Computer-Aided Design 42 (2010) 432–444

Contents lists available at ScienceDirect

Computer-Aided Design

journal homepage: www.elsevier.com/locate/cad

A desktop virtual reality-based interactive modular fixture configurationdesign systemPeng Gaoliang a,∗, Wang Gongdong b, Liu Wenjian a, Yu Haiquan aa School of Mechanics and Electronics, Harbin Institute of Technology, Harbin 150001, Chinab School of Aeronautics and Astronautics, Shenyang Institute of Aeronautical Engineering, Shenyang, 110136, China

a r t i c l e i n f o

Article history:Received 23 February 2008Accepted 7 February 2009

Keywords:Modular fixture designVirtual realityVirtual assembly model3D manipulation approach

a b s t r a c t

Modular fixture configuration design is a complicated task requiring strong professional backgroundand practical experience. However, automated or semi-automated computer aided modular fixturesystems based on CAD packages still are not well accepted by the manufacturing industry due to thelack of intuitive interaction and immediate feedback compared with traditional models such as paperand physical models. In this paper, a novel Virtual Reality-based system for interactive modular fixtureconfiguration design is presented. We use a multi-view based modular fixture assembly model to assistinformation representation and management. In addition, the suggested strategy is compatible withthe principles of virtual environment and it is easy to reutilize the element model. Based on geometricconstraints, we propose a precise 3Dmanipulation approach to improve intuitive interaction and accurate3D positioning of fixture components in virtual space. Thus, themodular fixture configuration design taskcan precisely be performed in virtual space.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Modular fixture design is a complex task that is traditionallyaccomplished heuristically, based on both knowledge and experi-ence of designers. Due to development and extension of ComputerAided Design (CAD) based tools in the area of engineering, Com-puter Aided Fixture Design (CAFD) approaches have dramaticallybeen increased. Since the 1980s, much work has been carried outin order to improve the fixture design process.Generally, in a CAFD system, fixture design can be divided into

three phases: setup and fixture planning, fixture configurationdesign, and fixture design verification [1]. Set-up planning could bea subset of process planning where the number of setups required,the orientation of theworkpiece, andmachining surfaces in a setupare determined. Fixture planning is to determine the locating,supporting and clamping surfaces and points on the workpiece.The task of fixture configuration design is to select fixture elementsand place them into position to locate and hold theworkpiece. Thiscan be viewed as the structural design of the fixture. Fixture designverification is to ensure that fixture configuration is well designedto hold machining parts accurately and strongly. However, mostcurrent systems do not equally emphasize these three phases, evenif all are performed. Most previous research has focused on fixture

∗ Corresponding author. Tel.: +86 451 86413262; fax: +86 451 86413262.E-mail address: pgl7782@hit.edu.cn (G. Peng).

0010-4485/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2009.02.003

planning and fixture verification, by using a computerized methodto facilitate fixture design, while fixture configuration design hasnot been given equal regard.Scientific research has been undertaken in the field of Virtual

Reality (VR) for several decades, having recognized it as a powerfultool for creating more natural and intuitive human computerinterfaces. Now VR has matured to become useful technology tosupport efficient and effective product design and developmentapplications. The objective of this paper is to develop a VRsupported interactive system that enables the designers to rapidlydesign and validate modular fixture configuration design.This paper is organized as follows. Section 2 discusses related

research on computer-aided modular fixture design and VRtechnique applied in manufacturing systems. Section 3 presents adetailed description of our VR-basedmodular fixture configurationdesign research. Firstly, the information representation methodto support modular fixture configuration design in VE is given,instead of squeezing all assembly related information into a singlemodel, which uses amulti-viewmodelingmechanism to representthe design and assembly information from three parts. Thisrepresentation method offers an opportunity to organize requiredinformation in a manner that allows efficient retrieval, easymaintenance and transmission over thenetwork. Then, to fulfill therequirements of precise placement and 3D direct manipulation offixture components in virtual space, an efficient constraint-basedmethodology for intuitive and precise 3D manipulation of fixturecomponents in a VR environment is provided. In Section 4 the

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 433

implementation details of the suggested system, as well as therelated obtained results, are discussed. Finally, the work ends withseveral concluding remarks.

2. Related research

We structure the related work into two categories. On the onehand, we recall some related works in the field of CAFD, andon the other hand, we discuss the VR technology applied in themanufacturing system.

2.1. Computer aided modular fixture design

A vast amount of research has been carried out in the area ofcomputer-aided fixture design. In this section, some of theseworkswill be presented.Based on literature, it can be concluded that the development

of CAFD is conducted towards automation and visualization. Basedon the degree of automation, fixture design systems can becategorized into three different types: interactive, semi-automatedand automated systems [2]. Early research works [3] were mainlyfocused on the development of interactive computer-aided fixturedesign systems, which usually provide informative user-interfacesfor fixture designers. Subsequently, many researchers haveaddressed the issue of automating the fixture design task usingvarious design strategies and methodologies. Many analyticalapproaches, such as spatial relationships [4] and kinematicalconstraint analysis [5], have been applied to facilitate the fixturedesign. The use of artificial intelligence techniques aswell as expertsystems in CAFDwas developed in some of the reported works [6].Most of the automated methods merely addressed the first

two stages of fixture design, whereas relatively less study canbe found regarding fixture configuration design. Some previousresearch has made contributions towards developing automatedmodular fixture configuration design method — for example, Baiet al. [7] presented the method of modular fixture elementsmodeling and assembly relationship analysis. In thiswork, a specialkind of modular fixture elements relationship graph (MFEARG)is established to manage the mate relationship between fixtureelements. Based on their earlier work, Ma et al. [8] developed anautomated modular fixture configuration design system which isnamed FIX–DES. Once the surfaces and points, which are to befixed, on the workpiece model are selected, then fixture unitsare automatically generated and will be positioned appropriatelywith the assistance of fixture components assembly relationships.Similar work regarding automated modular fixture configurationdesign can be found in [9]. Although these automated methodsmade academic contributions, most of them are focused on simpleprismatic parts located using the 3-2-1 principle. Therefore, it isdifficult to carry out automated fixture configuration design inpractical applications.In terms of visualization, CAD technology plays a vital role in

both the fixtures’ geometrical modeling and graphical renderingof the design solution. Some previous works on modular fixturespresented methodologies for automated configuration of fixturingpoints. For instance, Trappey et al. [10] used a projective geometryapproach for an autonomous selection of feasible fixturing points.A complete algorithm for synthesizing modular fixtures forpolygon parts with three round locators and one translatingclamp was suggested by Brost and Goldberg [11]. Wu et al.[12,13] expanded the Brost–Goldberg algorithm to 3D objectswith horizontal, vertical or cylindrical surfaces. Using approaches,all the location plan candidates are identified, and automatedmodular fixture planning for a givenworkpiece can only be appliedto cylindrical objects with small height. Much effort has been

made for fixturing 3D objects, yet the object surfaces are piecewiseplanar or cylindrical.As CAD software became widely available and the commercial

CAD market began to grow rapidly, some previous research hasmade contributions towards incorporating fixture design modulesinto commercial CAD systems, for example, see Refs. [14–16].

2.2. Virtual reality technique applied in manufacturing system

VR is a technology to simulate the real world in a virtualcomputer-generated environment. VR technology has maturedenough to warrant serious engineering applications. The integra-tion of this new technologywith software systems for engineering,design and manufacturing will provide a new boost to the field ofcomputer-aided engineering [17].VR has become widely used over the last decades throughout

the product design process. In engineering, VR is widely usedto create digital prototypes to save time and money spent onmanufacturing physical prototypes [18]. Sung and Ou [19] havediscussed many ways in which Virtual Reality Modeling Language(VRML) can be used for the design of manufacturing systems.The authors have developed virtual reality reusable modules forvisualization and have proposed a framework for web basedmanufacturing simulations using virtual reality models.VR technology including a haptic interface has been used for

maintainability analysis of Rolls–Royce aircraft engines weighingmore than 35000 lbs. A haptic system called REVIMA [20]was developed and used for the maintainability analysis. Theauthors have concluded that the virtual haptic interface canbe used directly in industries to address maintainability and toeliminate expensive physical mock-ups. The research applicationsof Antonya et al. [21] demonstrated the practicality, flexibility andversatility of the visualization in a virtual environment in designevaluation and modification.Virtual assembly is one of the applications using VR technology.

It allows a user to perform mechanical assembly tasks in a virtualenvironment, so that the user can evaluate the possibility of assem-bly before those mechanical parts are actually manufactured. Theuser canmove around the virtual environment, use his hand, repre-sented by a virtual hand in a virtual environment, to grip parts andassemble them. This brings the user a great feeling of immersion.This feeling will be enhanced if the interactive dynamic simulationis implemented in the virtual environment. Jayaram et al. [22] havedeveloped a virtual reality based application to facilitate the plan-ning, evaluation and verification of a mechanical assembly system.Ye et al. [23] presented an experiment which examines the poten-tial benefits of using VR environments to support assembly plan-ning. To this end, the assembly-planning performance of subjectsin traditional and VR environments are compared. The obtained re-sults show that a VR environment has the potential to offer a morenatural, powerful, economic, flexible platform than a traditionalengineering environment to support assembly planning. Jayaramet al. [24] have presented case studies in using immersive virtualassembly technology for projects in industry. The case studies se-lected real-life industry situations from industry members of theconsortium and used the immersive virtual assembly technologyto create a meaningful simulation.Unlike fully immersive VR systems which use specialized

interaction devices such as head-mounted displays to create asense of presence for the user within the 3D world, desktopsystems exploit general-purpose hardware for interaction (PC,mouse, keyboard) and although they obviously offer a muchreduced sense of presence in the VE, they are still useful for manyapplication areas [25]. Gupta et al. [26] have developed a desktopsystem called the virtual environment for design assembly (VEDA).Li et al. [27] developed a desktop VR system for maintenance

434 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

training known as V-REALISM. It provides the users with a desktopvirtual environment to practice the disassembly for maintenancefor certain components. Zhou [28] developed a virtual injectionmolding system. This initial prototype systemproves the feasibilityof this design enhancement tool, and can provide a testbed andvaluable information of injection molding that otherwise requirestime-consuming and expensive physical experimentation. Thevirtual environment can also assist in training mold designersand process engineers with machine operation, mold design andmolding behaviors.

2.3. Discussion on related research (Objective of our work)

Fixture design work is a typical experience-based process.Despite the recent research achievements in this field, by offeringcomputerized methods and tools to reduce cost and improveproductivity, there are still some gaps between academic researchand industrial demands. Most intelligent and automated methodsare focused on the fixture planning and fixture verificationstage. Relatively less study can be found regarding the fixtureconfiguration design. Due to the complexity of fixture design,most published comprehensive CAFD systems adopted manualmethods to design and assemble a modular fixture configurationin popular CAD software. Based on the graphic functions of CADpackage, a system was developed to select fixture elements tohold the workpiece for given locating and clamping points on theworkpiece surfaces. However, despite the advanced functionalityof CAD software, none of them offers an intuitive simulation forthe whole fixture process involving the fixture planning, fixtureconfiguration design, and fixture design verification. Current CADand CAE systems run under their own environments without theintegration of the fixture design and fixture analysis. In addition,the assembly operation in CAD software is result-oriented. Thepart model is automatically placed into an assembled positionaccording to the matched features manually specified by theuser. During the assembly process, the assembly path for a givenelement is ignored. There may be interference between elementsand it cannot be found during the fixture construction. Althoughfew static approaches, by using geometric analysis or sweptvolume approach, can detect interference between workpiece andfixture elements or possible interference of moving cutter andfixture components during themachining process, they often needcomplicated computing and are time consuming. In particular, thedynamic interference during the fixture construction cannot bedetected. In summary, a more powerful 3D interface for modularfixture configuration design will be promising.Compared to CAD software, current VR systems provide an

enormous potential for enhancing the visualization of 3D-designdrafts. Based on new navigation techniques, the designer is ableto interact and model in a more intuitive and efficient way.In manufacturing systems, much VR based research has yieldedsignificant achievements. In particular, due to its low cost andportability, desktop VR has been widely applied and got greatsuccess in the area of product design, assembly and maintenance.The great success of desktop VR applied in manufacturing

system inspires us to develop a VR based system for modularfixture configuration design. More importantly, VR can provide amore efficient tool to support fixture configuration design overCAD software. For example, VR offers a more natural interfaceto the user for interacting with fixture elements during structureconception and design. Furthermore, the manipulation of fixturecomponents in VE is direct and process-oriented to match the realsituation, so that interference between fixture components duringassembly or workpiece setup process can be detected and thus beavoided in fixture design phase.By using VR technologies, the research presented in the paper

develops an in-house desktop based, low-cost, independent and

practical modular fixture configuration design system named asIVMFDS. Besides being low cost, familiar to user and easy tointegrate with other CAD/CAM systems, there are other reasonswhy we prefer desktop VR technique in this work. To implementsuch a VR based system, the information representation schemeof modular fixture and a constraint based precise 3Dmanipulationapproach for fixture configuration design in VE is presented.

3. A desktop VR based interactive modular fixture configura-tion design system

3.1. Introduction to the proposed system

The architecture of the IVMFDS system is shown in Fig. 1.It illustrates the three main functional modules of the system:the information management module, virtual design module andvirtual assembly module.The function information management module contains two

major sub functions. The first deals with the loading, storing andprinting of all the data and drawing information in the system. Theother one serves an open interface for integrating with anotherdesired system like Computer Aided Process Planning (CAPP).The virtual design module provides a natural design environ-

ment for convenient and fast operations of fixture configurationdesign. It is mentioned that, in the traditional manual modularfixture design, the designer often selects suitable fixture elementsand puts them together (like ‘‘building blocks’’) to generate afixture structure. Following modification and adjustment, a feasi-ble fixture configuration is finally constructed to meet the fixtur-ing function requirements. However, the suggested virtual designmodule offers users an opportunity to interact with a virtual pro-totype, rather than physical fixture elements, and allows them tobuild a fixture configuration in a realistic way.After fixture configuration design is finished and most consti-

tutive fixture elements are generated, the virtual assembly mod-ule assembles these elements one by one in their appropriatepositions. In this process, joint elements such as bolt and T-key areused to fix assembled elements. By means of intuitive 3D manipu-lation of virtual models, users can interactively perform assemblyoperations, modify fixture structure and check assembly interfer-ence in a realistic way.

3.2. Information representation of modular fixture in VE

3.2.1. A multi-view based assembly modelFor modular fixture design applications, the simulated virtual

environment requires precise geometric representation of thefixture configuration. It is common that the correspondinggeometric objects in VE are represented as polygon modelsto satisfy the requirements of real time display and collisiondetection. However, the polygon model loses the topologyand feature information. Without topological relationships andconstraint information, it is difficult to perform modeling andassembly operation. Therefore, it is necessary to develop asuitable assembly model for representing related informationthroughout the fixture design process. In this paper, a multi-viewassembly model is designed to support modular fixture assemblydesign in a VR environment. Instead of squeezing all assemblyrelated information into a single model, this model describes thedesign and assembly information from three aspects, namely theelement information view, structure/function view and assemblyrelationship view, as shown in Fig. 2. A brief description of thismodel is provided below.(1) The Element information view is focused on the represen-

tation of fixture elements information, such as geometrical data,

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 435

Fig. 1. Architecture of IVMFDS.

Fig. 2. The use of multi-view based fixture assembly model.

physical data, visualization data etc. These parts information areindependent of assemblymodel and are founded on the character-istics of modular fixture and fulfill the requirements of real-timeand distributed sites. The detailed discussion about the modularfixture element information representation will be illustrated inthe Section 3.2.2.(2) The Function/structure view is used to represent the

composite structure and function relationship of the modularfixture component. Function/structure view is defined as thetree structure in which the root node of the tree representsthe assembly product, the intermediate nodes represent thesubassemblies and the leaf nodes represent the single components.Other than the hierarchical relationships, it also captures thefunctional relationships among different parts of the assembly.(3) The Assembly relationship view is focused on the representa-

tion of themating relationships among components. They are usu-ally represented as graphs. In the graphs, the nodes represent thecomponents while the arcs represent the mating relations. There

may be only one or more arcs for each pair of the components. Thearcs store the homogeneous coordinate transformation that spec-ifies the relative position of one component with respect to theother. According to the feature of modular fixture, a kind of As-sembly Relationship Graph (ARG) is defined and used to representthe relationship model.

3.2.2. Fixture element information representationIn VE, a part is only represented by a number of polygon

primitives. In this manner, the topological relationships andparametric information are lost during the translation processof models from CAD to VR systems. This important informationshould be appended to support fixture design and assembly. Inthis section a modeling scheme is presented for fixture elementsrepresentation.Assembly feature of fixture elementThe modular fixture elements are pre-manufactured parts

with standard dimensions. After designing the fixturing scheme,

436 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

Fig. 3. Definition of the assembly feature mark.

suitable standard elements should be selected. Following that,these selected elements are to be assembled in a feasible andeffective manner to configure a fixture system. Consequently, inthe modular fixture design system, only the assembly features ofthe elements need to be considered.In this paper, an assembly feature is defined as a property of

a fixture element providing relevant information of the modularfixture design and assembly/disassembly. The following eightfunction faces are defined as assembly features of fixture elements:supporting faces, supported faces, locating holes, counterboreholes, screw holes, fixing slots, and screw bolts.Because the modular fixture elements are high standard

designed components, in the local coordinate of the element, theposition and orientation of assembly feature is fixed. Therefore, wecan utilizemark to represent the position of assembly feature. Themark is used to calculate the related position of two assembledelements when an assemble operation is executed. The mark isdefined as a point in the local coordinate of the element. The formaldefinition is as follows:Mark:Mar → (Pnt , Vec)Point: Pnt → (x, y, z)Vector: Vec → (vx, vy, vz).The mark definition of plane feature and cylinder feature is

shown in the Fig. 3. For a plane feature, themark is the centric pointof plane. For a cylinder feature, the mark is the centric point of axisof the cylinder. The mark of each assembly feature is defined andstored as a property of the element model. During the assemblyoperation, the position and orientation should be transformed intoa global coordination framework.XML based fixture element information representationAs a fundamental aspect of the CAFD system, fixture element

information representation is crucial to the success of the VRbased modular fixture design system. The element model isnot only described as a data set which contains geometricprimitives, assembly features and other necessary attributes, butalso represented in a manner that allows efficient retrieval,easy maintenance and transmission over the network. ExtensibleMarkup Language (XML) [29], is a simple, very flexible text formatderived from SGML andwhich is beingwidely used as an exchangeformat of data on the Web and elsewhere. XML is not restricted toa fixed number of tags and that XML allows us to define our ownstructure and tags necessary for fixture element representation.As it was previously pointed out, a strategy should be rendered

to compensate the loss of topological information during thetranslation process of models from CAD to VR systems. To thisend, the following kinds of information should be contained infixture elements information model: (1) attribute functions suchas the fixture element type, name and id; (2) physical informationsuch as weight and material; (3) display attributes such as modelcolor, texture for rending and visualization; (4) bounding box ofgeometry model for collision detection; (5) assembly features ofelement model; (6) polygon primitives.

When representing data using XML, first a document typedefinition (DTD) has to be specified. This would govern the datastructure contained by the XML file. Fig. 4 shows the structureof the XML object for fixture element information representation.Tags in XML follow a hierarchical structure. Necessary informationof fixture elements can be organizedwell in a single *.xml file. Fig. 5shows a clamper and its XML file representation.The XML file contains information not only on the vertices

and facets of the element polygonal model used for visualization,but also on assembly features for assembly operation. Besides,the information about the feature such as type, dimension, andother parameters (i.e. the relative position and orientation of thefeature in the element’s local coordinate system) are also containedin the XML file. When one element assembles with another, theinformation about the mated features is retrieved and employedto decide the spatial relationship of the two elements.

3.2.3. Hierarchical structure representationThe hierarchical structure model represents the functional

and compositional relationships among components. Generally,the entire assembly product can be separated into differentfunctional units that are usually taken as subassemblies. Afunctional unit (FU) is a combination of fixture elements such that aconnection between the baseplate and aworkpiece is provided [6].Usually, based on basic structure characteristics, a modular fixturestructure may be divided into three functional units: namely alocating unit, clamping unit, and supporting unit. Themajor task ofthe modular fixture assembly is to select the supporting, locating,clamping and accessory elements to generate the fixture FUs toconnect the workpiece to the baseplate. Consequently, the FUscan be regarded as subassemblies of a modular fixture system.The structure of a modular fixture system can be represented asa hierarchal structure.A scene graph is the most common data structure used to

represent objects in a VE. Objects are represented as nodes inthe scene graph and the relationship between the objects and theenvironment is described by the edges [30]. Also, a scene graph isa hierarchical structure that describes the position of each nodein the environment as well as the dependency of the node withrespect to its parent nodes. As shown in Fig. 6, the data structure ofscene graph can be utilized to represent the function structure of amodular fixture,The scene graph contains information related to the geometry,

material and other physical attributes of a node and the relativedisplacement and orientation with respect to its parent nodes.Simulated operations in the VE can be performed by appropriatelymanipulating the scene graph structure. However, the scene graphdoes not have a mechanism to maintain the state of the objects inthe VE [31].For modular fixture assembly design, a component or element

in the VE needs to possess several physical attributes other thangeometric, location and material data. The properties and theirinterconnectivity are summarized and encapsulated at the node

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 437

Fig. 4. DTD of fixture element information model.

Fig. 5. A clamper and its XML file representation.

Fig. 6. Hierarchical fixture assembly model as part of scene graph.

level in a 4-tuple structure, represented as ‘(M , F , S, X)’. Theseinclude the geometric data, relationships with other objects, statusinformation and other data essential for design and assembly of amodular fixture system in the virtual world.(1)M: defines the mark and state information of an object. The

mark refers to the component ID of an element. State informationrefers to the assembly state of a fixture element or component,which means the element or component is assembled or not.The system assumes that the elements of a sub assembly can bemoved and assembled as a whole only when all of the constitutiveelements are completely assembled.

(2) F : defines the function information of an object. Theinformation includes the function of a FU or the function of a singleelement in FU.(3) S: defines the visualization information and associated

behaviors of an object, which includes the color, texture etc. Thedisplay effect of an object can be changed in VE by modifying its S.(4) X: defines the position information of an object in a

virtual world, which contains the local coordinate frame and itshomogeneous transformation matrix with respect to the globalcoordinate frame. Moving and rotating an object can be realizedthrough changing the X value.

438 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

(a) Face against. (b) Axis fit. (c) Axis align.

Fig. 7. Three common use mating relationships between fixture elements.

3.2.4. Assembly relationship and constraint representationMating relationships have been used to define assembly

relationships between part components in the field of assembly.According to the assembly features summarized above, thereare five types of mating relationships between modular fixtureelements, Namely against, fit, screw fit, across, and T-slot fit,which are illustrated in Fig. 8. Based on thesemating relationships,the possible assembly relationship of any two assembled fixtureelements can be described.Constraint is defined as the explicit related position restriction

between two elements. According to the assembly features andtheir mating relationships, two basic fundamental geometricelements, namely line and plane, are utilized to represent theassembly relationship of fixture elements. As shown in Fig. 7, themate relationship of any two assembly feature can be described asthe constraints of these two fundamental elements. For example,the fit and screw fit can be described as the alignment of two lines.A mark is defined to describe position orientation of an

assembly feature. It is beneficial to model all kinds of constraintsamong fixture elements conveniently. For example, datum part P1which contains face F1 is denoted by the mark Mar 1(Pnt1, Vec1).Also, the mating part P2 which contains face F2 is representedby the mark Mar 2(Pnt2, Vec2). We also set d as the distance ofprojection point of Pnt1 and Pnt2 to Vec1. Consequently, the case of‘‘against of F1 and F2’’ can be described as: d = 0; Vec1 · Vec2 = −1.The assembly relational model contains the information of

constraint relationship and constraint state, which is needed forlocation and motion of fixture elements during the assemblydesign process.One drawback of traditional assembly relational models is that

the mating conditions are modeled at a very rough level. Theyshow the way components mate (component A is fit or againstwith component B). Yet, they do not explain how the componentsmated (which surface of component A is fit or against with whichsurface of component B) [32]. In contrast, in the virtual assemblyapplication it is necessary to model the mating relationshipsexplicitly at the form of feature level.According to the feature of the modular fixture, a kind of ARG

is defined and employed to denote the relationship model. Theformal definition is as follows:

Definition 1. ARG is defined as a 4-tuple g = (V , E, α, β)whereV = {Pi|i = 1, 2, . . . , n} is a finite set of nodes (or components),

Pi represents the fixture element;E = {Mij|i = 1, 2, . . . , n; j = 1, 2, . . . , n} is a finite set of edges

(or component relationships), Mij is a direct arc and representsthe assembly relationship of part Pi and part Pj, moreover, Pi isan assembled component and part Pj is an assembling componentduring the assembly operation;A = {(Di, Ci)|i = 1, 2, . . . , n} is the set of node attributes, Di is

the id of Pi, Ci represents the constraint status of Pi;

B = {Ri|i = 1, 2, . . . ,m} is the set of edge attributes, Ri ={ck|k = 1, 2, . . . , l} is the set of feature mate information, and isstored as link table, ck is defined in Definition 2.α : V → A is a functionwhich associates a set of node attributes

with each node;β : E → B is a functionwhich associates a set of edge attributes

with each edge.

Definition 2. ck = (T , F1, F2, C) represents the information of twomated assembly feature, whereT is the mate type;F1 is the feature of assembling part;F2 is the feature of assembled part;C is the constraint information from the mated feature, which

is represented as allowed motion (degree-of-freedom) DOF.

The advantage of the graph-based structure is that it is moreconvenient to establish a graph for interactions. By adoptingsuch a representation, adding or deleting a node can easilybe done through graphical interactions. The ARG is establishedand maintained during the assembly process. According to therecognized and confirmed assembly relationship, the system addsa relevant arc and related mapping function to the ARG.

3.3. Constraint based precise 3D manipulation approach

Within the virtual design environment it is necessary to providea certain amount of realism within the environment when theuser is performing their fixture configuration task and interactingwith the fixture models. The fundamental function requirementsincludes precise placement and 3D directlymanipulation of fixturecomponents in virtual space.Although VR technology provides users with an intuitive and

immersive 3D interactive interface, it tends to be inaccuratebecause humans have difficulty in performing precise positioningtasks [33]. From the literature reviewed, it can be concluded thatthe most common 3D manipulation approach in the VR systemsare based on haptic feedback, snapping, geometric constraint andknowledge, while among them, the most popular and useful isthe geometric constraint based method, in which objects areaccurately positioned in terms of their geometric constraints. Thekey techniques employed in the constraint based 3Dmanipulationmethod in VE are automatic geometric constraint recognition,constraint solving and constraint based motion navigation.

3.3.1. Automatic geometric constraint recognitionHow to efficiently satisfy the designer’s assembly intention,

and how to automatically and accurately recognize the geometricconstraints between assembling and assembled elements, are thepreconditions of modular fixture virtual assembly design. At thebeginning of each main loop of scene rendering, a relationship

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 439

recognition program, embedded in the locating managementmodule, will check the possible assembly relationship betweenassembling elements and the other assembled elements. This isperformed through geometric constraints recognition in real time.In most of the virtual assembly applications, such as assembly

simulation and assembly planning, the product model is built andassembled in CAD software and imported into VE with a dedicatedinterface. Therefore, the task of constraint recognition is matchingassembly features among established assembly relationships.However, in modular fixture virtual assembly design systems,the assembly relationships are not pre-built and constraintsrecognition should be found from a larger number of candidateassembly features to meet the user’s operation intention. Inthis section, a fuzzy based comprehensive judgment approach isutilized tomatch and evaluate the assembly features of assemblingelement and assembled element. Adopting such an approach leadsto constraints which mostly satisfy the operation intend.Let assembling element be E1 and datum element be E0, when

the user moves E1 close to E0, if there is intersection between thebounding boxes of E1 and E0, the constraint capturing process willnot be carried. The detailed steps are described as follows:Step 1: Construct a set of possible assembly relationships which

should be recognized according to the function and shape of E1, aswell as its relative position with respect to E0.Step 2: Construct possible assembly relationships set A =

{a1, a2, . . . , am}, let ak = (Fi, Fj), where Fi is the feature of E0, themark of Fi after coordinate transformation is Mar i(Pnt i, Vec i). Fj isthe feature of E1, the mark of Fi after coordinate transformationis Mar j(Pnt j, Vec j). Let Pnt iPnt j represent the vector generated byconnecting these two marks, and 〈Vec i, Vec j〉 represent the anglebetween vector Vec i and Vec j.Step 3: Determine the influencing factor set V . Considering the

assembly intent of the user, an influencing factor set is proposedwhich contains the following variables: the position matching v1,orientation matching v2 and number of constrained DOF v3. So theinfluencing factor set is defined as: V = {v1v2, v3}.Step 4: Compute the performance norm for every factor.(1) Position matchingThe position matching of two features could be computed as

following:{Vec k = Pnt iPnt j

σk =∣∣Vec k∣∣ · ∣∣∣sin (π2 − 〈Vec i, Vec k〉)∣∣∣ (1)

where σk — the distance of two features of ak.Let

r1j =√

σj

max(σj)j = 1, 2, . . . ,m. (2)

Thus the position matching of each candidate can be calculatedand hence R1 can be computed.

R1 = (r11, r12, . . . , r1m). (3)

(2) Orientation matchingThe orientation matching of two features can be computed as

follows:Let F1 be the feature on an assembled component, after

transforming let its mark be Mar 1(Pnt1, Vec1), and let F2 be thefeature on an assembling component, and after transforming letits mark beMar 2(Pnt2, Vec2).

β =∣∣sin(〈Vec1, Vec2〉)∣∣ (4)

φ =∣∣cos(〈Vec1, Vec2〉)∣∣ . (5)

If the constraint geometric element type of F1 and F2 isplane–plane or line–line, then r1j = β , and if F1 and F2 is plane–line,then r1j = φ. As a result, the orientation matching of eachcandidate can be calculated and hence R2 can be computed.

R2 = (r21, r22, . . . , r2m). (6)

(3) Number of constrained DOFThe number of constraining DOFs of two features may be

computed as following:

r3j =

√1−

dj6j = 1, 2, . . . ,m (7)

where dj is the number of constrained DOFs following the use of aj.For instance, thematch of two plane features will constrain 3 DOFsand the alignment of an axis with a hole will constrain 4 DOFs.Consequently,we can calculate the number of constrainedDOFs

of each candidate and form R3.

R3 = (r21, r22, . . . , r2m). (8)

Step 5. Construct the judgment matrix R.

R =

[r11 r12 , . . . , r1mr21 r22 , . . . , r2mr31 r32 , . . . , r3m

]= (rij)3×m. (9)

Step 6: Compute and form the weight set.

W = (w1, w2, w3) = (0.3, 0.3, 0.4). (10)

Step 7: Perform computation to find the optimal object.

B = W • R = (b1, b2, b3, . . . , bm). (11)

Get the decision-making set, and select the optimal assemblyrelationship.

bk = min{bj}. (12)

According to the results of the assembly relationship evaluation,if bk ≤ ζ (ζ are the constraint thresholds which are set inaccordance with the tracker accuracy of position and orientation),the corresponding two features will be highlighted and will awaitthe user’s confirmation. If the user cancels this relationship withina given time, the recognized relationship is invalid, otherwise, thisrelationship will be established and the constraint solving will becarried out to adjust the position and orientation of the assemblingcomponent automatically, according to the constraint type.

3.3.2. Constraint solvingOnce the recognized assembly relationship is confirmed, the

assembling component will be transformed to precisely satisfythe newly created geometric constraint. In this process, theposition transformation is restricted by the pre-built constraint ofassembling component. That is, the manipulation of a componentshould ensure that the existing constraints will not be violated.The geometric constraints that applied to the component

restrict its motion in certain directions and can be mapped tothe remaining motion DOFs of this component. Therefore, therepresentation of constraints can be obtained by analyzing andreasoning the DOFs of a component. For modular fixture, themating relationship of any two assembly feature can be describedas the constraints of these two fundamental elements, line andplane. Moreover, the constitutive elements of a function unitare perpendicularly aligned in local unit Coordinate System (CS).Following this, a constraint matrix C is utilized to represent theallowable motions of a component, which is defined as follows:

C =

[Tx Rx AxTy Ry AyTz Rz Az

]. (13)

440 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

(a) Without rotational DOF around special axis. (b) With rotational DOF around special axis.

Fig. 8. CS establishment for constraint based motion navigation.

In Eq. (13), the first column elements Tx, Ty and Tz are thelinear translations along X-, Y -, and Z-axis, respectively, and thesecond column elements Rx, Ry and Rz are the rotations about thecorresponding axes, respectively. The values of these elements inthe matrix are either 0 or 1. Integer 1 indicates that the motionis allowed in the direction along the corresponding axis. Integer0 indicates that the motion is not allowed in the correspondingaxial direction. The third column elements Ax, Ay and Az describewhether the three rotations are about a given axis. The values ofthese elements in the matrix are either 0 or 1.In practical situations, one component often has several

geometric constraints. We can construct the equivalent remainingDOF for every geometric constraint, and then calculate thecomponent’s allowable motion space by DOF reduction [34]. Inmost virtual assembly applications, the DOF analysis and reductionis founded on rule-based methods. Using mathematical matrix C ,the procedure of DOF reduction can be conveniently accomplishedand the allowable motions of an object can be derived.

3.3.3. Constraint analysis in terms of DOFThe objective of motion navigation is transferring 3D motion

data from the 3D input devices into the allowable motions of thecomponent [35]. In this process, the real transformation matrixis calculated according to the theoretical matrix from the trackerin each frame, so that not only the movement of parts meetconstraints but also the adjusted error between real and theoreticalpositions and orientation is minimal [33].By taking the theoretical increment matrix of tracker relative

to its position and orientation in the last frame, denoted asMFOB, as input, the task of motion navigation is calculated usingthe real increment transformation matrix (Mpr ) of the graspedcomponent according to its allowable motions. The details ofmotion navigation procedure are as follows:Step 1: Computing the theoretical increment matrix of data

gloveMth.{MFOB → (T (Ep), R(Ek, θ))Mth → (a · T (Ep), R(Ek, bθ)).

(14)

In Eq. (14), T (Ep) is the translation matrix, R(Ek, θ) is therotational matrix (Ek = (n1, n2, n3) is the rotation axis and θ is theangle about Ek), a is the mapping factor of translation motion and bis the rotation motion factor.Step 2: Establishing DOF CS Cd.As shown in Fig. 8, let assembled component be P1 and

assembling component be P2. Let current function unit CS is C0,and M(C0 → Cg) represent the transform matrix from C0 to Cg .Let the constraint matrix of P2 be C = [cij]3×3. According to C ,if C = Cnull, then this procedure is aborted and Mpr = Mth. Ifneither values of third column elements in C are 1, then Cd = C0

is utilized, as shown in Fig. 10(a). Otherwise, Cd is constructed asdepicted in Fig. 10(b). To this end, let the relevantmating feature ofP2marked as P2(p2, En2), then p2 is the origin point of Cd, and En′2 is Zaxis direction, the direction of X and Y axes are consistent with C0.Step 3: Converting Mth to Cd as M0, and then computing

translation projections and rotation projections of M0 at thedirection of three axes in Cd denoted as (∆x, ∆y, ∆z) and (θx, θy,θz) respectively.Step 4: Translation decomposition by computing the real

translation projection (c11∆x, c12∆y, c13∆z) and constructing thetranslationmatrixMT in Cd. After transforming, the real translationmatrix in global CS can be constructed asMpT .Step 5: Rotation decomposition by computing the real rotation

projections (c12θx, c22θy, c32θz) and constructing the rotationmatrix MR in Cd. After transformation, the real translation matrixin global CS can be constructed asMpR .Step 6: Constructing the real increment transformation matrix

of grasped component based on the real translationmatrixMpT andthe real rotation matrixMpR .

4. System implementation and testing

Based on the key techniques mentioned above, togetherwith other technologies, a prototype system named IVMFDS hasbeen developed. IVMFDS is built upon the Windows platform,WorldToolKit, andVC++/MFCdeveloping environment. The systemconsists of a standard desktop PC, a magnetic tracker, a HeadMounted Display (HMD) and a data glove etc.

4.1. Graphical user interface (GUI) design

According to the system architecture introduced in Section 3.1,IVMFDS consists of three modules: Information Management(IM), Virtual Design Environment (VDE) and Virtual AssemblyEnvironment (VAE). IM is designed so that a familiar userinterface is provided for the designer to conveniently manage theinformation of fixture design process and is obtained from otherCAD/CAM systems. The GUI of IM is designed with reference tothe interface layouts of popular CAD software, which are widelyused by the industry, as shown in Fig. 9. VDE is a user friendlyvirtual assembly design environment, which provides a naturaldesign environment for convenient and fast operations of fixtureconfiguration design. As shown in Fig. 10, the GUI of VDE includes:(1) WIMP based menu utilized to set VR environment parameterssuch as camera, lighting and rendering parameters. (2) Virtualmenu used for fixture elements selection. (3) Virtual toolbarfor some simple operations such as loading and deleting fixtureelements. (4) Virtual hand as a main interaction tool. After thefixture configuration design in VDE is finished, the formal fixtureassembly task, such as assembling, adjusting and planning etc.

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 441

Fig. 9. GUI of information management module.

Fig. 10. GUI of virtual design environment.

is carried out in VAE. Compared to VDE, VAE is a more realisticenvironment in terms of providing the designers with a pseudo-immersive feeling of the environment. Also, it contains moreenvironment models such as workshop, workbench etc.

4.2. Modular fixture configuration design with proposed system

The fundamental requirements of IVMFDS are to generatea fixture configuration by using modular fixture elements forgiven fixturing points on the workpiece surfaces and to place thefixture elements into the correct positions to locate and hold theworkpiece strongly.The process of modular fixture configuration design with

the proposed system is shown in Fig. 11. According to theinput of workpiece model, machining information and technicalrequirements, the user first chooses suitable fixture elements anddesign fixture structure in VDE. In this stage, primary fixtureconfiguration will be constructed. Then detailed assembly andadjustment of fixture structure in VAE can be performed. In thisprocess, the user assembles selected elements, one by one, in theirappropriate positions. Joint and fixed elements such as bolt andT-key are used to fix assembled elements. By means of intuitive3Dmanipulation of virtual models, users can interactively performassembly operations, modify fixture structure and check assemblyinterference in a realistic way.A case study on the modular fixture design for a pump part

(see Fig. 12) is used here to demonstrate the functionality of theIVMFDS. The workpiece is to be machined on a vertical drillingmachine. The machining process includes drilling and boring two

blind holes on the top face. From the results of fixture planning, thelocating faces include the bottom face and two through holes.In VE, the designer can select suitable fixture elements and put

them together to generate a fixture structure just as a ‘‘buildingblocks’’ process. Without physical fixture elements, he/she can trydifferent structure schemes and finally design a feasible fixtureconfiguration to meet the fixturing function requirements. VDEprovides a conceptual design environment to facilitate modularfixture structure layout planning. During such a process, the fixtureelements do not need precise placement, and hence the locatingkeys and fixed elements are not considered. The procedure ofconfiguration design in VDE is shown in Fig. 13.After the fixture configuration design in VDE is finished, the

designer will start VAE for carrying out formal fixture assembly.Fig. 14(a) demonstrates the modular fixture elements layout onthe workbench. In assembly process, locating keys are placed onnecessary positions and fixed elements are utilized to fix theassembled elements. The assembly operation in VAE is shownin Fig. 14(b) and (c). Also, the final designed modular fixtureconfiguration is depicted in Fig. 14(d).

4.3. Test cases and results

Several cases have been conducted to test and verify the per-formance and capabilities of the proposed system for supportingmodular fixture configuration design. Two of these typical casesare presented here. All users are mechanical engineering grad-uates, and they had finished the fixture design course and hadknowledge of fixture design. In addition, they were familiar withthe CAD package (Pro/Engineer wild fire 3.0) and proposed a mod-ular fixture configuration design system.Test case 1: Assembly operation experimentIn this experiment, users were separated into two groups. Each

group had five users.Giving the final fixture configuration scheme (see Fig. 15),

which is amedium-scale fixture assemblywith 83 elements, group1 and group 2 perform an interactive assembly task in CADpackageand the proposed VR system, respectively. Users selected modularfixture element models from the database and assembled theseelements to form the given configuration. We recorded the totalassembly time taken by each user (see Fig. 16) as well as theassembly errors occurring in the test cases. The assembly errorsrefer thewrong assembly features to theuser point upongeometricmodels, which results in reconstructing constraints during theassembly process.Test case 2: Conception structure design experimentIn this experiment, users were separated into three groups.

Each group had four users. Given a workpiece as well as its CADmodel, group 1 were asked to design an initial fixture structure byusing physical elements, while group 2 and group 3 were askedto design a fixture in the CAD package and proposed a VR system,respectively. We recorded the total design time taken by each user(see Fig. 17) as well as the number of design schemes and fixtureelements which were taken in the test cases.The main findings of the study were as follows:(1) During the first study involving a modular fixture assembly

task, the average time of group 1 to finish the assembly task inproposed VR system is 24 min. While for group 2 in CAD package,the average time is 59 min. Moreover, the error frequency duringthe work of group 1 and group 2 is 15 and 30 respectively. In thiscase, users in group 1 spent less time and got less operation errorsthan users in group 2 on the fixture assembly task. These resultsclearly show that our system makes fixture assembly operationmore efficient and intuitive over CAD packages.(2) User shows different performance at three design styles. The

average time of group 1 to construct a fixture configuration for

442 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

Fig. 11. Function model of IVMFDS.

Fig. 12. A pump shell to be machined.

a given workpiece in proposed VR system is 51 min. During thedesign process, on average, the user generated 6 structure schemesand selected 121 fixture elements. However, the correspondingdata of group 2 with CAD package is 74, 3 and 91; the data ofgroup 3 with physical models is 92, 4 and 70. These results clearlyshow that our system is more convenient and efficient to facilitateinteractive modular fixture configuration conception and design.

5. Summary

Owing to the complexity of fixture designs, human contributionin the process of decision making can improve the speed andefficiency of the modular fixture design. VR provides the designera 3D display for convenient and fast navigation and manipulationof the models of the products in the virtual space. In this paper, adesktop VR system for interactive modular fixture configurationdesign known as IVMFDS is developed and the relevant keytechniques are presented. The main contributions of this paper areas follows:(1) A multi-view based modular fixture virtual assembly model

is proposed. Instead of squeezing all assembly related informa-tion into a single model, the model exploits the advantages of hi-erarchical structure model and assembly relationship model. Thesuggested model represents three views which are element infor-mation view, structure/function view and assembly relationshipview.(2) An efficient constraint-based methodology for intuitive and

precise 3D manipulation of fixture components in a VR envi-ronment is offered. To achieve direct manipulation and accuratepositioning of fixture components for interactive assembly, theapproach of constraint recognition based on fuzzy comprehensivejudgment is developed. This approach can catch the assembly planand improve the efficiency of recognition procedure. A constraint

Fig. 13. Fixture structure design in VDE.

G. Peng et al. / Computer-Aided Design 42 (2010) 432–444 443

(a) Components on workbench. (b) A locating element assembling.

(c) A supporting element assembling. (d) Final modular fixture configuration.

Fig. 14. Fixture elements assembly in VAE.

Fig. 15. A test modular fixture assembly.

matrix is utilized to represent and treat the constraint status of thefixture components based on DOF analysis. Moreover, to conductthe assembly operation and realize the final accurate positioning ofcomponents, a constraint-basedmovement navigation approach isdiscussed.Moreover, we have conducted several test cases to test the

performance and effectiveness of the proposed system. The

user study has shown that the MF-VADS worked effectively insupporting modular fixture assembly and configuration design.However, a major limitation of the current system is thatit does not incorporate fixture planning and fixture designverification modules and just supports interactive modular fixtureconfiguration design. This limitation reduces the practicabilityof our proposed system. To conquer this limitation, we plan toextend the function of our proposed system. This can be doneby providing an intelligent decision-making function, such asautomated fixturing points planning and optimizing, accuracy andtolerance analysis, stability and deformation analysis. We alsointend to improve the VR based design environment to assistthe designer by providing more information and guidance duringassembly design. To achieve this, more modular fixture designknowledge and rules should be gathered and integrated intothe proposed system. Finally, we plan to implement a VR basedsimulation module to simulate the fixture setup and machiningprocess. This is to ensure that the designed fixture structure isconvenient for installing and that there is no interference betweenfixture components and cutting tool or machine components.

(a) Recorded total time for fixture assembly. (b) Recorded error frequency for fixture assembly.

Fig. 16. Recorded time and error frequency for fixture assembly.

444 G. Peng et al. / Computer-Aided Design 42 (2010) 432–444

(a) Recorded total time for fixture structure design. (b) Recorded used elements number during design procedure.

Fig. 17. Recorded time and used elements number for fixture structure design.

Acknowledgments

The support of National Natural Science Foundation of China(No. 60775060), Research Fund of Chinese Postdoctoral (No.20070420870) and National Defense Fund (No. 20030119) incarrying out this research is gratefully acknowledged. Sincereappreciation is extended to the reviewers of this paper for theirhelpful comments.

References

[1] Rong Y, Bai Y. Automated generation of modular fixture configuration design.Transactions ASME Journal of Manufacturing Science and Engineering 1997;119:208–19.

[2] Nee AYC, Whybrew K, Senthil kumar A. Advanced fixture design for FMS. UK:Springer; 1995.

[3] Grippo PM, Gandhi MV, Thompson BS. The CAD of modular fixturing systems.International Journal of Advanced Manufacturing Technology 1987;2(2):75–88.

[4] Gandhi MV, Thompson BS. Automated design of modular fixtures for flexiblemanufacturing systems. Journal of Manufacturing Systems 1986;5(4):243–51.

[5] Bausch JJ, Youcef-Toumi K. Computer planningmethods for automated fixturelayout synthesis. Proceedings of Manufacturing International 1990;90(1):225–32.

[6] Kumar AS, Nee AYC, Prombanpong S. Expert fixture-design system for anautomatedmanufacturing environment. Computer-Aided Design 1992;24(4):316–26.

[7] Bai Y, Rong K. Modular fixture element modeling and assembly relationshipanalysis for automated fixture configuration design. Engineering Design &Automation 1998;4(2):147–62.

[8] MaW, Lei Z, Rong Y. FIX-DES: A computer-aidedmodular fixture configurationdesign system. International Journal of Advanced Manufacturing Technology1998;(14):21–32.

[9] Dai JR, Nee AYC, Fuh JYH, et al. An approach to automating modular fixturedesign and assembly. Proceedings of the Institution of Mechanical Engineers,Part B, Journal of Engineering Manufacture 1997;211(7):509–21.

[10] Trappey AJC, Liu CR. Automated fixture configuration using projective geom-etry approach. International Journal of Advanced Manufacturing Technology1997;8:297–304.

[11] Brost RC, Goldberg KY. A complete algorithm for designing planar fixturesusing modular components. IEEE Transactions on Robotics and Automation1996;12(1):31–46.

[12] Wu Y, Rong Y, Ma W, LeClair SR. Automated modular fixture planning:Geometric analysis. Robotics and Computer-Integrated Manufacturing 1998;14(1):1–15.

[13] Wu Y, Rong Y, Ma W, LeClair SR. Automated modular fixture planning:Accuracy clamping and accessibility analyses. Robotics and Computer-Integrated Manufacturing 1998;14(1):17–26.

[14] Kow TS, Kumar AS, Fuh JYH. An integrated approach to collision-freecomputer-aided modular fixture design. International Journal of AdvancedManufacturing Technology 2000;16:233–42.

[15] Kumar S, Fuh JYH, Kow TS. An automated design and assembly of interference-free modular fixture setup. Computer-Aided Design 2000;32:583–96.

[16] Hou JL, Trappey AJC. Computer-aided fixture design system for comprehensivemodular fixtures. International Journal of Production Research 2001;39(16):3703–25.

[17] Jayaram S, Connacher H, Lyons K. Virtual assembly using virtual realitytechniques. Computer-Aided Design 1997;29(8):575–84.

[18] Nwoke B, Nelson D. An overview of computer simulation in manufacturing.Industrial Engineering 1993;25(7):43–57.

[19] Sung W-T, Ou SC. Using virtual reality technologies for manufacturingapplications. International Journal of Computer Applications in Technology2003;17(4):213–9.

[20] Savall J, Borro D, Gil JJ, Matey L. Description of a haptic system for virtualmaintainability in aeronautics. In: International conference on intelligentrobots and systems. 2002.

[21] Csaba Antonya, Doru Talaba. Design evaluation and modification of mechani-cal systems in virtual environments. Virtual Reality 2007;11:275–85.

[22] Jayaram S, Wang Y, Jayaram U, Lyons K, Hart P. VADE: A virtual assemblydesign environment. IEEE Computer Graphics and Applications 1999;19(6):44–50.

[23] Ye N, Banerjee P, Banerjee A, Dech F. Assembly planning in traditional andvirtual environments. IEEE Transactions on Systems, Man and Cybernetics1999;29(4):546–55.

[24] Sankar Jayaram, Uma Jayaram, Young Jun Kim, et al. Industry case studies inthe use of immersive virtual assembly. Virtual Reality 2007;11:217–28.

[25] Sayers H. Desktop virtual environments: A study of navigation and age.Interacting with Computers 2004;16(5):939–56.

[26] Gupta R, Whiney D, Zeltzer D. Prototyping and design for assembly analysisusing multimodal virtual environments. Computer Aided Design 1997;29:585–97.

[27] Li JR, Khoo LP, Tor SB. Desktop virtual reality for maintenance training: Anobject oriented prototype system (V-REALISM). Computers in Industry 2003;52(2):109–25.

[28] Zhou H, Shi S, Ma B. A virtual injection molding system based on numericalsimulation. International Journal of Advanced Manufacturing Technology2008 [Online].

[29] Skonnard A, Gudgin M. Essential XML quick reference: A programmer’sreference to XML, XPath, XSLT, XML Schema, SOAP andmore. 1st ed. Addison-Wesley Pub. Co.; 2001.

[30] Burdea GC, Coiffet P. Virtual reality technology. New Jersey: Wiley; 2003.[31] Banerjee A, Banerjee P. A behavioral scene graph for rule enforcement in

interactive virtual assembly sequence planning. Computer in Industry 2000;42:147–57.

[32] Wang A, Nagi R. Complex assembly variant design in agilemanufacturing, Part1: System architecture and assembly modeling methodology. IIE Transactionson Design and Manufacturing 2005;37:1–15.

[33] Liu Z, Tan J. Constrained behavior manipulation for interactive assemblyin a virtual environment. International Journal of Advanced ManufacturingTechnology 2007;32:797–810.

[34] Turner JU, Subramaniam S, Gupta S. Constraint representation and reductionin assembly modeling and analysis. IEEE Transactions on Robotics andAutomation 1992;8(6):741–50.

[35] Yang RD, Fan XM, Wu DL, et al. Virtual assembly technologies based on con-straint and DOF analysis. Robotics and Computer-Integrated Manufacturing2007;23:447–56.