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┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ 裝 ┊ ┊ ┊ ┊ ┊ 訂 ┊ ┊ ┊ ┊ ┊ 線 ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ 長(zhǎng) 春 大 學(xué) 畢業(yè)設(shè)計(jì)（論文）紙 開題報(bào)告 一、設(shè)計(jì)題目 汽車同步帶精密測(cè)長(zhǎng)機(jī)設(shè)計(jì) 二、課題研究的目的和意義 同步帶是利用齒輪與帶齒輪之間的嚙合來(lái)傳遞運(yùn)動(dòng)和動(dòng)力的，它可實(shí)現(xiàn)無(wú)滑動(dòng)的同步傳動(dòng)及多軸傳動(dòng)。由于其具有傳動(dòng)準(zhǔn)確、適用于高速運(yùn)轉(zhuǎn)、維護(hù)方便、結(jié)構(gòu)緊湊、傳動(dòng)效率高、沖擊性小、速比大、載荷范圍小、噪音小等優(yōu)點(diǎn)，故可以滿足機(jī)械工業(yè)中高速化、自動(dòng)化、精密化和省力化的發(fā)展要求，因而被廣泛應(yīng)用于縫紉機(jī)、汽車、紡織機(jī)械、機(jī)床、辦公機(jī)械以及各種儀器儀表中，而且使用的領(lǐng)域還在日益擴(kuò)大。 同步帶的精度主要是指節(jié)線長(zhǎng)和節(jié)線精度。他的精度將直接影響到所傳遞運(yùn)動(dòng)的精度，從而影響整個(gè)機(jī)器設(shè)備的性能及精度，例如影響打印機(jī)字體的形狀、縫紉機(jī)跳針等。此外同步帶的精度將影響嚙合時(shí)的干涉，從而影響傳動(dòng)帶的使用壽命。 隨著機(jī)械傳動(dòng)發(fā)展，對(duì)同步帶的精度提出了極嚴(yán)格的要求，比如某個(gè)縫紉機(jī)公司引進(jìn)的GC20210高速平紉機(jī)上的250SL075G型同步帶，其節(jié)線長(zhǎng)L為632.19mm，因其工作轉(zhuǎn)速為4000r/min ，且上、下帶輪中心距不可調(diào)，為使帶的工作張力不致太小或太大，該帶的節(jié)線長(zhǎng)極偏差的要求為正負(fù)0.1mm，而同步帶生產(chǎn)中許多因素都會(huì)對(duì)精度造成影響，因此對(duì)要求較高的同步帶每跟都必須進(jìn)行長(zhǎng)度檢測(cè)。作為檢測(cè)批量生產(chǎn)的同步帶的儀器設(shè)備，同步帶測(cè)長(zhǎng)機(jī)的精度必須超過同步帶要求的精度而且必須方便、快速且穩(wěn)定可靠。 三、國(guó)內(nèi)外現(xiàn)狀和發(fā)展趨勢(shì) 同步帶在我國(guó)起步較晚，但發(fā)展較快，已形成生產(chǎn)規(guī)模，但面臨的問題也很多。同步帶為節(jié)能產(chǎn)品，具有良好的經(jīng)濟(jì)效益和社會(huì)效益，為了大力發(fā)展我國(guó)同步帶行業(yè)，一方面要做好宣傳推廣工作，擴(kuò)大同步帶的應(yīng)用范圍;另一方面要進(jìn)一步提高同步帶的質(zhì)量，替代進(jìn)口產(chǎn)品 我國(guó)自改革開放后，傳動(dòng)帶的標(biāo)準(zhǔn)陸續(xù)按國(guó)際標(biāo)準(zhǔn)和歐美標(biāo)準(zhǔn)制定，這些標(biāo)準(zhǔn)長(zhǎng)度是按基準(zhǔn)制和有效制表示的，擯棄了我過沿用幾十年內(nèi)周制，因此 需要專用的測(cè)量工具測(cè)量。我國(guó)在上世紀(jì)80年代中，上海飛機(jī)設(shè)計(jì)所為配合《汽車V帶尺寸》標(biāo)準(zhǔn)的制定開始研制汽車V帶測(cè)長(zhǎng)機(jī)。隨著我國(guó)V帶新標(biāo)準(zhǔn)的實(shí)施，V帶測(cè)長(zhǎng)機(jī)成生產(chǎn)廠家必備的測(cè)量工具。青島橡膠工業(yè)研究所，營(yíng)口實(shí)驗(yàn)機(jī)廠，將都名著材料實(shí)驗(yàn)機(jī)廠均有生產(chǎn)，同步帶測(cè)長(zhǎng)機(jī)精度要求較高，一般采用比較法測(cè)量，無(wú)錫橡膠廠從SCHOLZ引進(jìn)一套同步帶測(cè)長(zhǎng)機(jī)，動(dòng)南大學(xué)為南京汽車制造廠研制過一臺(tái)，青島宜利大公司有生產(chǎn)。 同步帶為彈性嚙合件，需在一定張緊力的條件下實(shí)現(xiàn)傳動(dòng)，為保證同步帶與帶輪良好的嚙合，要求膠帶生產(chǎn)廠對(duì)帶長(zhǎng)進(jìn)行逐條測(cè)量，因此，汽車同步帶測(cè)長(zhǎng)機(jī)是生產(chǎn)必須的檢測(cè)設(shè)備。同步帶測(cè)長(zhǎng)機(jī)是就同步帶的跳動(dòng)誤差和長(zhǎng)度誤差來(lái)判斷同步帶質(zhì)量的測(cè)量設(shè)備，它根據(jù)測(cè)量結(jié)果來(lái)判斷同步帶是否符合相關(guān)的標(biāo)準(zhǔn)要求，以此來(lái)判定是“合格”還是“不合格”，在同步帶生產(chǎn)過程中，該機(jī)是確保各種傳動(dòng)帶產(chǎn)品質(zhì)量、提高產(chǎn)品合格率的必備設(shè)備之一。 目前國(guó)內(nèi)研制的同步帶測(cè)長(zhǎng)機(jī)測(cè)量精度最高達(dá)到，且沒有帶傳動(dòng)的橫向擺動(dòng)量的測(cè)量，2003年汽車同步帶GB12734-2003標(biāo)準(zhǔn)實(shí)施以來(lái)，國(guó)內(nèi)尚沒有測(cè)量精度為的測(cè)長(zhǎng)機(jī)。而日本、法國(guó)等國(guó)家的膠帶生產(chǎn)企業(yè)均有高精度、自動(dòng)化的同步帶測(cè)長(zhǎng)機(jī)、無(wú)錫貝爾特膠帶公司就從德國(guó)SCHOLE公司引進(jìn)了一套同步帶數(shù)控測(cè)長(zhǎng)機(jī)。而且采用光機(jī)電一體化技術(shù)研究帶的動(dòng)態(tài)測(cè)量是目前國(guó)內(nèi)外帶生產(chǎn)技術(shù)的發(fā)展方向。 總之，帶傳動(dòng)在現(xiàn)代機(jī)械傳動(dòng)中占據(jù)著重要的地位。帶傳動(dòng)品種開發(fā)和理論研究、帶傳動(dòng)檢測(cè)裝置和試驗(yàn)設(shè)備、傳動(dòng)帶和帶輪制造設(shè)備和工藝控制技術(shù)等等方面，我國(guó)與工業(yè)發(fā)達(dá)國(guó)家都有相當(dāng)大的差距。我們應(yīng)針對(duì)帶傳動(dòng)行業(yè)發(fā)展現(xiàn)狀，切實(shí)解決一些基本和關(guān)鍵問題，使帶傳動(dòng)技術(shù)真正為滿足各行業(yè)機(jī)械裝備對(duì)帶傳動(dòng)日益增長(zhǎng)的需求和提高質(zhì)量的要求服務(wù)。 四、方案擬定 （1） 測(cè)試臺(tái) 測(cè)試臺(tái)由上臺(tái)面、支撐架、直線導(dǎo)軌組成。支撐架用地腳螺栓牢固地固定在底板上；上臺(tái)面左右裝有稱輪，引導(dǎo)張緊裝置的張緊力；定同步帶輪架固定在直線導(dǎo)軌左端，動(dòng)同步帶輪固定在直線導(dǎo)軌的滑塊上；導(dǎo)軌末端裝有擋鐵。 （2） 中心距測(cè)量裝置 此裝置中光柵尺安裝在測(cè)試臺(tái)上，與直線導(dǎo)軌平行安裝，其動(dòng)頭用連接板與動(dòng)同步帶輪連接，與動(dòng)同步帶輪保持同步。動(dòng)同步帶輪可以在直線導(dǎo)軌上自由移動(dòng)，根據(jù)被測(cè)同步帶長(zhǎng)度確定位置。測(cè)量之前應(yīng)用標(biāo)定裝置標(biāo)定光柵尺，光柵尺讀數(shù)直接由工控機(jī)記錄。 （3）轉(zhuǎn)速測(cè)量裝置 光電轉(zhuǎn)速傳感器安裝在傳感器架上，在電機(jī)聯(lián)軸器上裝有帶孔鋁板，轉(zhuǎn)動(dòng)時(shí)光電傳感器即可記錄轉(zhuǎn)速數(shù)據(jù)，直接輸入工控機(jī)處理。 （4）橫向擺動(dòng)量測(cè)量裝置 激光測(cè)位儀是一種非接觸的測(cè)量?jī)x器。激光測(cè)位儀由測(cè)位儀架安裝在動(dòng)同步帶輪左側(cè)，通過測(cè)位儀架可以在豎直和水平方向進(jìn)行微調(diào)。測(cè)位儀架的長(zhǎng)度保證了測(cè)量位置在距動(dòng)同步帶輪中心125cm位置處。測(cè)量得到的數(shù)據(jù)直接輸入工控機(jī)進(jìn)行處理。 （5）張緊裝置 張緊裝置由重砣和鋼絲繩組成，用于使同步帶張緊。 （6）帶輪 該裝置配有與不同型號(hào)同步帶相配的成套標(biāo)準(zhǔn)帶輪，測(cè)量不同型號(hào)的同步帶時(shí)，可以方便而迅速地更換相應(yīng)的帶輪。 （7）控制系統(tǒng) 控制系統(tǒng)負(fù)責(zé)數(shù)據(jù)的采集、計(jì)算、處理、報(bào)表生成、結(jié)果判斷和動(dòng)作控制。它由PC工控機(jī)、顯示器、打印機(jī)和各外部信號(hào)處理器組成。 測(cè)長(zhǎng)機(jī)結(jié)構(gòu)圖 五、進(jìn)度安排 3月24日——4 月4日： 翻譯科技文獻(xiàn)，寫開題報(bào)告，確定方案。 4月7日—— 4 月11日：設(shè)計(jì)計(jì)算。 4月14日——6 月20日：測(cè)長(zhǎng)機(jī)整體設(shè)計(jì)并畫裝配圖 6月23日——6 月27日：整理說(shuō)明書。 6月30日——7月4日： 評(píng)審、答辯。 六、參考文獻(xiàn) [1] 濮良貴、紀(jì)名剛主編.機(jī)械設(shè)計(jì).北京：高等教育出版社 [2] 邵芳，姚俊紅.我國(guó)汽車傳動(dòng)帶技術(shù)分析與展望.機(jī)械制造42卷第478期.2004.6 [3] Sachio H. Structure and mechanical properties of HNBR/ zinc dimethacrylate [A]polymer Blends "Toward 2000. Kasetsart University,Japan: 1997- 08- 18 [4] Michael E.W. Synchronous belt compounds: the new bench markin dynamic performance[A].ACS RDM[C].Orlando, Florida [5] 吳貽珍.汽車用傳動(dòng)帶技術(shù)進(jìn)展[J].橡膠工業(yè)，1992, 39( 5)299～303 [6] 吳立言，王步流.同步帶傳動(dòng)的受力分析.西北工業(yè)大學(xué)科技資料,1991 [7] 秦書安.帶傳動(dòng)技術(shù)現(xiàn)狀與發(fā)展前景.機(jī)械傳動(dòng).2002,26(4):1～6 [8] 保城武，齒付きべルト，機(jī)械設(shè)計(jì)，27〔1〕,54(1983). [9] 尼曼G,溫特爾H(著).機(jī)械零件(第二卷)[M].余夢(mèng)生(譯).北京:機(jī)械工業(yè)出版社,1989 [10]吳振彪主編.機(jī)電綜合設(shè)計(jì)指導(dǎo).北京：中國(guó)人民大學(xué)出版社 [11]機(jī)械工程手冊(cè)編委會(huì)編.機(jī)械工程手冊(cè)。第2版.北京：機(jī)械工業(yè)出版社，1995 [12]周開勤主編.機(jī)械零件手冊(cè).第四版.北京：高等教育出版社，1994 [13]吳宗澤主編.機(jī)械結(jié)構(gòu)設(shè)計(jì).北京機(jī)械工業(yè)出版社，1988 共 5 頁(yè) 第 5 頁(yè) 序號(hào)（學(xué)號(hào)）： 長(zhǎng) 春 大 學(xué) 畢 業(yè) 設(shè) 計(jì) 開 題 報(bào) 告 汽車同步帶測(cè)長(zhǎng)機(jī)設(shè)計(jì) 姓 名 學(xué) 院 機(jī) 械 工 程 學(xué) 院 專 業(yè) 機(jī)械工程及自動(dòng)化 班 級(jí) 指導(dǎo)教師 教授 2007 年 6 月 20 日 Modelling cloud data for prototype manufacturing Abstract In this paper, the authors have developed a novel method to integrate reverse engineering (RE) and rapid prototyping (RP). Unorganised cloud data are directly sliced and modelled with two-dimensional (2D) cross-sections. Based on such a 2D CAD model, the data points are directly converted into RP slice data and fed to an RP machine for fabricating. In this process, neither a surface model nor a STL file is generated. This is accomplished from the 3D data points in several steps: first, the cloud data are sliced into a number of layers along a user-specified direction. The points in each layer are projected onto a plane. Secondly, the points on each plane are sorted and compressed. Data point smoothing is then carried out using a discrete curvature based method. Thirdly, a local interpolating method is used for adding additional points to the slice-lines having insufficient points. Fourthly, the cross-sections between every two neighbouring planes are created by directly connecting the feature points (FPs) with straight-line segments. Finally, an RP layered file is generated for an SLA machine. The developed methods have been implemented with C/C++ on the Unigraphics platform. Author Keywords: Cloud data; Rapid prototyping; Reverse engineering; Segmentation 1. Introduction Reverse engineering (RE) refers to creating a CAD model from an existing physical object, which can be utilised as a design tool for producing a copy of an object, extracting the design concept of an existing model, or re-engineering an existing part [1]. In RE, a product model designed by the stylist, usually in the form of wood or clay mock-up is first sampled and then the sampled data are transformed to a CAD representation for further fabrication. The shape of the stylist’s model can be rapidly captured by utilising optical non-contact measuring techniques, e.g. laser scanner. This normally produces a large cloud data set that is usually arbitrarily scattered. Approaches to transform a dense unstructured data set to a CAD representation can be classified into two categories: triangular polyhedral mesh based method and segment-and-fit based method [1, 2 and 3]. In the former approach, an initial triangular mesh is constructed to capture the unknown topological structure of the scattered data. Then the mesh is optimised to reduce the redundant vertices and afterwards a curvature-continuous surface is reconstructed based on this structure. Many triangulation techniques can be found in the literature, e.g. Delaunay triangulation algorithm [4 and 5], triangulation based on signed distance function [6] and triangulation based on α-shapes [7]. Triangulation for cloud data is however a computationally inefficient process [6 and 8]. For the second, the cloud data is divided into a suitable patchwork of surface regions to which an appropriate single surface is fitted [9]. Since manually segmenting 3D measured data is a laborious and error-prone process, some researchers have attempted to implement an automatic segmentation algorithm [2, 9 and 10]. Nevertheless, in general, present segmentation algorithms are sensitive, computationally complex or can only be applied to simple topology data [10]. Hence, in recent years, some novel RE approaches take into account a direct manufacturing of cloud data without involving surface reconstruction for more efficient rapid product development (RPD) [8]. However, these algorithms can only be applied to structured point data. In this paper, the authors propose an error-based segmentation approach to arbitrarily scattered cloud data. Our goal is to integrate RE and rapid prototyping (RP) to assist manufacturers and designers in meeting the demands of reduced product development time. This is accomplished in the following steps. First, the cloud data are sliced into a number of layers along a user-specified direction. The points in each layer are projected onto a plane. Secondly, the points on each plane are sorted and compressed. An initial curve for each layer (so-called C-curve) is then generated. Thirdly, a local interpolating method (constructing R-curves using the corresponding points in each layer) is used for adding additional points to the slice-lines having insufficient points. Finally, a layer-based RP model is constructed and directly fed to RP machine for prototype manufacturing. Based on these techniques, experiment results are presented to illustrate the efficacy of the developed approach. 2. Cloud data segmentation In essence, a C-curve is made up of a series of feature-point based planar curves. It is constructed in three steps. First, cloud data is pre-processed through slicing, projecting and sorting to generate initial C-curve. Secondly, the initial C-curve is compressed by removing all the redundant points except feature points (FPs) that represent the original shape information recorded in the data link. Lastly, the C-curve is constructed by linking all the FPs using straight-line segments. In the constructing process of these two curves, the shape accuracy is controlled by several user-specified parameters. 2.1. Data pre-processing The first step towards constructing C-curve is to directly slice cloud data along a user-specified slicing direction and interval. The whole data set is then uniformly sliced into many subsets by computing the projecting errors of the points. Suppose that user-defined slicing direction and a data subset is X={P1,P2,…,Pn}, respectively. The centre of the data set X is calculated by (1) Assume that point OX is the closest to Pc, denote a plane associated with the centre point O and unit normal vector by , we define to be the projecting plane of data set X. The projecting error of point PiX to is then calculated by (2) If ei is greater than the pre-defined shape error, data set X is uniformly re-subdivided into two subsets. This process repeats for all the subsets until all ei meet the demand. After slicing, all the points in the subset are projected onto the corresponding projecting planes and a “cleaning” process is carried out to sort the projected points. The aim of sorting is to set up a topological structure for the planar data as well as remove spurious data such as peaks and duplicate data to construct initial C-curves in the projecting plane. Due to the projected data points in the layer are unorganised and error-filled, it is important to pick up a correct point as the start in the sorting algorithm. The sorting algorithm is based on an estimated oriented tangent vector, which consists of five steps as follows: Estimate the oriented tangent vector of each point.Suppose PiX is a point in the plane, we call k points of X nearest to Pi to be the k-neighbourhood of Pi, and denote this data set with . k is an user-specified parameter used to control the estimating accuracy of the originated tangent vector. As shown in Fig. 1(a), the originated tangent vector of Pi is calculated as (3) where Pc is the centre of determined by Eq. (1). Retrieve the next point of the start point.Any point PiX can be selected as the first start point. Assume that the first start point and its oriented tangent vector is P0, , respectively (Fig. 1(b)), the retrieving algorithm would start with P0 and . When an end point is detected, algorithm goes back to P0 and retrieving resumes in the direction of ?, and stops when the other end point is determined.For each point PiX and its oriented tangent vector , we determine the next point of Pi, Pi+1, by (4) where ρ is the given shape error. Pi+1 is then taken as a new start point and retrieving continues with this point and its oriented tangent vector. Delete the spurious points.In step (2), when the next point of the start point is determined, we define a circle using these two points whose diameter is equal to the distance of the points and delete all the points within the circle. Terminate the sorting algorithm.Steps (1)–(3) form a retrieving cycle. When a cycle is completed, all the retrieved points in the cycle are flagged and linked together to form a C-curve. If all points in the plane are flagged, the algorithm terminates. Otherwise, a new retrieving cycle resumes with an un-flagged point that produces a new C-curve in the plane. The number of C-curves in different projecting planes may be different. (6K) Fig. 1. Data sorting. 2.2. Data compressing Data pre-processing constructs initial C-curves for each projecting plane. However, the data size of the curve is extremely large that could plummet the computational robust and exceed the limited memory storage of the hardware. To resolve this, a feature-point based compressing algorithm is developed to compress redundant points on each plane using parametric cubic polynomial. To obtain a solution for a parametric form of a cubic polynomial curve, there should be at least four points. Hence, for each projecting plane, the C-curve is taken into account only when the corresponding point number is more than 4. Employing a least-square method, the unknown coefficient of the cubic polynomial can be obtained. Since the basic shape information of a planar curve is exhibited by its FPs: corners or high curvature points, we define the parameter values corresponding to the FPs of the approximating curve as follows: The present compressing algorithm is based on the above-mentioned FPs, which consists of the following steps (see Fig. 2): Find all the FPs. Link all the FPs with straight-line segments to generate a polygon. Calculate the distances from the points in the C-curve to the polygon. If the distance is greater than the pre-defined shape error, this point is added as a new FP. Go to step (2). This process repeats until all the points in the curve satisfy that their corresponding distances are within the given shape error. (2K) Fig. 2. Data compressing. All the points except FPs are deleted. The final C-curve is then constructed by connecting all FPs using straight-line segments. 3. Data interpolation After the C-curves are established, the data in the C-curves serve to construct curves across the layers (rows) to form the so-called R-curves. In essence, the goal of construction of R-curve aims to establish a topological structure for points in rows, thus assisting in interpolating new points for C-curves with inadequate points. Take the example shown in Fig. 3(a), the construction of R-curve is based on an estimated tangent plane, which consists of the following steps: Estimate the tangent plane of each point.Suppose point PiX, denote m-neighbourhood of Pi with , and m is a user-specified parameter used to control the estimating accuracy of the tangent plane. The unit normal vector of the tangent plane can be determined by calculating the unit eigenvectors of a 3×3 symmetric matrix A as described as follows: (5) If λi1≥λi2≥λi3 denote the eigenvalues of A associated with unit eigenvectors , respectively, the estimated tangent plane is determined by . Identify the oriented points in rows.Denote C-curve with Ci(z), R-curve with Ri(p), point data set with X and the tangent plane of point PiT(z0) with . Assume that the algorithm commences with projecting plane T(z0), as shown in Fig. 3(b), the oriented point of Pi in rows is determined by searching all the points pX in C-curves using (6) where ρ is the given shape error. If the above inequality is tenable, p is termed as the next/front row point of Pi. Otherwise Pi has no oriented row points. In order to improve the efficiency, only points in n-neighbourhood of projecting plane T(zi) are selected for calculating (n is specified by user). If n is selected along the positive normal of T(zi), the oriented point identified in rows is defined as the positive/next row point of Pi. If n is done along correspondingly negative normal, the identified point is the negative/front point of Pi. In this way, for each point in the C-curve, its two oriented points in rows can be determined. Generate R-curves.Based on the point relationship in rows determined in step (2), generation of R-curve is carried out plane by plane in two directions. In our algorithm, a projecting plane that contains the maximal number of points is chosen as the start position. As show in Fig. 3(b), suppose that the plane is T(z0), we take point P0 as an example. First, along the positive normal direction , the oriented point of P0, P1, is linked as the next row point with P0. Because there is no more rows in this direction, the algorithm returns to P0 and searches for the oriented points along the negative direction . P?1 is thus added into the link as a front row point of P0. Searching continues with P?1 and hereby P?2 is added. The data link P?2→P?1→P0→P1 is an R-curve. R-curves are constructed in this way by retrieving all the points in C-curves (Fig. 3(b)). Interpolate new points.The constructed R-curves are then intersected with every plane. A new point is therefore added to the respective C-curve on a plane if it does not exist before the intersection (Fig. 3(c)).The achieved C-curves are then faired using an algorithm based on discrete curvatures. 4. Construction of RP model Although STL file has been the de facto industrial standard for RP machine, layer-based slice file such as CLI or SLC file format is also acceptable by RP machine. Here, the RP model is constructed based on the faired C-curves using a constant slicing strategy. As shown in Fig. 4, assume that the slicing layer Li(zi) lies between C-curve Ci(zk) and Ci+1(zk′), the corresponding point in Li(zi), Pj(zi), is calculated by (7) where Pm(zk) and Pm′(zk′) are the two nearest points located in Ci(zk) and Ci+1(zk′), respectively. (5K) Fig. 4. Data points in slicing layers and C-curves. When all the points for slicing layers are generated, points in each layer are closed to generate an RP model that is directly sent to an RP machine for fabrication. 5. Application example The algorithm described above has been implemented with C/C++ on HP-C200 workstation in the Unigraphics environment. A case study is presented here to illustrate the efficacy of the algorithm. The case is of a mask, which is composed of four range data patches. The original data cloud contains 104,175 points (see Fig. 5). (4K) Fig. 5. The original data cloud. The slicing direction was given interactively as shown in Fig. 6(a). Based on this direction, the cloud data is processed to construct an RP model. Using a user-specified shape error shape=0.1?mm, the thickness of each layer is chosen as 0.2?mm. After data sorting and compressing, only 16,324 points are kept for modelling (see Fig. 6(b)). It took about 1?h for the algorithm to run on the HP-C200 workstation. The final C-curved model is shown in Fig. 7(a) and the constructed RP model in Fig. 7(b). This model is fed to an SLA RP machine and needs approximate 3?h to complete the fabrication. (18K) Fig. 6. The modelling process. (22K) Fig. 7. The final models. 6. Conclusions In this paper, a new approach to deal with arbitrarily scattered cloud data for RP is presented. In our approach, a layer-based RP model is directly extracted from the cloud data through slicing, projecting, compressing and intersecting. Neither a surface model nor the STL file is generated. The method has been proven effective in dealing with complex surfaces and computational efficient through experiments. However, our approach currently can only handle cloud data that has no holes and lobes. Research on the multi-loops caused by the slicing of cloud data is still under developing. On the other hand, research on setting the slicing direction and other parameters automatically is also underway.