JZC-22F型繼電器性能檢測機(jī)總體結(jié)構(gòu)與自動進(jìn)、出料機(jī)構(gòu)設(shè)計(jì)【自動檢測機(jī)】

JZC-22F型繼電器性能檢測機(jī)總體結(jié)構(gòu)與自動進(jìn)、出料機(jī)構(gòu)設(shè)計(jì)【自動檢測機(jī)】,自動檢測機(jī),JZC-22F型繼電器性能檢測機(jī)總體結(jié)構(gòu)與自動進(jìn)、出料機(jī)構(gòu)設(shè)計(jì)【自動檢測機(jī)】,jzc,22,繼電器,性能,機(jī)能,檢測,總體,整體,結(jié)構(gòu),自動,機(jī)構(gòu),設(shè)計(jì),自動檢測 文獻(xiàn)綜述 課題題目 ： JZC-22F型繼電器性能檢測機(jī)總體結(jié)構(gòu)與自動進(jìn)、出料機(jī)構(gòu)設(shè)計(jì) 所在學(xué)院： 班 級： 姓 名： 學(xué) 號： 指導(dǎo)教師： 合作導(dǎo)師： 日期： 2014 年 3 月 15 日 1.繼電器的原理以及應(yīng)用 繼電器是一種當(dāng)輸入量（電、磁、聲、光、熱）達(dá)到一定值時(shí)，輸出量將發(fā)生跳躍式變化的自動控制器件[1-5]。通常應(yīng)用于自動控制電路中，它實(shí)際上是用較小的電流去控制較大電流的一種“自動開關(guān)”。故在電路中起著自動調(diào)節(jié)、安全保護(hù)、轉(zhuǎn)換電路等作用[6-8]。 JZC-22F型繼電器是一種固態(tài)繼電器，它的原理是：繼電器是一種兩個(gè)接線端為輸入端，另兩個(gè)接線端為輸出端的四端器件，中間采用隔離器件實(shí)現(xiàn)輸入輸出的電隔離[9-12]。 1.1繼電器的主要檢測參數(shù) 1、額定工作電壓是指繼電器正常工作時(shí)線圈所需要的電壓，也就是控制電路的控制電壓。根據(jù)繼電器的型號不同，可以是交流電壓，也可以是直流電壓。 2、直流電阻是指繼電器中線圈的直流電阻，可以通過萬能表測量[13-15]。 3、吸合電流是指繼電器能夠產(chǎn)生吸合動作的最小電流。在正常使用時(shí)，給定的電流必須略大于吸合電流，這樣繼電器才能穩(wěn)定地工作。而對于線圈所加的工作電壓，一般不要超過額定工作電壓的1.5倍，否則會產(chǎn)生較大的電流而把線圈燒毀。 4、釋放電流是指繼電器產(chǎn)生釋放動作的最大電流。當(dāng)繼電器吸合狀態(tài)的電流減小到一定程度時(shí)，繼電器就會恢復(fù)到未通電的釋放狀態(tài)。這時(shí)的電流遠(yuǎn)遠(yuǎn)小于吸合電流[16-17]。 5、觸點(diǎn)切換電壓和電流是指繼電器允許加載的電壓和電流。它決定了繼電器能控制電壓和電流的大小，使用時(shí)不能超過此值，否則很容易損壞繼電器的觸點(diǎn)。國內(nèi)外長期實(shí)踐證明，約70% 的故障發(fā)生在觸點(diǎn)上，這足見正確選擇和使用繼電器觸點(diǎn)非常重要[18-20]。 2.繼電器自動檢測的研究現(xiàn)狀 長期以來，繼電器由于自身優(yōu)良的控制性能，在各種儀器設(shè)備上得到了廣泛的應(yīng)用，隨著測控技術(shù)的不斷發(fā)展，對它的性能要求也就越來越高。繼電器的性能測試要求能夠準(zhǔn)確、快速地測試?yán)^電器的吸合電壓、釋放電壓、延時(shí)吸合時(shí)間、延時(shí)釋放時(shí)間及各觸點(diǎn)的接觸阻抗等各種參數(shù)。基于以上要求，我們設(shè)計(jì)了一套基于PC的繼電器性能測試系統(tǒng)。它可適用于各種電磁繼電器的性能測試．測試過程全自動進(jìn)行，測試結(jié)果除界面顯示外，還能進(jìn)行數(shù)據(jù)存貯、查詢及打印等。 根據(jù)文獻(xiàn)21，吳何畏設(shè)計(jì)一種繼電器的檢測系統(tǒng)[21]，其中的硬件結(jié)構(gòu)如圖1所示：其中直流供電系統(tǒng)由恒流源、無級調(diào)壓器及啟動繼電器構(gòu)成；接觸電阻測量模塊主要用于測量繼電器常閉及常開觸點(diǎn)的阻抗；調(diào)壓驅(qū)動系統(tǒng)主要用于調(diào)節(jié)輸出控制電壓到所需的要求；分布式采集模塊主要用于傳遞上位機(jī)控制信號，并將現(xiàn)場信號回送至上位機(jī)。系統(tǒng)采用了上位計(jì)算機(jī)與分布式采集模塊相結(jié)合的集散控制方式，屬于典型的PC—BASED架構(gòu)。 圖1.繼電器檢測系統(tǒng)硬件結(jié)構(gòu)圖 他設(shè)計(jì)的繼電器檢測系統(tǒng)采用PC—BASED 系統(tǒng)架構(gòu)， 用集散控制方式及HF2510A 和TSFAL-560電源模塊， 通過I-7000分布式采集模塊和RS485／232接口電路， 實(shí)現(xiàn)了數(shù)據(jù)采集和數(shù)據(jù)傳輸?shù)墓δ?。在組態(tài)王軟件平臺下開發(fā)了監(jiān)控程序．程序基于DDE協(xié)議實(shí)現(xiàn)了對Excel數(shù)據(jù)的訪問，設(shè)計(jì)了歷史數(shù)據(jù)查詢、調(diào)用和打印輸出的控制程序。實(shí)現(xiàn)了對繼電器性能的全自動測試。 他還進(jìn)行了為繼電器檢測系統(tǒng)設(shè)計(jì)了軟件，該系統(tǒng)的上位機(jī)軟件采用組態(tài)軟件實(shí)施控制、顯示與模擬．基于組態(tài)王6．5開發(fā)。通過人機(jī)交互界面，建立計(jì)算機(jī)實(shí)時(shí)測控系統(tǒng)，同時(shí)利用DDE協(xié)議實(shí)現(xiàn)了對Excel數(shù)據(jù)的訪問，設(shè)計(jì)了歷史數(shù)據(jù)查詢、調(diào)用和打印輸出的控制程序．實(shí)現(xiàn)了對繼電器性能的全自動測試。軟件結(jié)構(gòu)如圖2所示。 圖2.繼電器自動檢測系統(tǒng)軟件結(jié)構(gòu)圖 從文獻(xiàn)22中，我們可以看到交流固態(tài)繼電器應(yīng)用。他分析了交流固態(tài)繼電器的結(jié)構(gòu)與工作原理, 闡述了固態(tài)繼電器的特點(diǎn), 并介紹了幾個(gè)交流固態(tài)繼電器在自動控制系統(tǒng)中的應(yīng)用實(shí)例。他指出交流固態(tài)繼電器可分為過零輸出和非過零( 隨機(jī)) 輸出2 種類型, 下面以過零輸出型為例介紹交流固態(tài)繼電器的結(jié)構(gòu)與工作原理。過零輸出型交流固態(tài)繼電器的內(nèi)部電路原理圖如圖3所示。 圖3. 過零輸出型交流固態(tài)繼電器的內(nèi)部電路原理圖 文獻(xiàn)23介紹了溫度繼電器檢測的發(fā)展?fàn)顩r以及對溫度繼電器的檢測[23]。文獻(xiàn)中指出：溫度繼電器因周圍環(huán)境溫度升高或自身通過的電流生熱引起溫升而發(fā)生動作，由于繼電器的接通電阻很小，因此電流熱效應(yīng)引起的溫升也很小，與環(huán)境溫度溫升相比可以忽略不計(jì)，所以一般都是通過控制環(huán)境溫度的變化來實(shí)現(xiàn)溫度繼電器的動作溫度和回復(fù)溫度的檢測[23-25]。 文獻(xiàn)中的作者還指出，部分廠家研制出帶有一定智能化的溫度繼電器檢測設(shè)備的溫度繼電器生產(chǎn)線。把計(jì)算機(jī)合測試系統(tǒng)融為一體，采用計(jì)算機(jī)軟件代替?zhèn)鹘y(tǒng)以其的某些硬件。在這種系統(tǒng)中用計(jì)算機(jī)直接參與測試信號的產(chǎn)生測量特征的解析，即通過計(jì)算機(jī)直接產(chǎn)生測試信號合測試功能。一般是用電阻加熱爐來模擬實(shí)現(xiàn)檢測溫度場以及對溫度場的控制。檢測溫度場以空氣作為傳熱介質(zhì)，空氣熱對流對溫常的分布起主要作用。用大功率風(fēng)機(jī)加速熱對流，使同一水平高度的溫場每一點(diǎn)溫度近似相等[23]。 文獻(xiàn)24中指出力固態(tài)繼電器的電參數(shù)的測試。張炳武利用計(jì)算機(jī)、PLC、各智能儀器和各程控設(shè)備組建一套帶GPIB接口的自動測試系統(tǒng),根據(jù)測試要求,分別編寫PLC的邏輯控制程序和計(jì)算機(jī)的測試程序,從而實(shí)現(xiàn)對固態(tài)繼電器各項(xiàng)電參數(shù)的自動測試。本系統(tǒng)應(yīng)該能為今后研制先進(jìn)的SSR提供可靠的分析和檢測手段,同時(shí)更為生產(chǎn)出高質(zhì)量與高可靠性的軍用SSR提供了技術(shù)保證[24]。 文獻(xiàn)中提到，固態(tài)繼電器的參數(shù)繁多,因所用元器件不同,結(jié)構(gòu)不同,參數(shù)也不盡一致, 下面就是其中電參數(shù)加以說明。 1.輸入?yún)?shù) 控制電壓范圍(輸入電壓范圍):加在輸入端的,可使輸出保持導(dǎo)通狀態(tài)(少數(shù)常閉輸出SSR與此相反)的電壓范圍。 最大輸入電流:最大輸入電壓下輸入電流的最大值,它反映了固態(tài)繼電器對驅(qū)動功率的要求,也可以用給定電壓下的輸入阻抗來表示。 最大導(dǎo)通時(shí)間:從加導(dǎo)通控制信號到繼電器輸出器件完全導(dǎo)通所需的最大時(shí)間。 最大關(guān)斷時(shí)間:從去掉導(dǎo)通控制信號到繼電器輸出器件完全關(guān)斷所需的最大時(shí)間。 輸入端出現(xiàn)的瞬態(tài)干擾,可以使固態(tài)繼電器誤動作,尤其是當(dāng)繼電器響應(yīng)時(shí)間等于或小于噪聲脈沖持續(xù)時(shí)間時(shí),繼電器就會導(dǎo)通,對輸入信號進(jìn)行濾波有助于減少這種現(xiàn)象的發(fā)生。 2.輸出參數(shù) 工作電壓范圍:在這個(gè)電壓范圍內(nèi),固態(tài)繼電器可在輸入信號控制下正常工作。 最大負(fù)載電流:它反映了繼電器的最大穩(wěn)態(tài)負(fù)載能力,它還受到散熱器和環(huán)境溫度的熱限制。 瞬態(tài)電壓:加在固態(tài)繼電器輸出端,保持固態(tài)繼電器斷開狀態(tài),不會使固態(tài)繼電器損壞或產(chǎn)生誤動作的最大允許電壓,超過這個(gè)值固態(tài)繼電器的輸出端就可能導(dǎo)通,當(dāng)電流限制在額定范圍內(nèi)時(shí),固態(tài)繼電器不會因此損壞,瞬態(tài)過程,一般幾秒左右。 電氣系統(tǒng)峰值(非重復(fù)):在標(biāo)稱線路頻率下允許加到輸出部分的一個(gè)全波周期的最大非重復(fù)正弦峰值電壓。通常除規(guī)定該峰值電壓外還給出電壓和時(shí)間的關(guān)系曲線,在浪涌期間或其后,繼電器可能失控,直到輸出器件結(jié)溫下降到低于最大允許值為止。 輸出電壓降:加額定輸入電壓時(shí),繼電器輸出端之間的有效值電壓降。零點(diǎn)交越:對切換交流電壓的固態(tài)繼電器所要求的一種特性,設(shè)計(jì)繼電器具有此特性以使它在串聯(lián)負(fù)載進(jìn)行交流電壓和電流循環(huán)時(shí),只在接近零電壓時(shí)接通,只在接近零負(fù)載電流時(shí)關(guān)斷,而與輸入電壓施加或切除的時(shí)間無關(guān),此設(shè)計(jì)特性對延長繼電器壽命并降低電磁輻射干擾是有益的。 輸出漏電流:以常開觸點(diǎn)為例,輸出漏電流是指在規(guī)定的溫度下,繼電器的輸入端端的最大電壓。電壓指數(shù)上升率:輸出端能承受的不致產(chǎn)生誤動作的開路電壓上加最大關(guān)斷電壓,輸出端加額定電壓時(shí),在輸出端的漏電流。零電壓接通最大值:在開始導(dǎo)通的瞬時(shí),輸出升率。 對繼電器自動化檢測的研究都是集中在了控制系統(tǒng)和控制原理方面，而對自動控制裝置機(jī)械部分的研究就是少之又少了，所以我們應(yīng)該在這個(gè)方面多下工夫。 參考文獻(xiàn) [1]正泰電器股份有限公司．繼電器產(chǎn)品總匯[Z].浙江：正泰電器股份有限公司．2006． [2]錢金川, 金林升. 固態(tài)繼電器簡介[ J] . 機(jī)床電器, 2004( 4 ) : 58-59. 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[24] 張炳武. 固態(tài)繼電器電參數(shù)測試技術(shù)研究和測試系統(tǒng)軟件設(shè)計(jì)[D].2007，合肥工業(yè)大學(xué). ORIGINAL ARTICLE Fast collision detection approach to facilitate interactive modular fixture assembly design in a virtual environment Gaoliang Peng the objects not Int J Adv Manuf Technol (2010) 46:315328 DOI 10.1007/s00170-009-2073-0 G. Peng (*) : X. Hou : T. Jin : X. Zhang School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin, China e-mail: C. Wu School of Management, Harbin Institute of Technology, Harbin, China penetrating into others must be guaranteed. Therefore, a fast interactive collision detection (CD) algorithm is fundamen- tal in such a VR system. However, collision checking for a complex VE is computationally intensive. Researchers have addressed some “universal” algorithms to reduce the computational costs. But these algorithms often need auxiliary data structures and require intensive preprocessing time cost. In addition, the implementation of such algorithm is very complicated. Therefore, based on the well study of modular fixture characteristics and practical requirements, we develop a “special” CD algorithm to keep the associated costs as low as possible for VR-based modular fixture assembly design. The paper is organized as follows. A review of related work of the existing CD algorithms is presented in Section 2. Section 3 gives an overview of our proposed algorithm. In Section 4, we describe the space subdivision model used in our algorithm. Section 5 provides the details about the broad phase of our proposed algorithm, in which irrelevant objects are discarded and a set of objects that can possibly collide are determined. The narrow phase for exact polygon based overlap tests is described in Section 6. Section 7 presents some experimental results of our algorithm, and finally, in Section 8, we give concluding remarks and outline directions for future extensions of this work. 2 Related work During the past few years, a great deal of effort has been made to solve the CD problem for various types of interactive 3D graphics and scenarios. For a workspace filled with n objects, the most obvious problem is the O(n 2 ) problem of detecting collisions between all objects, which is time consuming and not bearable if the number n is large. Thus, some necessary techniques are needed to reduce the computational costs. Generally, a CD algorithm consists of two main steps, namely broad phase and narrow phase 9. The first phase aims to filter out pairs of objects which are impossible to interact and determine which objects in the entire workspace potentially interact. The second phase is to perform a more accurate test to identify collision between those selected object parts in the first phase, moreover if necessary, to find the pairs of contacting primitive geometric elements (polygons), and to calculate the overlapping distance. For a CD algorithm, it is critical to reduce the number of pairs of objects or primitives that need to be checked. Therefore, a number of different techniques have been used to make coarse grain detection, among which space decomposition and bounding volumes is most popular. In space decomposition methods, the environment is subdivided into space grids using hierarchical space subdivision. Objects in the environment are clustered hierarchically according to the regions that they fall into. These objects are then checked for intersection by testing for overlapping grid cells exploiting spatial partitioning methods like Octrees 10, 11, BSP-trees 12, k-d trees 13, etc. Using such decompositions in a hierarchical manner can further speed up the collision detection process but leads to extremely high storage requirements. Bounding volume (BV) approach is used in previous computer graphics algorithms to speed up computation and rendering process. The BVof a geometric object is a simple volume enclosing the object. Typically, BV types are axis- aligned boxes (AABBs) 14, spheres 15, and oriented bounding boxes (OBB) 16. Since AABBs method is simple to compute and allows efficient overlap queries, it is often used in hierarchy, but it also may be a particularly poor approximation of the set that they bound, leaving large “empty corners.” The systems utilizing AABBS include I-COLLIDE 17, Q- COLLIDE 18, and SOLID 19, etc. Bounding sphere is another natural choice to approxi- mate an object as it is particularly simple to test pairs for overlap, and the update for a moving object is trivial. However, spheres are similar to AABBs as they can be poor approximations to the convex hull of contained objects. In comparison, an OBB is a rectangular bounding box at arbitrary orientations in 3D space. In an ideal case, the OBB can be repositioned such that it is able to enclose an object as tightly as possible. In other words, the OBB is the smallest possible bounding box of arbitrary orientation that can enclose the geometry in question. This approach is very good at performing fast rejection tests. A system called RAPID 20 for interference detection based on OBB has been built, which approximates geometry better than AABBs. The shortcomings of OBB-tree against sphere tree lie in its slowness to update and orientation sensitive 9. Most CD-related researches are involved in “universal” algorithms, and few literatures are found to develop CD approach in a special application like virtual assembly. Actually, a fast and interactive collision detection algorithm is fundamental to a virtual assembly environment, which allows designers to move parts or components to perform assembly and disassembly operations. Figueiredo 21 presented a faster algorithm for the broad and narrow phases of the collision detection algorithm of determining precise collisions between surfa- ces of 3D assembly models in virtual prototype environ- ments. The algorithm used the overlapping AABB and the R-tree data structure to improve performance in both the broad and narrow phases of the collision detection. This approach is for such a VE with objects dispersed in the 316 Int J Adv Manuf Technol (2010) 46:315328 space. In addition, the R-tree data structure is very memory intensive. Stephane 22 worked on continuous collision detection methods and constraints to deal with rigid polyhedral objects for desktop virtual prototyping. Whereas such a 4D method is only useful for handling the path of known moving objects. Especially, the algorithm is so computa- tionally intensive that it has to run on high-end computers. Collision detection is a critical problem in multi-axis numerical control (NC) machining with complex machining environments. There has been much previous work on interference detection and avoidance in NC machining simulation. Wang 23 developed a graphics-assisted collision detection approach for multi-axis NC machining. In this method, a combination of machining environment culling and a two-phase collision detection strategy was used. Researches surveyed above provided various efficient techniques to carry out collision detection for polygonal models. However, these popular algorithms aimed at general polygonal models, most of which need expensive pretreatments or large system memory or both of them in order to improve the performance and meet real-time requirements. Therefore, when these algorithms are utilized in desktop VR application system such as modular fixture design, the requirement of real time cannot be well guaranteed. Few CD researches can be found in the area of computer-aided fixture design. Hu 24presentedan algorithm of fast interference checking between the machining tool and fixture units, as well as between fixture units, to replace the visually checked method. Moreover, in Kumars work 25, in order to automate interference-free modular fixture assembly design, the machining interference detection is accomplished through the use of cutter-swept solid based on cutter-swept volume approach. However, these algorithms are only capable of static interference checking and applied in CAD software packages. The research presented in this paper makes a solution to these issues by addressing a “special” collision detection algorithm for VR-based modular fixture design. The proposed algorithm uses the hybrid approach of space decomposition and bounding volume method to get high performance. 3 Algorithm overview 3.1 Requirements for proposed algorithm We aimed to develop a desktop VR-based modular fixture assembly design system, in which the designer can select suitable fixture elements and put them together to generate a fixture structure, like “building blocks.” Without physical fixture elements, he/she can test different structure schemes and finally design a feasible fixture configuration that meets the fixturing function requirements. In order to retain high degree of “reality” in engineering application, there are three main requirements for a CD algorithm to perform modular fixture configuration design: 1. Precise and fast: During the simulation of assembly and disassembly operations, finding precise collisions is an important task for achieving realistic behavior 26. When the user interactively assembles a part or a component, the “flying” object may collide with static models, thus the system must find out the “colliding” event immediately. The interval between two checking points should be near enough to achieve better performance. Otherwise, when objects move very fast, they may appear before checking, which will reduce the immersive feelings. Therefore, the proposed system carries out a CD checking task in each rendering loop of VE. In addition, in modular fixture assembly design process, the designer selects elements and assembles them to right position or disassembles them to change the fixture configuration. Once an element is assembled or disassembled, the “static” environment models are updated. Accordingly, the CD checking model needs restructure. So the preprocess should not take too long; otherwise, the performance of proposed system will be impaired severely for certain “smooth feel” cannot be achieved. 2. Low system requirements: Finding collisions in a 3D environment is time-consuming. In some cases, it can easily consume up to 50% of the total run time 21. However, in modular fixture design workspace, there are some other time-consuming tasks, such as design process control and reasoning, automatic geometric constraints recognition and solving, etc. In spite of the complexity of the 3D virtual prototypes due to thousands of polygons, the designed CD checking procedure must be done in real time with relatively low system resource demands. 3. Low hardware cost: In order to achieve wider engi- neering applications, the proposed modular fixture assembly system is designed to run on common PC like popular CAD commercial software. Although much research has engaged in developing hardware- accelerated CD algorithms, which utilize special graph- ic hardware, like graphics processing unit, to deal with the computing collisions, thus the systems CPU can be freed. Nevertheless, we did not plan to adopt this kind of method and optimize performance only from software implementation. The objective of this research is to develop a CD algorithm Int J Adv Manuf Technol (2010) 46:315328 317 Taking into account all above requirements, unfortunate- ly, these objectives usually are in conflict. To meet the precise demand, we must increase checking frequency which will enormously increase the computational com- plexity and the memory bandwidth requirement. So, how can a balance be reached with regard to these? In other words, how can the utilization of system resources be minimized yet the performance optimized without the help of extra hardware? It is the start point of our algorithm. 3.2 Modular fixture analysis The objective of this research is to develop a CD algorithm for assisting in modular fixture assembly design operations in VE. To simplify the algorithm and to gain high performance, the characteristics of modular fixture should be well studied. 1. Process of modular fixture assembly design: The tasks of modular fixture assembly design are to select the proper fixture elements and assemble them to a configuration one by one according to the designed fixturing plan. Thus, the CD problem in VR-based modular fixture assembly design can be stated as: the intersection checking between one moving object (assembling element or unit) with the static environ- ment objects (assembled elements) at discrete time. 2. Fixture element shape: Modular fixture elements with regular shape can be classified into three types, namely, block, cylinder, and block-cylinder 27. Other compli- cated assembly units can be regarded as compositions of these three meta-elements. It is well known that the OBB is tighter than the AABB and sphere. Moreover, when an object changes its position and orientation in VE, its OBB does not need to rebuild. Therefore, we can construct OBBs of modular fixture elements off- line and store them as attributes of element models. During the assembly design process, such attributes can be retrieved directly; thus, complex work for construct- ing bounding volume in run time can be avoided. 3. Fixture element layout: A modular fixture system often consists of supporting units, locating units, and clamp- ing units. These units lie out on the base plate and provide corresponding functions at certain positions. As Fig. 1 shows, in the projection view parallel to the base plate, the units are arranged in some kind of “regions.” In addition, to meet the height requirement of fixturing point, a unit often utilizes a number of supporting elements severed as blocking up objects. Therefore, at the direction perpendicular to the baseplate, the elements lay out hierarchically. Accordingly, we can decompose the space with regard to elements layout feature. 3.3 Algorithm flowchart According to the above characteristics of modular fixture, the proposed algorithm is designed to decrease the complexity and meet the requirements of VR-based modular fixture assembly design. As Fig. 2 shows, at the preprocessing stage, once an element or component is assembled or disassembled, the Layer-based Projection Model (LPM) is established in terms of OBBs of those assembled elements. Such an LPM is used for the CD checking when a new object is assembled. Just like the traditional CD method, proposed algorithm consists of two steps, namely, broad phase and narrow phase. The broad phase is responsible for filtering pairs of objects that cannot intersect. At this stage, it determines pairs of objects in the same subspace, whose silhouettes in LPM overlap and their OBBs intersect. These pairs of objects are candidates for exact polygon-based collision tests in the next narrow phase. During the broad phase, the (a)default view (b)downtown view Fig. 1 Modular fixture structure 318 Int J Adv Manuf Technol (2010) 46:315328 test may cease at any time if no intersection is found, which helps to reject many noncollision or trivial collision cases. In the narrow phase, the collision detection algorithm will calculate detailed intersection between geometrical meshes of the objects. If no intersection polygons are found, the collide will not occur, and the active object can keep on moving. Otherwise, whenever overlaps are detected, related reactions (for proposed system, it highlights objects and does back-tracking) may arise. 4 Space decomposition for identifying neighboring objects Considering the fact that most regions of the “universe” are occupied by only a few objects or left empty, it means that collision only happens among objects that are close enough. So we can use this phenomenon to filter out most of “far- away” objects. Space decomposition is the common approach to be used for this intention. It first splits the “universe” into cells and then does further collision tests for objects in the same cell. In order to keep generality, most of existing space subdivision approaches are based on a set of polygons. Such a “polygon-oriented” approach is so computationally intensive to deal with large number of polygons. Since standard components are almost with relatively regular shapes, we plan to develop an “object- oriented” space decomposition method. 4.1 Space decomposition model After the baseplate is arranged, the remaining work is to assemble the fixture elements or units onto the baseplate. As the assembling elements or units move to the assembled position, collisions may happen between active object and the assembled elements that have been fixed in the space around the baseplate. Hence, the CD checking process needs start-up only after the active object enters into this space. Firstly, as Fig. 3a shows, we define a valid collision space noted as , which is a cuboid whose bottom face is decided by the baseplate, and its height would change along with the assembling operation. The top of is determined by the vertex coordinates of OBBs. is defined to guarantee that all the assembled elements are inside. After the checking space is identified, we need to decompose the space into a number of cells. How can we organize these cells into proper structure and represent the relevant information to facilitate interaction checking? In literature, some kinds of hierarchical data structure, like R- tree structure 21, have been used to help find neighbors. In complex environment with lots of dispersed objects, this complicated data structure is useful. For modular fixture assembly design, the element models are relatively central- ized, and the number of objects is not so much. Conse- quently, the complex data structure is not needed as constructing such a model is time-consuming. We propose a novel data model to represent partition of the checking space. The model gets the advantages of easy intersection tests and simple information representation. As Fig. 3b shows, the checking space is decomposed into several layers along the axis vertical to the baseplate. Each layer can be represented as a 4-turple L i =h 1 , h 2 , V, B, where h 1 is the start height, h 2 is the end height, V is the grid information of this layer, and B describes the projection of elements OBBs belonging to this layer. For each layer, the stored information is illustrated in Fig. 3c. Easy to overlap checking, we orthogonally project the bounding box onto the x, y axis (convenient for illustration and does not lose universality). Then, with these projections, intervals are formed on each axis for each object. We construct one list for each axis. Each list contains the coordinate value of the endpoints of the interval on the corresponding axis. By comparing the endpoints, the corresponding pair of objects that are in contact may be determined. If the intervals do not overlap, the corresponding two objects are not in contact and can be discarded. Fig. 2 Overview of collision detection algorithm Int J Adv Manuf Technol (2010) 46:315328 319 4.2 Space decomposition model construction The above section gives the representation of our space decomposition model; this section will discuss how to construct and reconstruct this model. Most existing space partition methods decompose an entire space into cells in terms of primitive geometric elements (polygons), by computing the position of each polygon and assigning them into corresponding cells, which are often organized into a hierarchical data structure. Despite the data structure remarkably speeding up the CD checking procedure, the establishment of such structure is a complex process and time-consuming. In a situation that the objects in an environment are uniform or the environment models do not change frequently, the cost for preprocessing may be bearable. However, during the modular fixture virtual assembly process, objects within the checking space are changed with time. Therefore, the space composition model must be rebuilt once a fixture element is assembled. To reduce preprocessing time, we