Cover Sheet

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Contents

Cover Sheet 1

Table of Contents and List of Figures 2

Abstract 3

Introduction 4

Technical Discussion 5

1 Problem Statement 51.1 Background and Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.2 Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.1.3 Graphics Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Progress Report for Continuation Projects 8

3 Proposed Work 83.1 Application to the Domain of MEMS Design . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1.1 MEMS Filters for Signal Processing (Prof. Sequin’s Responsibility) . . . . . . . . . 83.1.2 MEMS Resonators for Energy Scavenging (Prof. Wright’s Responsibility) . . . . . 10

3.2 Injection Molding (Prof. McMains’ Responsibility) . . . . . . . . . . . . . . . . . . . . . . 113.3 Electronic-Mechanical Integration (Prof. Wright’s Responsibility) . . . . . . . . . . . . . . 15

4 Relevance to MICRO 16

List of Figures

1 Molds for an electro-mechanical part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Injection molding terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Two different suspension geometries found by an unsupervised search with a genetic algo-

rithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 An optimized layout of the suspension system after introducing higher-level primitives sug-

gested by the designer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Experimental geometries for improved piezo-electric oscillators . . . . . . . . . . . . . . . 116 PicoRadio Test Bed fit test between an injection molded component and a prototype board

and casing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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Interactive Design Exploration and Optimization Tools

Principal Investigators:

Sara McMainsDepartment of Mechanical EngineeringUniversity of California at BerkeleyBerkeley, CA 94720-1740mcmains@me.berkeley.edu

Carlo SequinDepartment of Computer ScienceUniversity of California at BerkeleyBerkeley, CA 94720-1776sequin@cs.berkeley.edu

Paul K. WrightDepartment of Mechanical EngineeringUniversity of California at BerkeleyBerkeley, CA 94720-1740pwright@robocop.me.berkeley.edu

Cooperating Company:

Ford Motor Company

Abstract

This anticipated multi-year project investigates design practices for electro-mechanical parts and systems.We will develop new algorithms and paradigms for interactive tools that will improve the joint human-computer design process. The focus will be on self powered (energy harvesting) sensor networks, boththeir internal micro-electrical components and their injection molded casings. We will explore how to moreeffectively integrate human design expertise and intelligence into refining the design space searched bygenetic algorithms, and how to provide injection molding manufacturability feedback orders of magnitudefaster than existing tools in order to provide real-time, automatic feedback to designers.

Keywords: CAD/CAM, Design Automation, Optimization, Electro-mechanical Design

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Interactive Design Exploration and Optimization Tools

Introduction

Great engineering design requires both innovative “big-picture” ideas and detail-oriented analysis. Mostengineering designers prefer to spend their time working on creative new ideas. Happily, as computersbecome ever more powerful, more and more of the tedious aspects of detailed analysis can be performed bymachine. In practice however, designers too often defer analysis if it takes a long time to run and requiresmanual set-up. We need faster, automated analysis tools. Another issue is that human designers can becomefixated on a particular approach and fail to explore a wider range of possible designs. Computer searchalgorithms such as genetic algorithms are an emerging approach to addressing this problem. The objectiveof our proposed research is to develop new algorithms and paradigms for interactive tools that will improvethe joint human-computer design process.

The specific design domain we will focus on is self powered (energy harvesting) sensor networks, both theirinternal micro-electrical components and their injection molded casings. In the Micro-electrical MechanicalSystems (MEMS) domain, our best conceptual designs have all come from human designers. Up to now, theinitial promise genetic algorithms showed for finding inventive new design solutions [Goldberg, 1989] havenot produced results superior to initial designs produced by expert human designers. In this project, we willexplore how to more effectively integrate human design expertise and intelligence into refining the designspace searched by genetic algorithms and more effectively integrating GAs with other computer-aided searchand optimization tools such as simulated annealing.

For the casings (Figure 1), aesthetic considerations mean humans will need to drive the design process. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Figure 1: Molds for top and bottom housing, theinjection molded parts, and assembled electro-mechanical product (a fingerprint reader) [Mc-Mains et al., 2001]

The primary non-aesthetic considerations include en-suring that the casing continues to interface with theboard it contains as the electrical designers revise theboard design, and ensuring that the casing geometry canbe successfully injection molded at the low cost. To ad-dress the former, we will build an object-oriented frame-work with “cross-couplers” that play an active role inhelping designers identify cross-domain design param-eters. To address the latter, we will develop new designfor manufacturability feedback tools that provide feed-back orders of magnitude faster than existing tools andintegrate our tools in a solid modeling system to pro-vide continuous, automatic feedback to the designer inreal time.

The electronics sub-division of Ford Motor Companyhas made a long-term commitment to Berkeley’s re-search in Computer Graphics and Integrated Manufac-turing. Accelerating the time-to-market of consumerproducts containing electronic devices and electro-mechanical components, and which at the same time mayrequire eye-catching designs for maximum consumer appeal, is a key economic concern of many Califor-nian companies. Our joint research brings together advanced techniques in computer graphics and computeraided design (CAD) (Sequin in Computer Science and McMains in Mechanical Engineering), with rapidprototyping and computer aided manufacturing (CAM) (McMains and Wright in Mechanical Engineering).

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Technical Discussion

1 Problem Statement

Many challenging engineering design problems can no longer be solved without computers. From bridgesto airplanes to integrated circuits (ICs), engineers have developed powerful programs to assist the designer:for bridges, they range from truss design to earthquake analysis, for airplanes, from wing shapes to enginedesign, and for ICs, from module placement and routing, to finding critical delay paths, to performanceanalysis. Most of these programs are analysis programs of fine-grain parametric optimization programs.

Noteworthy exceptions are placement and routing programs for ICs which depend on some stochastic searchtechniques such as simulated annealing or genetic algorithms (GAs) to escape a particular local minimumin solution space and to find better solutions based on layouts that might be quite different from the startingconfiguration. Computer searches have been less successful in the early conceptual stages of design, wherecreativity, “gut feelings,” and insightful sparks are needed to come up with truly new approaches.

1.1 Background and Related Work

1.1.1 Genetic Algorithms

Among the above mentioned search approaches, genetic algorithms [Kamalian et al., 2002, Narayanan andAzarm, 1999, Zhou et al., 2001] are the most “inventive.” The have been demonstrated in many playfulsettings and have often produced truly surprising results. However, they very rarely produce practical,usable engineering solutions for real-world problems. The reason is that the possible solution space for suchproblems is always humongous, and the sampling produced by GA in any finite amount of time is thus onlyvery sparse. Thus any “solution” found by GA, although good enough to beat out the competing machine-generated solutions, is rarely good enough to meet the stringent engineering requirements of a successfulsystem or consumer product.

Because of this, it is advantageous to subject the most promising “solutions” found by GAs to a morenarrowly focused search or to a greedy optimization that allows exactly matching some nonnegotiable designrequirements and to approach more closely other design objectives. This fine tuning will not typically changethe given structure, but will only adjust a few aspects of the current design, and optimize a few pre-definedparameters. The combination of stochastic search and greedy optimization can be quite powerful, if thesearch domain is kept narrowly enough focused.

For the broad-based search in the early stages of design this approach is still not good enough, mostlybecause of the vastness of the search space and the existence of a huge number of local minima that arequite unrelated to any practical solution. In general GAs waste considerable time producing, evaluating, andrefining quite ridiculous design configurations. Here introducing human intellect in the loop could act as avery efficient filter to weed out approaches that have no real chance of evolving into anything usable, and tofocus processing effort on other branches in the genealogy that hold more promise. The question is how tobest integrate human design knowledge and critical intelligence into this process without forcing a humanto sit and monitor the GA doing the entire time.

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1.1.2 Cost Functions

Like all optimization algorithms, GAs require a method to evaluate the cost function to be minimized. Forthe MEMS domain, we will use the SUGAR simulator [Clark et al., 1998,Lo et al., 1996,SUG, 2005] in theevaluation loop. For the injection-molded casings, costs depend on part size, which is simple to evaluate,and mold complexity and manufacturing cycle time, which cannot be evaluated automatically with existingtools.

In molding and casting manufacturing processes, molten raw material is shaped in molds from which theresulting part must be removed after solidification. The most economical reusable mold consists of tworigid halves that meet along a planar “parting surface” and are removed in opposite directions along the“parting direction” (Figure 2a). In order for a part geometry to be de-moldable, it must be oriented relativeto the parting direction so that the two mold halves can be removed from the part via translation withoutcolliding with it. Surfaces where collisions occur because the mold extends into the area between the partand the parting surface, preventing extraction of the part, are called undercuts (Figure 2b). Finding anundercut-free orientation for an arbitrary geometry is subject to geometric accessibility constraints; not allgeometries admit such an orientation. In order to manufacture these more complex parts using injectionmolding, additional mold inserts (cores) with different release directions are needed, adding considerably tothe cost of the mold and increasing the manufacturing cycle time.

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(a) Injection mold for a simple part incross section

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(b) An orientation of the same part with un-dercuts

Figure 2: Injection molding terminology

For determining if there is an undercut-free orientation for a geometry (and thus if it is a candidate forthe cheaper 2-part mold), visibility maps that partition the Gaussian sphere are among the most promis-ing approaches [Woo, 1994, Chen et al., 1993, Chen and Chou, 1995, Wuerger and Gadh, 1997a, Wuergerand Gadh, 1997b]. [Rappaport and Rosenbloom, 1994] analyze 2D polygons for 2-moldability, and [Mc-Mains and Chen, 2004] analyze 2D curved spline input. [H. K. Ahn et al., 2002a] show that a definitiveanswer to whether a polyhedron is castable in any direction can be obtained via building an arrangementon a sphere as a function of facet normals and orientations where facets may start to obscure each other.Their implementation, however, only tests a heuristically chosen set of directions because of the complexityof implementation and long running time of the complete algorithm. For curved 3D surfaces, [Elber et al.,2004] describe an algorithm limited to C3 NURBS surfaces only, and their implementation is not fast enoughfor interactive feedback. Commercial software for undercut analysis requires the user to choose the part-ing direction a priori [Cimatron, 2002, SolidWorks Corp., 2004], and in our experience occasionally missesundercuts, classifies non-undercut geometry as problematic, and/or incorrectly highlights whole faces asundercuts even if only a small portion is problematic. The robust algorithms we propose to develop and im-

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plement will identify multiple potential parting directions if they exist and will be be completely automated,allowing integration with machine search and optimization.

Commercial software is often used for mold flow analysis only after the detail design is complete because ofthe overhead of running it. The popular C-Mold/Moldflow package [Moldflow Corporation, 2005] analyzesfilling, post-filling, and cooling using finite element methods. To run it requires first constructing a mesh,and the user must specify the details of the gate and runner system, an obstacle to full automation. Many ofthe problems discovered during this detailed analysis, however, could be predicted by checking whether thepart geometry violated design rules for injection molding, such as minimizing sharp corners to reduce shearstress by using fillets, keeping the wall thickness uniform as much as possible, avoiding abrupt changesin wall thickness that could lead to unequal shrinkage and adding a slight taper (draft) to vertical wallsfor easier releasability, since deep holes can be made with straight sides only if they are highly polished,increasing mold finishing costs [Poli and Bergeron, 2004, Olmsted and Davis, 2001]. Our approach will beto develop automated algorithms that check for violations of these design rules in order to achieve interactivespeeds for feedback to the designer and allow optimization across a wider range of potential designs.

1.1.3 Graphics Hardware

A computer’s central processing unit (CPU) supports a large number of general purpose assembly languageinstructions. Special purpose hardware, such as floating point co-processors, performs limited operationsmore rapidly than carrying out the same operations “in software” (where multiple assembly instructionswould need to be used instead). Specialized graphics processing hardware that supports the rasterizationof a dynamic scene composed of shaded, textured 3D triangles, once available only on high-end graphicsworkstations, is now ubiquitous even on low-end PCs. While floating point operations are used as buildingblocks for a large variety of other programs, the applicability of graphics hardware to operations beyondthe specialized rendering tasks they were designed for is rarely exploited. Previous applications of graphicshardware to manufacturing and inspection problems used only the hidden surface removal capabilities, buttoday’s programmable hardware can speed up more complex calculations.

We will develop and implement new classes of algorithms that exploit recent advances in programmablegraphics hardware (GPUs). While these algorithms will be approximate due to the limited resolution ofgraphics cards, they have the potential to execute considerably faster than conventional CPU algorithmsbecause they will run on what is essentially a mass-produced, highly specialized, parallel supercomputer.Furthermore, “Moore’s law” seems to apply to GPUs but with an even faster improvement rate than forCPUs over the past decade and half: a speedup of roughly 2.4 times a year for GPUs, compared to a1.7 times speedup per year for CPUs over the same period [Lin and Manocha, 2003]. If these sustainedtrends continue, the performance advantage for algorithms that take advantage of the graphics hardware willcontinue to grow.

Until a few years ago, most graphics cards were not user programmable. Today, programmable graphicscards (referred to as Graphics Processing Units or GPUs) allow users to define their own vertex and pixelprograms. Vertex programs are run in parallel to transform the coordinates of every vertex describing theinput geometry before rendering; pixel programs (formally, “fragment” programs) are then run in parallelfor every pixel of the output image. Current GPUs can process hundreds of millions of vertices per secondand rasterize billions of pixels per second, orders of magnitude faster than a general purpose CPU couldperform the same specialized operations. Although the parallelism of the GPU is confined to these twoprograms, if a new algorithm can be designed in a way that it can be creatively mapped to vertex and pixelprograms, the potential speedup is huge.

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We believe that GPU-accelerated algorithms have the potential to significantly increase analysis speed, mak-ing it possible both to give human designers real-time feedback as they experiment with design changes, andalso to increase the size of the searchable design space by making it possible to test many more designs.

2 Progress Report for Continuation Projects

Not applicable, since this is a new project, not a continuation project. We do, however, describe somepreliminary results that we will build on within the following section.

3 Proposed Work

3.1 Application to the Domain of MEMS Design

The combination of exploratory computer search techniques and fine-grained greedy optimization algo-rithms, controlled in an interactive manner by a human operator with some application domain knowledgeand design experience can also be used fruitfully in the design of micro-electromechanical systems (MEMS).These miniaturized mechanical devices and components, often integrated or interfaced with electronics, andfabricated on silicon wafers [Petersen, 1982,Fedder, 1999], have moved from the research laboratories into awide range of commercial products ranging from automotive engine sensors to medical monitoring devices.Two MEMS applications that are intimately tied to our proposed research concern MEMS resonators thatcan act as band-pass filters in the communication channels of the distributed sensor network, and MEMSpiezo-electric resonators that can act as energy scavenging elements for sensor nodes that need to operatefor a long time away from the power grid and where replacing batteries is not an option. Both componentsoffer challenging and quite different design problems that cannot be solved with one single design/synthesisprogram.

3.1.1 MEMS Filters for Signal Processing (Prof. Sequin’s Responsibility)

We have started to do some preliminary experiments involving the design of MEMS resonators for signalfiltering applications. The focus on this exercise was on finding the best possible suspension design for somecentral mass to which are attached two capacitive comb drives, one acting as an input driver, and the otherone acting as an output sensor. In most cases that central mass is suspended with four spring-like poly-linebeams which at their other ends are anchored to the silicon substrate. Genetic algorithms (GA) were used todiscover potentially new and innovative geometries for these suspension springs [Kamalian et al., 2002].

With no extra constraints specified, and thus with a large high-dimensional potential solution space, it takesa very long time for these algorithms to find a layout geometry that gives the desired resonance frequencyand at the same time gives a stiffness ratio of at least 10 between the desirable direction of oscillation (inthe direction of the comb drive fingers) and the undesirable motion direction perpendicular to it. While theGA search did find solutions that met the above criteria, the crooked legs and asymmetrical layouts are notgeometries that one would seriously consider for manufacturing (Figure 3a). Fabrication experience readilytells us that we want to use symmetry to cancel out to first order effects of processing uncertainties and ofresidual stresses in the surfaces of the suspension beams. Adding these constraints to the GA search roughlyreduces the number of parameters that need to be adjusted (and thus the dimension of the search space) by

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a factor of four. The run-times are dramatically reduced, solutions closer to the desired design goals arefound, and the layout geometries are more suitable for manufacturing (Figure 3b) [Zhang et al., 2005].

(a) (b)

Figure 3: Two different suspension geometries found by an unsupervised search with a genetic algorithm

On the other hand, the open-ended search using GA may find intriguing patterns that trigger some asso-ciations in a designer’s brain and may suggest spirals or serpentines or nested frame structures that werenot previously in her/his repertoire of known design primitives. While the patterns produced by the GAmay only be tenuous, the designer can readily distill out the new concept, and create simpler and moreregular spirals, serpentines, or frames that can be characterized with just a few geometric parameters.

Figure 4: An optimized layout of the sus-pension system after introducing higher-level primitives suggested by the designer.

Such new higher-level primitives can then be added to the libraryof components from which the GA search or other optimizationprograms can draw in order to make further improvements to thebest designs found so far (Figure 4).

We believe that such a symbiosis between computer algorithmsand human intelligence can indeed yield a very powerful designenvironment that can give practical solutions superior to whatany single monolithic synthesis or optimization program couldyield. Today’s design environment typically do not have thesecomponents suitably integrated to make this approach workablein an industrial design environment. The various componentsoften run on different computers and may require significantdata conversion and recoding to take a design from one algo-rithm to the next one. Human input is often limited to explicitlyre-programming the core of the genetic algorithm and the costfunctions in the optimization programs.

We envision a framework where a design engineer obtains visualfeedback about the current state of the GA during the process ofevolution, including a rank-ordered display of the most promis-ing layouts in the current generation. At the same time, this

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display is also an input channel through which the designer can exert some control, e.g., eliminating somebranches of the genetic population, putting more emphasis on other ones and thus steer the evolutionaryprocess into a more desirable direction. But we want to go even further, and let the designer make explicitchanges to any one of the current phenotypes, which then in turn affects the internal genotype, i.e., theencoding of this particular piece of geometry.

This will be a particularly challenging part of our research, but one that has potentially a large pay-off. Thedomain of MEMS design, with the SUGAR simulator [SUG, 2005] in the evaluation loop, is well suited tothe exploration of this approach. The SUGAR simulator takes as input a symbolic, sticks-like description ofthe main features of a MEMS design, representing suspension beams as simple polylines with some attachedparameters specifying width and height. Thus the conversion from a graphical sketch by the designer to aninternal parametrization should be feasible with an appropriately designed user interface.

A further key aspect of the envisioned design framework is the ability to readily forward the most promisingdesigns found in the GA search to one or more optimization packages that will fine-tune the design by alocal optimization using conjugate gradient descent or some similar technique. In this phase, the evaluationwith respect to the intended task as well as with respect to the devices manufacturability and robustness todesign variations will then be carried out much more thoroughly than can be done during the GA phase. Ofcourse, the best designs found in this process can then be recirculated again through a GA phase, but thistime more narrowly focused, and perhaps with a newly focused set of evaluation criteria that reflect moreclosely the most critical selection criteria for a real usable design solution.

3.1.2 MEMS Resonators for Energy Scavenging (Prof. Wright’s Responsibility)

Another practical design challenge for which we want to explore this combined approach is the design ofa family of resonators for energy scavenging from vibrational sources, ranging from car wheels drivingon a rough surface to acoustic noise sources in manufacturing plants. In one of the designs, the basicelement is a cantilevered beam with one or two layers of a piezo-electric material, which is fabricated with aphotolithographic process such as is used to build integrated circuits or MEMS. To optimize energy pick-up,the beam should have a resonant frequency near the dominant frequencies available in the vibrational energysource. Furthermore, the stresses resulting from any accelerations of the sensor chip should be converted intostrains that lie in an optimal operating region and which do not lead to fatigue and eventual self-destructionof the sensor device. Assuming we know the materials properties of the beam, calculating good geometriesfor such a sensor beam is not a very difficult task, and gradient descent methods can readily be used tofine-tune a design and to optimize it for a particular application.

Unfortunately, the materials properties of such piezo-electric sandwich structures are not well known, andare quite unpredictable. The residual stresses resulting from the different thermal expansion coefficientscan thwart the use of any well designed geometry. Unless great care is taken in elastic layer selection andthickness, upon release from the growth substrate the residual stress in the thin beams can cause them totwist and curl up to a point where they become non-functional. We hypothesize that this problem can bealleviated if the sensor beams are tied at both ends into a two-dimensional framework. The kind of patternswe are contemplating comprise wheels with several spokes (Figure 5 a), possibly curled up in a spiral pattern(Figure 5 b), serpentine beams tied into frames (Figure 5 c) as well as more complicated lattices or evencheckerboard patterns. While the residual stresses may still lift or depress portions of such perforated two-manifolds, and may lead to some noticeable buckling, the overall deformation can probably be be kept ina range where the device is still functional as a basic resonator that can convert vibrations into electricalenergy.

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(a) wheel structure (b) spiral whirl structure (c) serpentine structure

Figure 5: Experimental geometries for improved piezo-electric oscillators

With such two-dimensional patterns, the range of possible geometries is very much larger than the designvariations one can possibly impose on an isolated beam. Thus more extensive search methods as well asmore creativity on the part of the designer will be required to find the most promising structures. Also,the evaluation of these two-dimensional geometries will be much more involved and time-consuming andwill likely require many hundreds of hours of computer time. An open-ended search through all possiblegeometries with GA techniques is not likely to produce any viable results, and an extensive optimizationof one particular type of design, say a wheel with spokes Figure 5 a, is likely to be too narrowly focusedand may well miss potentially much better designs. Thus we have again a situation where we believe thatthe proper combination of computer algorithms and of tight interactive control by a knowledgeable designerwill be needed to find the best designs.

Sticking for the moment with the example of the wheel with (possibly spiral) spokes, we can envision acomputer search/survey, possibly using genetic algorithms, to identify the approximate design types of thissort that will bring us near the desired device characteristics. We expect a knowledgeable MEMS designer tolook at these results and identify certain promising features that are common to the successful designs. Thedesigner may then distill out these features and define them more cleanly and more compactly in a moduleof procedurally generated geometry that has only a few parameters.

The exact values of the best parameter values can then be found with local optimization, e.g., by gradientdescent in the height field of a cost function that encodes the design requirements and performance goals. Ifthere is more than one local optimum within the range of the hard design specifications, all of these designswill be presented to the designer for further, more detailed analysis or for a possible selection based onattributes that have not been explicitly stated in the original design specifications. This approach has beenproven successful in the automatic optimization of operational amplifiers [Koh et al., 1990].

3.2 Injection Molding (Prof. McMains’ Responsibility)

For evaluating the manufacturability and the cost of the casings for the devices that will use these devices(Figure 6), we will develop and implement efficient new GPU-accelerated 2-moldability testing algorithmsusing a hierarchical, multi-resolution approach to control accuracy. During conceptual design, for geome-tries with multiple feasible molding directions, GPU-accelerated cost estimates will be used to suggest theleast expensive alternatives. We will integrate incremental versions of these algorithms into a commercialsolid modeling package using its API (application program interface) in order to study the effect of pro-viding continuous, real-time feedback to designers while they work. In later years of the project, we will

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combine the GPU-accelerated approach with accessibility map techniques to calculate manufacturing plan-ning, feasibility, and cost feedback for multi-piece molds with side pulls and internal undercuts. We willalso use the GPU as a tool to speed up calculations for warning the user about potential quality issues.

Figure 6: PicoRadio Test Bed fit test betweenan injection molded component and a prototypeboard and casing.

Since our manufacturability feedback must be reliableto be of use to the designer, we will also developmathematical models for calculating reliable boundson the possible error for these approximate solutions.The manufacturability feedback can then be displayedgraphically along with a visualization of the uncertainty.Both the estimates and the uncertainty will be validatedagainst exact arithmetic implementations of the mold-ability algorithms; we will run these slow but reliableexact algorithms as background processes for qualityassurance of the feedback from our fast, approximatealgorithms. The comparison data archive thus gener-ated will also guide us as we improve the accuracy ofthe approximate algorithms.

As preliminary work, we have developed a new GPU-accelerated algorithm to test a geometry’s moldabilityin a two part mold and provide graphical feedback tohighlight the undercut features for a given parting direc-tion [Khardekar and McMains, 2004, Khardekar et al.,2005]. For simplicity, we will describe the algorithm as-suming a vertical parting direction. Define a part facetas an “up-facet” if the angle between its outward facing surface normal and the positive (+z) parting direc-tion is less than 90◦. [Ahn et al., 2002a] proved that a given part geometry is vertically moldable if and onlyif it is vertically monotone, i.e. there exists no vertical line that intersects the part surface and/or interior inmore than one disconnected interval. We observe that as a consequence, for a part that is not moldable andhence not vertically monotone, vertical lines at the non-vertically-monotone locations will intersect at leasttwo up facets. Thus if we project the up facets of the boundary representation of the part orthographicallyonto a plane normal to the parting direction, the part is moldable in this direction if and only if none of theprojections of the up-facets overlap.

In our two pass moldability algorithm, we first place the center of projection above the part along the positiveparting direction to be tested. For the rendering operations described below, we use orthographic projectionin the parting direction. In the first pass, we render the visible (portions of) up facets using the z-buffervisibility capabilities of the graphics card. After this pass, the frame buffer’s pixels corresponding to visiblegeometry will have been updated, and the z-buffer will hold the distance to the visible up facet for eachpixel. In the second pass, we zero the frame buffer but re-use the z-buffer from the first pass. We re-renderthe geometry, this time setting the depth test function to compare distances to those stored in the z-bufferin the first pass, so that only the (portions of) up facets that were hidden in the first pass will be rendered.Thus if any pixels are rendered in the frame buffer during the second pass, they correspond to overlappingprojected up facets, telling us that the object is not moldable in that direction. On the most recent graphicscards, we can efficiently check if any pixels were rendered in this pass by using the graphics card’s occlusionquery functionality, rather than reading back the entire frame buffer. Our implementation of this algorithmon a GPU donated by nVidia was able to test the moldability of parts with over 20,000 facets in less than one

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millisecond per direction tested (Fig. 7), with running time growing only linearly with input size, in contrastto the O(n logn) growth rate of the Ahn et al. algorithm. The running times were over 200 times fastercompared to running on the same machine with an older GPU that does not support vertex and fragmentprograms, since the CPU had to execute them.

Undercuts40 facets 20,676 facets

(a) Sample parts with undercuts found by ouralgorithm highlighted (vertical removal di-rection)

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(b) Running times (QuadroFX 3000GPU, AMD Athlon 1.8 GHz CPU)

Figure 7: Preliminary Results

We use depth textures to highlight the (portions of) facets that are not moldable in the given direction so thatthe designer can make the necessary changes to the part geometry. This is analogous to finding the (portionsof) facets that would be in shadow if the part were to be illuminated by two light sources located at infinityin the positive and negative parting directions. We generate two depth textures with the graphics card byorthographically rendering the part looking at it from the positive and negative parting directions. The depthtexture holds the distance to the part for each pixel of the resulting image, copied from the z-buffer.

We can then allow the user to rotate the object and examine the highlighted undercuts in real time, accessingthe same two depth textures for each instantaneous viewing direction. We make use of vertex programsand fragment programs executed in parallel on the graphics card. We use a vertex program to transformthe vertices of each polygon by the orthogonal viewing transformation associated with the two partingdirections in turn, calculating the texture coordinates that the subsequent pixel program will use to checkif the transformed depths for each fragment are greater than the depth values stored in the respective depthtextures. (Textures are stored in texture memory on the GPU, eliminating the bottleneck of accessing generalpurpose RAM on the motherboard, but must be accessed in a prescribed manner optimized for texturemapping bitmapped images onto triangular meshes.) If both are greater, we highlight that fragment toindicate to the designer that there is an undercut on that section of the surface. Later, when we consider sidepulls, verification of their surface coverage is a natural extension of this algorithm: we add an additionaldepth texture from the point of view of each side pull.

Testing a pre-determined parting direction using the above algorithm will be useful to designers at the stagein detail design where they have begun to add bosses, ribs, and draft to a part, since these operations requireknowing the parting direction a priori. (If the user specifies a parting direction, we can also warn the userif minimum draft requirements have not been met by adding a check for facet inclination angle to our pixelprogram.) But during the conceptual design, we can use this same algorithm as a subroutine for determiningif any 2-moldable directions exist, and finding alternate feasible directions if so. Alternate directions allow

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greater freedom for subsequent design operations, and some directions may allow for more cost-effectivemolds than others. The efficiency of these algorithms lies in that they identify groups of candidate directionssuch that if any one direction in the group is not castable, none are, or if any one is castable, all are. Wewill use the fact that all combinatorially distinct casting directions correspond to 0-, 1-, or 2-cells in anarrangement of great circles on a Gaussian sphere, where the great circles are derived from the faces of theinput geometry.

In the first year, we will analyze the reliability of this direction testing algorithm, build a multi-resolutionversion of it, and develop improved algorithms that use it as a subroutine for finding alternate (if any) 2-moldable directions. Our proposed multi-resolution algorithm will use a hierarchical refinement approach.We will start by setting the viewing parameters so that the entire projected part fits in the frame buffer,and then if the user requests greater accuracy, we will subdivide this view into quadrants, processing eachquadrant sequentially to achieve four times the resolution of the parent. Based on statistics such as thenumbers of pixels rendered in each quadrant and their depth complexity, we can make informed decisionsabout which quadrants are the best candidates for further subdivision. To estimate the impact of this multi-resolution approach, we will gather data on how often we obtain different answers about moldability usingthe the higher resolutions.

For determining all feasible releasability directions, we believe that we can obtain speedups by perform-ing incremental calculations. For example, with an extrusion, the valid parting directions will include notonly the extrusion direction but also the valid parting directions for the 2D shape extruded. For efficientlyanalyzing the moldability of a 2D “polygon” bounded by edges that may be curved, without requiring thatthe shape be first tessellated into approximating straight line segments, we will implement a new algorithmwe have developed [McMains and Chen, 2004]. The complexity of our algorithm is O(n), where n is thenumber of “segments” bounding the input polygon, where we consider either a straight line segment or acurve with G1 continuity and positive or negative signed curvature everywhere to be a segment. For inputdefined by spline curves with a total of n control points, the running time is thus linear in the number ofcontrol points.

After looking at efficient moldability analysis for individual design primitives, we will study the effectsof combinations of primitives. For example, when multiple additive extrusion operations are combined,performing a Boolean intersection between the individual primitives’ valid parting directions will limit thepotential parting directions that need to be considered (a non-empty set is a necessary but not a sufficientcondition for a part to be moldable). A Boolean algebra of combinations of different primitive operators’parting directions can be implemented on a discretized representation of all possible parting directions, usingthe stencil buffer on the graphics card.

In later years of this anticipated multi-year project, there are a variety of directions we hope to pursue. Wewill incorporate the testbed as a plug-in to a solid modeler that supports notification of model changes. Eachtime a geometry change is detected, the plug-in will first call our GPU-accelerated algorithms to provideimmediate feedback to the user about the moldability of the new geometry (and the size of the potentialerror in the calculation), then fork a background process to perform slower, non-approximate moldabilitydirection testing. If this calculation obtains a qualitatively different answer, the user will be notified in apop-up window. The testbed will also link to a relational database where the geometry and the results ofboth tests will be archived.

We will implement reliable exact arithmetic versions of our direction checking algorithms. Recent advancesin implementing exact arithmetic packages can fix problems due to round-off errors [cgal.org, 2005], buttypically slow down computations by one or two orders of magnitude. Thus exact arithmetic is inappropriatefor interactive feedback, but shows promise for the slower, more accurate simulations we will implement

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to double-check the accuracy of the fast, approximate feedback. We will add cost estimation, taking the[Boothroyd et al., 2002] model as a starting point and developing new GPU algorithms to efficiently estimatecosts. We will develop and implement visualizations of the potential errors in our fast feedback (introducedmainly by discretization). We will extend the ideas from our 2-piece mold algorithms to develop multi-piecemold DFM feedback tools.

We will develop new design-rule checking tools to analyze quality issues, to replace current tools that relyon finite element methods that are lengthy to run and require manual setup. We believe much more efficient,automated feedback can be provided by using the GPU to build the “skeleton” of the geometry, thus reducingthe dimensionality of the problem and significantly speeding up the analysis. The skeleton consists of allpoints interior to the part that have at least two equi-distant closest points on the surface; these points,together with the distance to the surface for each, comprise the Medial Axis Transform (MAT). We willcalculate a discretized approximation to the MAT using the graphics hardware. Then we will use the MAT’sdistance information to find large material masses, and combine the distance information with the MATtopology to evaluate the rate of changes in part thickness and the potential for sink defects. We will alsobuild the MAT of the complement of the part to check for cooling problems, which can arise for examplewhen two parallel ribs are close together compared to their wall thickness.

3.3 Electronic-Mechanical Integration (Prof. Wright’s Responsibility)

For integrating the electronic and mechanical designs, we will need an interface for constraint specification.During the constraint specification process, designers must differentiate between “local” constraints thataffect only the ECAD or only the MCAD side, and “global” cross-coupled constraints. These constraintsmay be geometric, topological, parametric, or logical.

We will study the “as is” design process for the class of electronic-mechanical products, for a better un-derstanding of the inter-dependencies between the design tasks. We will then build an object-orientedframework with “cross-couplers” that play an active role in helping designers identify cross-domain de-sign parameters and relate the two. Unlike the MIT/DICE project [Sriram, 2002], we won’t be developingour integrative environment around an in-house CAD package; we want a scheme that can be integratedwith commercial CAD/CAE tools but at a finer level of granularity than provided by commercial productdata management (PDM) systems. Thus we are investigating how to represent cross-coupled constraints atan appropriate level of data granularity. This will involve intimate knowledge of ECAD/MCAD file formatsso that only key data is used and lower level data remains within the native format.

We propose to represent this mixed set of constraints and entities by bipartite graphs [Serrano and Gossard,1987] where the nodes and arcs are drawn from a standard set of topological, geometric, parametric entitiesand the relations between them, respectively. Standard algorithms are also available for the decompositionof such graphs [Sedgewick, 1999] into not only strongly connected components, but also into sub-problemsthat can be sent to different types of solvers. Graph based methods facilitate identification of over, underand improperly constrained conditions, even without solving. This will be used as the basis for constraintspecification validation. Many of the symbolic solvers have difficulty with large sets of equations, particu-larly in the presence of transcendental functions. Additionally, specialized geometric solvers may be moreefficient for maintaining geometric constraints, instead of general-purpose equation solvers. DCM3D fromD-Cubed is the leading commercial solver now embedded in many MCAD systems [dcu, 1999]. Geometricsolvers and solution selectors need to be combined with other types of solvers for our system.

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4 Relevance to MICRO

Particularly in the field of microelectronics, the design process is an iterative one, relying on the interactionbetween a human designer and computer-aided design and manufacturing tools. Our proposed work inintegrating human design expertise into computer-aided search and optimization is thus directly applicableto microelectronics design. Furthermore, the techniques we will develop in the course of this project willhave broad applicability in computer science and computer-aided design, not just to the design of the energyharvesting sensor network components we will be using as test cases. Efficient visibility calculations, forexample, are a central problem in a number of areas: efficient graphics display of complex virtual scenes,accessibility analysis in manufacturing, local wireless network layout, and 3D scanning, both for inspectionand model acquisition. The algorithms, analysis techniques, and implementation methods developed inthis project for injection molding will be applicable to many of these other application areas as well. GPU-accelerated algorithms could radically alter the ways in which CAD/CAM/CAE systems are built, expandingsearch spaces by reducing the cost of generating and testing alternate solutions, adding interactivity wherenone existed, and making problems that were once considered computationally infeasible tractable after all.

Additional Information on Our Sponsor

Our collaborators in the Ford Motor Company are establishing a line of products for driver guidance, per-sonal safety, and vehicle systems monitoring. Some of these devices are “wearable, sensor-based comput-ers,” for instance, earrings that monitor body condition and driver alertness. The needs for comfort andreliability present a host of “organic design” problems – designing for the human form – along with themanufacturing challenges that come from creating molds that can fabricate delicate and convoluted struc-tures. The upcoming federally mandated deadlines for incorporating built-in tire pressure monitors in thetires of new vehicles have also resulted in renewed interest in our work on sensors and sensor networks.Ford particularly encourages us to develop design and manufacturing methods that can be used to shortenthe time delay from the inception of a design to its realization as a manufacturable product.

We meet regularly with representatives from Ford Motor Company, including Russ Saul, the regional man-ager in San Ramon, CA, and Dr. Liou, our technical liaison. Dr. Liou’s expertise lies in the area ofKnowledge Based Engineering software to help designers with issues concerning Design for Manufactura-bility [Ahn et al., 2002b]. Many new electronic-mechanical, sensor-based devices will thus be developedduring our proposed collaboration using our interactive design tools. A variety of products of this naturewere developed by student design teams as part of ME 221, High-Tech Product Design and Rapid Manufac-turing. For the “Mock Trade Show” interdisciplinary teams of students from different departments (EE, CS,ME, Business) designed and prototyped projects such as: EZ-park, an RF ID tag parking garage parking spotlocation system; BabyOnBoard, a wireless temperature monitor and key chain alarm system for parents toalert them of potentially dangerous temperatures in their parked cars; BlindSIGHT, a driving aid that detectspersons, vehicles, and objects in a driver’s blind spots while driving; SafetyNET, for detecting falls in elder-care environments; Smart Shopper, a hand-held wireless retail platform that assists shoppers with productinformation, itemization and payment; TheraPad, an ice/heat pack with an attached sensor that monitorshow often, how long and at what temperature the patient is taking care of their injury; SmartLock, a bicyclesecurity device that is used to notify people when their bicycles are being tampered with; and CommuniCast,dynamic digital billboards triggered by a wearable wireless device in the form of a key-chain.

All these class projects were funded by our sponsor, even though most of the devices designed were notdirectly related to in-vehicle monitoring. Pushing the state of the art in interactive design tools is of very

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high interest to the industry, and good techniques are obviously transferable from one application domain toanother.

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