VOELCKER intended to do and can do, as contrasted with what it is (a physical entity). · Fabrication covers the possible and ac- tual means used to produce the product, and the methods used to mediate between alternative means. If we associate the three terms with arti- facts (call them "specifications" for present purposes) linked by transformations, we are led to the view shown in Figure 15, which extracts a portion of Figure 1: Form is in- duced from function through design, and fabrication is induced from form by manu- facturing planning. Usually there is feed- back (the dashed lines in Figures 1 and 15), with production planners recommending design changes to promote production effi- ciencies. Let us focus initially on the right half of Figure 15, because it is better under- stood than the left half. Form artifacts are what we call designs (design definitions, specifications of de- signs); they consist of the four entities listed earlier shape specifications, tolerances, and so forth and we know how to model and represent these entities (except perhaps for tolerances). Fabrication specifications govern the manufacture, inspection, and assembly of parts and products; they consist of machining process plans, NC programs, (?) ~ - - - Form me Desl~n Definitions (Speciflcatlons) · Component forms · Component tolerances \ \ Process Models Fabrication ~Manufacturing, Assembly, Inspection Specs · Process plans · NC programs · Assembly plans FIGURE IS Form induced from function by design, and fabrication induced from form by manufac- turing planning.

MODELING IN THE DESIGN PROCESS inspection plans, inspection-machine pro- grams, etc. We are learning how to repre- sent these specifications formally and model their effects mathematically and computa- tionally. (See, for example, Chan ~1987] and the earlier discussion of NC machining in this paper.) Fabrication specifications are induced from form specifications by the manufac- turing planner, whose main knowledge re- sources are sets of models for manufactur- ing and assembly processes, plus rules and procedures for selecting and sequencing processes. What is the nature of these mod- els, rules, and procedures, and how does the planner use them? Here is a capsule summary of one view of these matters from the realm of machining, which is a relatively well understood manufacturing process. One version of a machining-process mode} for use in machining planning is a function (cutter, position, orientation, feed-motion) {(surface-subset, position, orientation, precision)} that defines the machined surfaces that are produced by a specific cutter fully engaged with a workpiece and fed in a specified manner. Thus, for example, an end-mill fed on a linear trajectory normal to its axis can produce two planar-surface subsets parallel to each other and the cutter axis, a cylindrical-surface subset parallel to the axis, and a planar-surface subset normal to the axis. Precision parameters are associ- ated with each surface-subset to distinguish between nominally indistinguishable pro- cesses e.g., boring and reaming. An anal- ogous assembly-process model maps pairs of surface features on parts, a relative motion, and terminal conditions into "mated- feature" pairs with constraints such as a screw fully engaged in a threaded hole with a specified strain-induced residual torque. ~5 One family of machining-planning strat- egies now under study uses inverted forms of these process models, namely, (surface-subset, position, orientation, · · ~ precision) {(cutter, position, orientation, feed-motion) ~ to establish, for a surface-feature to be pro- duced by machining, a set of candidate cut- ters, setups, and feed motions. If a candi- date set is established for every feature to be machined, then in principle, a machin- ing plan can be constructed by combinato- rial optimization over the candidate sets, using the verification tests (for invasive ma- chining, etc.) discussed earlier to reject many candidate sets and ranking the survi- vors through such criteria as setup- and cutter-change minimization. Machining planning can thus be viewed as an iterative selection, instantiation, and sequencing of processes represented by inverted process models and subject to preconditions (e.g., on accessibility) and sometimes to postcon- ditions. Let us summarize the uses of modeling in the right half of Figure 15. We have models of solids under Form, and under Fabrica- tion we have process specifications whose effects we can model (as in machining sim- ulation). We also have, for use by the plan- ner, low-level models that associate pro- cesses with "features" of solids. For ma- chining, these are the forward (process ~ {surface-subset}) models and the back- ward (surface-subset~lprocess}) models. In the left half of Figure IS we have, under Form, models of solids as the "out- put" of design, but we have no models for Function, we have no intermediary models to aid the designer in associating "compo- nents of function" with "form-elements," and of course we have no procedures for aggregating"form-elements" into designed solids. Thus, the left half of Figure IS is largely open.

186 TWO (OF MANY) OPEN ISSUES Although it is tempting to speculate broadly about the mechanisms underlying design synthesis, we shall conclude by ad- dressing briefly two issues that can be framed with enough precision to generate experimentally testable hypotheses. Do Designers Have Too Much Geometric Freedom? Let us begin with some data. In 1974- 1975 a careful survey was made of the geo- metrical characteristics of the functional parts in a Xerox tabletop copier (Samuel et al., 1976~. The primary purpose of the sur- vey was to generate data on part geometry to guide the design of languages and proces- sors in the PADL (Part and Assembly De- scription Language) family of CSG-based modeling systems (Brown, 1982; Voelcker et al., 1978~. An important secondary pur- pose was to gather data on the geometrical characteristics of industrial parts as an end in itself, because we had been unable to find any such data before the survey. The survey was conducted mainly by an experienced Xerox tooling engineer who de- voted about 1 man-year to the task. He used the following versions of the PADL language as a meta-medium for survey pur- poses (the versions are distinguished by their sets of primitive solids; each is assumed to have general regularized Boolean operators and rigid-motion operators translations for versions l.n, translations and notations for versions 2.n3: 1.0 Orthogonal Blocks and Cylinders 1.4 Orthogonal Blocks, Cylinders, and Wedges 1.6 Orthogonal Blocks, Cylinders Wedges, and Cones 2.0 Orientable Blocks and Cylinders 2.8 Orientable Blocks, Cylinders, Cones, Spheres, and Tori In essence, he assessed each part in the sam- ple in terms of its describability in the lan- HERBERTB. VOELCKER guage and assessed also the size of the re- sulting PADL definition. Figure 16 shows some of the results.l° The abscissa of Figure 16 shows primitive- instance counts: these are a close measure of the size of a CSG definition. The right- hand ordinate shows the percentages of sur- veyed parts that are describable in various versions of the language. For example, about 30 percent of the parts are describ- able in PADL-1.0 (the orthogonal blocks and cylinders version), with the largest PADL-1.0 definition requiring about 45 primitive instances; about 99 percent of the parts are describable in PADL-2.8, with the largest definition (that for the copier's base plate) requiring some 500 primitive in- stances. The curve in Figure 16 labeled "Rede- si~ned to PADL-1.0" is our present focus. This curve shows that 60 to 65 percent of the parts can be designed (or redesigned) in PADL-1.0 under criteria dictating that the parts be true functional and physical re- placements (Samuel et al., 1976~. Figures 17 and 18 provide a part-redesign example, with Figure 17 being the original and Fig- ure 18 the redesigned part. If the copier had been designed from the outset with simple (PADL-1.0) geometry as an important de- sign goal, the percentage of PADL-1.0 parts would have been considerably higher than 60 to 65 percent. One can argue on various grounds that PADL-1.0 parts are technically and eco- nomically preferable to higher-version parts (Samuel et al., 1976), but here we conjec- ture merely that designers' "geometric free- dom" can be restricted (put differently, de- signers can be subjected to "geometric discipline") with little or no loss in their ability to meet functional requirements. We believe that this conjecture warrants exper- ~°Interested readers should consult Samuel et al. (1976) to understand the methodology and the under- lying assumptions, which are important, and also to assess the many results not noted here.

PADL - 2.8 128 120 110 100 90 a' 80 Al - o ED 53 E z E c' 70 60 50 40 30 1 _ 20 _ 10 o EXPLICITLY SPECIFIED GEOMETRIC DETAILS DEFINED AS AtrRIBUTES 1 1 1 2 _- 1 1 1 1 111 ,_~ PADL- 2.0 ~PADL- 1.6 -1.0 PADL- 1.4 100 90 80 70 _~ PADL- 1.0 ~S 60 `t ~D 50 ~ u) o ~D ~n ~_ ~ ~D q, 30 2n _ 10 1 1 1 1 1111 1 1111 1 1 11 1 1 11 1 1 o 15 20 25 30 40 50 70 80 100 150 200 300 400 500 650 3 4 5 6 7 8 910 Number of Primitive Instances FIGU~ 16 Some resulb from the Xerox part survey. ~,=~ 1; 1 . ,1, . ~ . I , . 1'~ '~ ' 1 1 ~ l _ I = 1--' 'l/(- 1'- , FIGURE 17 A production part as originally de- signed. - I ( - ' r- ~~~ 1 1 d_. ~ ~ 1 ' .J 187 FIGURE 18 A redesign of ~e production part of Figure 17, using PADL-1.0 primitives.

188 i] mental testing in industry and that exceri- ments can be designed that will yield near- term practical benefits as well as longer- term insight into the nature of design. Is Conditional Process Planning Preferable to "Open-Loop" Process Planning? In current industrial practice the manu- facturing processes needed to produce a part, and their sequencing, are wholly pre- specified, and deviations are not allowed. This can be termed "open-loop" planning. If done correctly, it ensures that a correct part Drill be produced if each prespecified step is done correctly and that a part can be rejected if any step fails. Open-loop plan- ning can be viewed as a factory- or produc- tion-organizing principle. It apparently arose from the master-gauge practices of the past century, and it had a subtle but profound effect on early tolerancing prac- tice. (Or perhaps one should say that gaug- ing and tolerancing practices have had a profound effect on manufacturing-plan- ning and factory-organizing principles.) Figure 19 shows a simple limit-toleranc- ing specification in which C = A + B (Requicha, 1977~. This specification may be precisely what a designer needs to meet functional requirements efficiently, but it is not acceptable under current practice be- cause the part cannot be made to the given specification by open-loop manufacturing :~_0.~ B ~o.~: ~f2 f3 FIGURE 19 An over-dimensioned (or"over- toleranced") part. HERBERT B. VOELCKER methods. (Figure 19 would be termed "over-dimensioned" by almost all drafting supervisors.) To see why it cannot be made "open-loop," suppose that face fl is pro- duced first and used as a datum for the machining of f2 and f3. Face f2 is then machined, using a process with only enough precision to meet the fl,f2 tolerance of 0.1. If a planner can determine by measurement that the resulting f2 physical face lies near the center of its tolerance band, then a 0.1- process can be used to produce f3. If f2 lies near the edge of its band, however, a more precise process must be used for f3 to meet the fl,f3 tolerance of 0.15. This simple example suggests several in- teresting questions, all researchable. For ex- ample, are designers capable of generating graph-structured tolerance relations, as in Figure 19, rather than the simple tolerance trees of traditional practice, and do such graphs really capture important functional relations? Are there families of useful man- ufacturing processes in which precision can be traded against cost, and are the trade- offs well understood? One might finish with a third issue that follows from the above, namely, should the doctrine of interchangeability be examined to see if its benefits continue to outweigh its costs? For reasons of brevity we shall not pursue this topic and will close with the observation that interchangeability doc- trines are already changing. Specifically, many modern products have a "replace- ment-module level" that is well above the single-part level and is rising steadily. For example, when the water pump in a car fails, the whole water pump is replaced rather than the one or two defective com- ponents of the pump. This means that the manufacture of artifacts that lie below the replacement-module level need not obey interchangeability criteria, but it is not clear that the implications of this new condition are being explored and exploited systemati- cally.

MODELING IN THE DESIGN PROCESS SUMMABY AND CONCLUSIONS Solid modeling is the most promising technology for defining mechanical com- ponents and products unambiguously if certain theoretical gaps (notably toleranc- ing) and technological limitations (geomet- ric coverage, speed, complexity limits) can be overcome. Contemporary solid model- ing systems provide good support for ana- lytical procedures that can be used to verify final designs and to optimize parametric (nearly final) designs. However, current systems do not provide much support for the conceptual and preparametric phases of design, which are wholly unautomated at present. Human designers may find a fu- ture generation of systems that admit in- completely specified solids, "implied" sol- ids, and solids defined through constraints to be more congenial, but difficult research problems must be solved before such sys- tems appear. Automation of the manufacture and as- sembly of mechanical goods is progressing systematically, with two kinds of modeling playing key roles. Solid modeling provides unambiguous definitions of what is to be made and also provides directly or through coupled analytical procedures models of the effects of processes on solids. Lower-level (feature, process) models provide primitives for planning automata now wholly in the research stage that eventually should pro- duce complete sets of plans and programs for making, inspecting, and assembling parts automatically. Now consider design: Mechanical-design automation and, more fundamentally, the understanding of mechanical design in a scientific sense are progressing slowly if at all. Thus, we have a growing technological imbalance, with manufacturing striding ahead of design in terms of both scientific understanding and automation. One of the major gaps in the understanding of design is the lack of means for modeling mechani- ~9 cat "function" in a manner that links func- tion to form. APPENDIX NOTES ON THE EVOLUTION OF DESIGN AND MANUFACTURING In the view of design and manufacturing developed above, form is central. It defines a part or product as a spatial entity and, when a material specification is added, as a physical entity. Form is induced from func- tion by designers using processes we under- stand poorly. Fabrication is induced from form by manufacturing planners, using processes we understand better but still not well enough. Broadly speaking, the back- ward mappings from fabrication to form through process simulation, and from form to function through analysis are better understood than the forward mappings. In current industrial practice, form spec- ifications ("designs") carry no explicit rep- resentations of function and no explicit specifications for manufacturing and as- sembly. Thus, modern part prints and as- sembly drawings or their solid-modeling equivalents include no descriptions of what parts are supposed to do and how they in- teract functionally (as opposed to spatially) with other parts. Similarly, there are no form specifications such as "Mill Slot A 1 inch wide" or "Mill Slot A of Part B to mate with Slider C of Part D." In current prac- tice, holes, slots, and almost all aspects of form are defined wholly geometrically through toleranced parameters of surface subsets. (Threads, knurls, and a few other "process-defined" features are exceptions.) The current focus on pure form as the medium for design specification is a recent development. We shall review briefly the evolution of design and manufacturing to

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MODELING IN THE DESIGN PROCESS see how we arrived at our current situa- tion. i~ In the beginning (see Figure 20a) a prod- uct was its design i.e., there were no ex- plicit, separable specifications that could be called "a design for a product"; further, the designer and builder (and sometimes the customer) were one and the same. But ex- plicit designs soon appeared (Figure 20b), usually as crude physical models or sketches prepared by the artisans before launching into construction. As products became more elaborate, a class of artisan-designers (for example, the master cathedral builders and master shipwrights) became distinguishable from the artisan-builders (Figure 20c), and customers' specifications took on a more formal structure that evolved toward con- tractual descriptions and performance spec- ifications. Through most of history, multiple copies of a product were almost always built by craft methods, i.e., single artisans or teams built a whole product from start to finish, as suggested in Figure 20d. This mode of fabrication, whether done in parallel, as in Figure 20d, or singly for one-off products, as in Figure 20c, may be termed adaptive serial assembly (colloquially, "file-and-fit") because (see Figure 21a) parts were manu- factured to fit the evolving assembly. A ma- jor change came in the mid-nineteenth cen- tury, when the doctrine of gauge-based interchangeability began to be adopted. Figure 20e shows that versatile artisans were replaced with specialist builders of standard parts and specialist assemblers and that "gauge artisans" appeared as the pre- cursors of manufacturing planners; prod- ucts emerged through the intrinsically par- allel, hierarchical tree of Figure 21b. From Figure 20e it is a relatively short step to the contemporary product cycle shown earlier in Figure 1. iiThe history of technology is a young field that Is only beginning to study the history of manufactur- ing in a systematic manner and has touched design only in a few isolated areas. 191 Pam Subassemblies (a) m of/ ].! I] [ m Component (b) Subassemblies FIGURE 21 Serial and parallel assembly: (a) "file-and-fit" serial assembly; (b) hierarchical as- sembly of interchangeable parts. Figure 22 shows how the component technologies in the product cycle evolved over time. Manufacturing Technology Because cutting was the dominant man- ufacturing process for most of history, the right-hand column in Figure 22 covers only cutting technology. (Casting is the other manufacturing technology with a long his- tory.) The main trend is evident (Rolt, 1965, 1970; Woodbury, 1972~: The free cutters of antiquity (early equivalents of a jackknife or single-edge cutting bit), with which persistent artisans could make al- most anything, were gradually enveloped in machines that progressively reduced the need for human dexterity and strength. The change from animate to inanimate power was pure progress, but dexterity require- ments were reduced at the cost of restrict- ing a free-cutter's versatility through mo- tional constraints imposed by mechanical guides. Much of the lost versatility was re- covered, however, and precise repeatability was added, when separately guided mo- tions were coupled mechanically, as in screw-cutting lathes, and later made elec- tronically commendable, as in modern NC machines. It is worth noting that the introduction

192 1000 BC O BC 1000 AD 1400 AD 1600 AD 1700 AD 1800 AD 1900 AD 1950 AD HERBERT B. VOELCKER Functional Representation and Design Analysl~ Do~lgn Manufacturlng Deeply Synthosls Tools Representatlon Planning Toole Technology Technology Crude physical models and sketches Geometry (Stereography) Ad hoc evolution Parallel pro|octlon Notions of perapecUve Algebraic Trlgonometry Geo metry (Descart - ,1 638) Mechanical Descriptive programing Geometry (Jacquard, 1728) Solutions of (Monge, 1795) dmorentlal Isometric equations Perspec~dve Master gale - (Farlsh, 1820) Standardizatlon Numerical methods Drafting of common conventions Material science components Drafting standards Flnlto-dfflerence Toler. ncing 1929 (French) Flnite-element 1940 MMC Computer 1944 True Computer graphics poalUon sImulatlon 5O11d 1973 ANSI Y14.5 Manufacturlng Technology l Free cutters Gulded cutters Water-powered cutters Coupled-motlon cutters Steam-powored— cutters I Preclelon metrology 1000 BC O BC 1000 AD 1400 AD 1600 AD 1700 AD Mechanl2atlon 1800 AD Interchangeabillty Mechanically programed cuttem Eloc~lflcadon Group technology NC and robot programing] languages Electronic control NC machine tools Industrlal robots FIGURE 22 Historical evolution of component technologies in the product cycle. Of steam power liberated early factories from the tyranny of locale imposed by wa- ter power and thus sparked the wave of mechanization that is often called the (First) Industrial Revolution. (Factory electrifica- tion around 1900 fostered further decen- tralization by liberating machines from me- chanical couplings to central factory steam engines.) Broadly, mechanization caused human dexterity and muscle to be replaced 1900 AD 1950 AD with mechanically induced precision and power, but humans functioning as plan- ners, sensors, and controllers of machines continued to be essential components of manufacturing enterprises. The Second In- dustrial (or Automation) Revolution, whose advent may be marked by the invention of computers and NC machines around 1950, is now eliminating the need for human planning, sensing, and control.

MODELING IN THE DESIGN PROCESS Manufacturing Planning Technology Codified history in the area of manufac- turing planning technology is at best frag- mentary, with Hounshell's recent book (1984) standing as an exemplary treatment of the evolution of interchangeability and Noble's polemic (1984) offering a biased but interesting view of the emergence of NC technology. One might mark the advent of planning craft. technology by the Jacquard loom's use of mechanical programming a textile tech- nology that took more than a century to propagate into the mechanical industries (e.g., in the form of screw machines). The most notable event was the introduction of master-gauge principles in American ar- mories in the early 1800s; this led to inter- changeability and "the American system of manufacture." The rise of metal-cutting science and material science in the later 1800s fostered engineering assignment of manufacturing parameters (e.g., speeds and feeds in machining) rather than cut-and-try values. Group technology appeared in Eu- rope early in the current century and, after considerable elaboration in different con- , ~ . . .. ~ 193 tools to develop a systematic engineering graphics, but did not do so. Booker (1979) speculates on why they did not do so and provides a great deal of additional infor- mation in this area. Technical graphics, as we now know it, began to evolve in a largely ad hoc manner in the first half of the present millennium. Figure 23 shows typical twelfth-century "practice," and Leonardo's drawings exemplify the highest Descartes laid the foundations for mod- ern geometry in the 1600s by coupling al- gebra and geometry, and Monge's "descrip- tive geometry" set in the late 1700s the main techniques and conventions used in modern engineering graphics. (Monge's work was regarded as so important that for a period in Napoleonic times it was classified as a military secret.) Figure 24 (Booker, 1979) shows an English drawing of 1804 that de- fines part of the valve gear for one of Rich- ard Trevithick's steam engines. Observe that multiview parallel projection and sec- tion views were well established and that there are no dimensions on the half-size as- sembly drawing. There were no detailed drawings for the separate parts of the as- texts Design stanuaro~zat~on, manufactur- 'I ' ' ' ~ a- t-- ing-method standardization, etc.), remains controversial and largely devoid of scien- tific foundations. The invention of comput- ers, NC machines, and industrial robots at midcentury led to the development of NC and robot programming languages, and some current research is focused on devel- oping manufacturing-planning automata that can write NC and robot programs automatically. Design Representation Technology Crude models and sketches were used to represent man-made artifacts from the ear- liest eras of recorded history. In the late pre-Christian era the Greeks, through stud- ies of astronomical stereography, had the sembly, and the valve was mace oy a craftsman who scaled the assembly draw- ing using a proportional divider. Drafting conventions for example, American third-angle drawing-layout con- ventions and dimensioning practice evolved in the later 1800s and began to be standardized in the 1900s. Drafting began to be "computerized" in the late 1950s with the advent of computer graphics, and now drafting is being replaced by solid modeling as the primary medium for design specifi- cation. The evolution of tolerancing practice warrants special discussion. Levy (1974) notes that tolerancing was not introduced into American industry until about 1900 and that the first mention of the subject appeared in one paragraph in the 1929 edi-

FUGUE 23 A twelfth-century drawing of an undershot waterwheel. Drawing is from "Hortus-Deliciarum," a manuscript containing draw- ings compiled by the Abbess Herrad of Landsperg in about 1160. ~ : =.~04 , ~ I,. . Am, ~ IL' 1 FUGUE 24 An undimensioned drawing of 1804. SOURCE: Science Museum, London. 194

MODELING IN THE DESIGN PROCESS tion of French's classic textbook on engi- neering graphics, now in its tenth edition (French and Vierck, 1966~. The first American drafting standard, ASA Z14.1, appeared in 1935 as an 18-page document containing two paragraphs on limit ("plus-minus") tolerancing. The de- velopment of "geometric" or "true-posi- tion" tolerancing was done largely in Eu- rope in the 1930s and 1940s. Chevrolet brought maximum material condition (MMC) concepts to this country in 1940, and Parker and Gladman (Levy, 1974) cod- ified true-position principles in Britain in 1941-1944. The new system was refined in a series of draft standards that culminated in this country in ANSI Y14.5 in 1973, and O _ m' r o.g 1 .; : 8 x _~ Face square Widl Dawn "Y'' within '~ .001" RFS ~p ~002~1 Y my; ~ 8 0 _ - , ~' ,_ ~1 1 1 .001 1 YE FIGURE 25 Evolution of tolerancing practice. Reproduced from A His- tory of Engineering Drawing by P. J. Booker, courtesy of the author and Mechanical Engineenng Publications. 195 that standard has subsequently been amended in detail. Figure 25 shows the rapid evolution of tolerancing practice. The 1920-vintage drawing of Figure 25a contains no explicit tolerances but specifies manufacturing processes (bore) for two holes and a preci- sion for one hole through a functional re- quirement running-fit (R.F.) on Spindle C. The 1950s drawing of the same part in Figure 25b specifies limit tolerances for the two holes and requires that a face be per- pendicular RFS ("regardless of feature size"- Y's size, in this case) to hole Y. The 1970s drawing in Figure 25c retains the limit tolerances (but with subtly different interpretations) and the squareness toler- ~) R.F. on Spindle C (a) 1920s practice it\ ~ \\\\\\\\\\\ ~~ ~ <~J it\ ~ \\\\\\\\\\\ (b) 1950s practice it\ ~ \\\\\\\\\\\ _ _ _ _ ~~ \\\\\\\\\\\\ (c) 1970s practice A' O — ', ~ ~Q~ ,- If)

196 ance, and also requires that the smaller hole be concentric with the larger to an MMC tolerance. Figure 26 shows a table of symbols for interpreting Figure 25c, but more impor- tantly, it illustrates the direction of modern tolerancing practice, which is to specify al- lowable "size," positional, and relational variations on or between "features" of parts. Alas, all of this work on tolerancing lacks mathematical foundations and thus, in the current era of informationally complete solid modeling, tolerancing stands as an open problem in engineering science. Design Analysis Tools The evolution of design analysis tools fol- lowed closely developments in mathemat- ics, physical science, engineering science, and now computer science. Euclidean ge- ometry became available in pre-Christian times, and trigonometry became a practical tool after Arabic numerology and arith- metic had been adopted. Analytical activity accelerated in the 1700s and thereafter when Euler, Fourier, and others developed methods to solve Newtonian differential equations in simple domains; this work laid the foundations for the development of nu- merical methods in the nineteenth and twentieth centuries. The invention of prac- TOLERANCE CHARACTERISTIC SYMBOL _ STRAIGHTNESS FOR FLATNESS D INDIVIDUAL FORM FEATURES . CIRCULARITY (ROUNDNESS) O CYLINDRICITY FEY FOR PROFILE OF A LINE OR RELATED PROFILE PROFILE OF A SURFACE ANGULARITY ORI ENTATION PERPENDICULARITY PARALLELISM // FOR POSITION RELATED LOCATION FEATURES CONCENTRICITY ~ CIRCULAR RUNOUT /< RUNOUT TOTAL R UNOUT FIGURE 26 Attributes covered by modern toler- ancing practice. HERBERT B. VOELCKER tical mechanical calculators about a cen- tury ago brought numerical methods into engineering use, and over the past 20 years electronic digital computation has brought finite-element and digital-simulation meth- ods into widespread engineering use. Thus, the near-term future in design analysis seems to lie with increasingly powerful and parallel numerical computation. But limits set by the physics of known computing components, and also by the asymptotic complexity of known algorithms, are on the horizon, and we might see a return to quasi- analog methods through such routes as con- nectionist machines. Functional Representation and Design Synthesis Tools The first column in Figure 22 has but one, weak entry the standardization of common components. The dilemma here is that engineers often can represent the "functionalism" of a product phenomeno- logically through stress/strain equations in structures, heat-transfer and energy- exchange equations in combustors, and so forth but we have almost no mathemati- cal couplings from phenomenological mod- els to the forms of artifacts that can exhibit specific phenomena. (Proceeding from form to function through analysis is easier, at least in principle, as we have already noted). Thus, the induction of physical form from mechanical function mechanical de- sign synthesis continues to stand as an ill- understood "human creative activity." COMMENTS There are some striking trends, facts, and anomalies in the history just summarized. Five are considered here. · Military needs have stimulated prog- ress in design and manufacturing from the earliest to the most modern times. To cite but three examples: The first significant

MODELING IN THE DESIGN PROCESS water-driven cutting machines were can- non-boring mills; the codification of draft- ing and tolerancing standards was driven largely by military procurement needs, the development and early dissemination of NC technology were undertaken to meet the stringent technical requirements posed by military supersonic flight. · Mechanization and interchangeability are often thought to be linked or even syn- onymous practices, but they are in fact in- dependent. Neither implies or requires the other. · The century-long gap between the rise of interchangeability and the codification of tolerancing seems at first astonishing, for how can one manufacture interchangeable parts without strict manufacturing toler- ances? The key lies in understanding gaug- ing. Parts built to fit adequately designed gauges will be precise in the serrse of being interchangeable, but they may not be "ac- curate" in the sense of meeting measure- ments to an absolute standard external to the set of gauges. One of the technical mys- teries in manufacturing history is how early tooling engineers (the gauge artisans of Fig- ure 20e) designed adequate gauges in the pretolerance era. Today the relationship between gauges and tolerances is clear: Gauges are built to reflect tolerances given in design specifica- tions, and hence tolerances implicitly spec- ify inspection procedures. Thus, we have, for example, "Principle 5: The gage de- signer should not have to make arbitrary decisions regarding gage element size or lo- cation, since a complete product specifica- tion dictates these design and interchange- ability criteria. The drawing Is not complete if such decisions are required . . ." (Roth, 1970, 5~. · The prohibition in design specifications of explicit links to either function (R.F. on Spindle C in Figure 25a) or manufacturing Whether they do so unambiguously is an open research question. 197 processes (Bore in Figure 25a) is largely a post-Worlcl War II development. It was promoter] vigorously by military agencies to facilitate multisource competitive procure- ment and also as interchangeability insur- ance, it was subsequently adopter] by many civil manufacturers for roughly the same reasons. The result Is the current practice of defining parts and assemblies almost wholly through geometrical mechanisms. (Com- panies that have retained explicit links to function or process in their design specifi- cations are almost always vertically inte- grated and do little outsourcing.) Those who advocate the currently fashionable doctrine of "design the process with the product" should be aware of the conse- quences of applying that doctrine too rig- icily, because in some senses it is a retro- grade step. · We conclude these comments by not- ing again the lack of understanding of methods by which form can be induced from function. Architects have pondered this problem for several decades (Alexan- der, 1964; Habraken, 1987), and over the past decade mechanical engineers have at- tacked the problem on several fronts (Dixon et al., 1987; Rinderle 1986, in press, Sub et al., 1981; Ullman et al., in press). REFERENCES Alexander, C. 1964. Notes on the Synthesis of Form. Cambridge, Mass.: Harvard University Press. Bezier, P. 1972. Numerical Control: Mathematics and Applications. New York: Wiley. Booker, P. I. 1979. A History of Engineering Draw- ing. London: Northgate Publishing. Brown, C. M. 1982. PADL-2: A technical summary. IEEE Computer Graphics and Applications 2(2):69-84. Chan, S. C. 1987. MPL: A New Machining Process/ Programming Language. Ph.D. dissertation, Uni- versity of Rochester. Available as Technical Report CPA-1 from COMEPP, Kimball Hall, Cornell Uni- versity. Chan, S. C., and H. B. Voelcker. 1986. An introduc- tion to MPL—A new machining process/program- ming language. Pp. 333-334 in Proceedings of the

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