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Analysis of automated modular fixture configuration design system
RONG Yi – ming，LI Jie，MA Wei-dong
（Worcester Polytechnic institute，MA 01609，U. S. A）
Abstract To counter the fixture planning of computer-aided fixture design (CAFD) an automated modular fixture configuration design system is developed. Having fixture surface accessibility analysis as the core, the optimum selection of fixturing surfaces and points on workpiece is fullfilled. Firstly, several basic criteria for evaluating the eligibility of a surface being a preliminary candidate fixturing surface are discussed. Secondly, by applying a discretization technique, an accessibility model of fixturing surfaces is established based on an overall evaluation of the accessibility of discrete points on the surface. Finally, the implementation issue and an analysis/design example are presented.
Key words computer-aided fixture design; fixture planning; fixturing surface
1 INTRODUCTION
Important manufacturing activity in the production cycle. Computer-aided fixture design (CAFD) technique has been developed and become part CAD/CAM integration. The development of CAFD contributes to the reduction manufacturing lead time, optimization of manufacturing operations, and verification of manufacturing process designs. CAFD plays an important role in flexible manufacturing system(FMS) and computer-integrated manufacturing system (CIMS)
Figure one outlines the activities of fixture design in manufacturing systems which basically include three major aspects: setup planning, fixture planning, and fixture configuration design}'}. The objective of setup planning is to determine the number of setups needed, the position and orientation of workpiece in each setup, and the machining surfaces in each setup. Fixture planning is to determine the locating, supporting, and clamping points on workpiece surfaces. The tasks of fixture configuration design is to select fixture components and place them into a final configuration to fulfill the functions of locating and clamping the workpiece. An automated modular fixture configuration design system has been developed where when fixturing surfaces and points are selected on the workpiece model fixture units are automatically generated and placed into position with the assistant of fixture component assembly relationships. In the development of automated fixture planning, it is desired that the fixturing surfaces and positions on workpiece be selected automatically. As shown in Figure2, several factors which attribute influences on fixture planning should be taken in- to consideration, ie., workpiece geometric information and operational information need to be extracted and retrieved， accuracy relationships and surface accessibility of workpiece need to be analyzed, fixturing stability and easiness of workpiece loading/unloading operation need to be verified. In this paper, the research focus is on resolving the problem of fixturing surface accessibility analysis.
2 BASIC REQUIREMENTS ON FIXTURING SURFACES
Fixturing surfaces are the surfaces on workpiece used to locate and clamp the workpiece where functional fixture components (locators and clamps) are in contact with these surface. As the focus of this research is on analyzing the accessibility of fixturing surface on workpiece, first of all, the study is started with the discussion on the basic requirements for a surface on workpiece to be eligible as a preliminary candidate fixturing surface. In automated fixture planning, once the primary locating direction is determined in setup planning, the accessibility property of each candidate fixturing surface should be assessed so as to help the fixture planning fulfill the optimum selection of fixturing surfaces and point distributions. In this research, the accessibility analysis is investigated briefly on the basis of pure geometric information of the workpiece and its surfaces which can be extracted from the CAD solid model. Other information such as surface finish and tolerance are excluded from concern because they are the factors considered in the accuracy analysis of fixture planning.
On a complex workpiece, some surfaces might be obviously ineligible to be the candidate fixturing surfaces and should be filtered out at first. In our current research, only the surfaces which satisfy the following basic requirements can be selected as preliminary candidate fixture surfaces, imachining surfaces,planar surfaces,surfaces with accessible normal directions, and surfaces which are large enough. The main purpose of identifying these requirements is to filtez out those obviously ineligible surfaces on workpiece and assume all re-maining surfaces as preliminary candidate .fixturing surfaces.
2.1 Non-machining Surfaces
In a real fixture design, it is well known that the surfaces to be machined at one setup should not be used as fixturing surfaces and hence are definitely inaccessible to any fixture component Therefore a candidate fixturing surface must be a non-machining surface.
2.2 Planar Surfaces
The fixturing surface types are commonly divided into the planar surface type and the cylindrical surface type. However, the accessibility analysis approach developed in this research is limited to planar surfaces on workpiece, though the method presented may be applicable to cylindrical surfaces. In many cases, planar surfaces are selected as fixturing surfaces with high priority in fixture design.
2.3 Surfaces with Accessible Normal Direction
In most fixtures, the primary locating surfaces is perpendicular to other locating surfaces, which can be defined as the bottom-locating and side-locating form while the common clamping forms are top-clamping and side-clamping. This assumption is especially true when modular fixtures are employed in production. For these locating and clamping forms, a constraint is valid that the side-locating direction n S} and side-clamping direction nsc are perpendicular to the bottom-locating direction n}L, and the top-clampin direction nTC is negative to the bottom-locating direction, and nsc are all normalized vectors and could be regarded as the accessible directions in one setup. Generally, nBL is always set equal to the primary locating direction which is obtained from setup planning. Unlike curved surfaces, a planar surface on workpiece has a unique normal direction, which is written as n.r. If n.t is not coincident with any accessible directions mentioned above, the surface is regarded inaccessible to fixture components and ineligible to be the candidate fuxturing suface. In another word, the fixturing surface should have an accessible normal direction.
2.4 Surfaces Which are Large Enough
It is a common sense of fixture design that the surfaces with too small size or a too slim shape are also inelegible to be the candidate fixutring surface. To roughly determine whether the size of a surface is large enough for fixturing, a simple rule can be applied. The eule states that a surface is eligible in size if the smaller edge length of its bounding rectangle is bigger than a threshold lT. The value of lT is set based on the sized of fixture components used in fixture de-sign, which can be specified and modified by user.
After filtering out apparently ineligible surfaces according to above requirements, the remaining surfaces on the workpiece can be regarded as the preliminary candidates of fixturing surface and their accessibility properties needs to be evaluated.
3 ACCESSIBILITY ANALYSIS
Fixturing surface accessibility is a vague concept, which is associated with the fixture components used in fixture design. To determine accessible to a regular fixture component whether a candidate fuxturing surface of workpiece is and figure out a numerical value to represent the corre.
A. Geometry of the fixturing surface which contains the information of surface area and shape
B .Possible obsturctive workpiece geometry along the normal direction of fixturing surface or around the geometric region of fixturing surface.
C. The size and shape of functional fixture components.
Factor A merely refers to the geometric representation of the fixturing suface. In a feasible fixture design, the selected fixturing points usually locate inside the region of fixturing surface and the contact area between this region and the fixture component should be over half of the area of relevant functional surface of the fixture component. In fact, the accessiblility analysis result should reflect the real effective accessible area of the fixturing surface especially when there exists obstructive workpiece geometry along the normal direction of fixturing surface or around the geometric region of fixturing surface.
Factor B also greatly affects the actual accessibility of the fixturing surface because possible obsturctive workpiece geometry along the normal direction of fixturing surface or around the geometric region of the fixturing surface may block the approaching of the fixture component to fixturing surface in some sub-areas of suface region and hence lead to a decrease of the effective accessible area. For a workpiece as shown in Figure4, even though the face F, is large enough in size and not complex in shape, its accessibility to a regular fixture component reduces a lot because of the inherent obstructive geometry of workpiece.
It is obvious that the accessibility analysis can not be made without considering the functional sizes and features of fixture components. To obtain a more accurate evaluation of accessibility to guide the later fixture configuration design, factor must be involved into the comprehensive analysis. However, in the real circumstance, before the fixture configuration design is finished, the fixture component selected from the library is unknown at the stage of fixture planning. To circumvent this problem, a least accessing unit size, T, is applied to represent t卜e minimum functional size of fixture components, which can be specified and modified by user. It implies that if a fixturing suface is accessible, at least a fixture component with the functionally bounded surface size of Tx T can be placed in contact with the surface.
To establish the accessibility model for a fixturing surface, several basic facts of evaluating the property of the accessibility are considered.
1)With the same shape and no obstruction along/around the surface by the workpiece, the surface with larger area will have a higher accessibility value.
2) With the same area and no obstruction, the surface with simple shape complexity will have a higher accessibility value.
3) With the same area and same shape, the surface with less obstruction along or around it will have higher value.
In complex gion. It practical accessibility situations, it is very possible that the planar surface of the workpiece has a shape and fully/partially obstruction along its normal direction or around its geometric reis thus required tinned above date surface that a that the accessibility model should reasonably comparable accessibility comprehensively reflect the facts men- value can be applied to every the workpiece no matter how complex the grometry of the surface might can be.
A discretization modeling method is preferred since it is generic in principle and the algorithm is easy to implement on computer. The methodology is made up of three steps: 1)The surface is sampled into a set of discrete point, 2) Both individual and neighbor related accessibility of each sample point is assessed, and 3) The overall accessibility of the surface is evaluated based on the results of all sample points.
3.1 Surface Discretization
As the accessibility analysis is prior to the fixture planning, the accessibility model between an arbitrary planar surface and fixture component surface is difficult to be established if the fixturing point is undetermined. Before the final position of workpiece on the baseplate is settled down, the possible candidate fixturing points on a planar surface may be enormous in number and hard to handle by a continuous model. Thus in our approach, the surface is sampled into grid-arrayed discrete points with equal interval length T. In order to make the sampling algorithm generic, the outer-bounding rectangle of the surface is used as the sampling region instead of the surface region itself. When a certain set of fixture components are used in fixture design, T can be reasonably selected in terms of the smallest functional surface size of fixture components
The outer-bounding rectangle of a planar surface can succinctly information of the exterior shape limitations, and also is very helpful for provide the geometric restraining the sampling region and enabling the sampling algorithm more generic. The rule for extracting the outer bounding rectangle is very simple. For a bottom-locating/top-clamping surface which normal direction ns is identical/negative to two edges of the outer-bounding rectangle must be paralled to X axis and two other edges parallel to Y axis since the bottom-locating direction is identical to the negative vector of Z axis in the workpiece coordinate system, as illustrated in Figure. For a side-locating/clamping surface where ns__n}}, there must be two edges parallel to Z axis, while the other two edges should be parallel to the cross product of ns and nBL, as shown in Figure Sb. In such a way the surface can be sampled into a set of discrete points within the outer-bounding rectangle, as shown in Figure 6. Some points are sampled outside the outer-bounding rectangle. In this approach, these points are not exorbitant because they may be useful to check the possible obstructions around the fixturing surface.
3.2 Point Accessibility (PA) of Sample Fixturing Point
In our model, the surface accessibility is a statistical value based on the Point Accessibility(PA) of every valid sample point. PA consists of two parts: the point Self Individual Accessibility (STA) and the point Neighbor Related Accessibility (NRA). The SIA is mainly corresponding to the isolated accessibility of the fixturing point while the NRA reflects the extended accessibility of the fixturing point. A sample point cab be regarded valid if it is tested to be at least not inaccessible to a fixture component with a functional surface size T x T. The definitions and calculation methods of SIA and NRA are given below.
SIA of a virtual sample point is defined on the basis of three attribute tags which are separately assigned by s, representing the position status of a sample point on the surface, representing the obstruction status of the surface in the normal direction at the sample point, ands, representing the contact area matching extent in the text area.The tag of s, is used to indicate whether the square tset grid with a center at current sample.
淺析CAFD中的自動裝夾規(guī)劃系統(tǒng)
融亦鳴， 李杰， 馬衛(wèi)東
（伍士德理工學(xué)院，美國 01609）
摘要 針對計(jì)算機(jī)輔助夾具設(shè)計(jì)(CAFD)中裝夾規(guī)劃問題，開發(fā)了自動裝夾規(guī)劃系統(tǒng)，并以工件裝夾表面的影響性分析為核心，完成工件上裝夾表面及點(diǎn)的優(yōu)化選擇:討論了幾個(gè)用以評佑候選裝夾表面的適合性的要點(diǎn)；利用離散技術(shù)，基于所有表面離散點(diǎn)影響性的評佑，建立了裝夾表面影響性模型；并給出了系統(tǒng)運(yùn)行要。汽和分析設(shè)計(jì)實(shí)例。
關(guān)鍵詞 計(jì)算機(jī)輔助夾具設(shè)計(jì)；裝夾規(guī)劃；裝夾表面
1. 簡介
生產(chǎn)制造工藝活動在生產(chǎn)周期中很重要。計(jì)算機(jī)輔助夾具設(shè)計(jì)工藝已經(jīng)發(fā)展起來并且成為CAD/CAM集成中的一部分。計(jì)算機(jī)輔助夾具設(shè)計(jì)的發(fā)展主要有助于減少機(jī)械加工的時(shí)間和產(chǎn)生最佳的機(jī)械制造方法，還有驗(yàn)證最佳的制造工藝設(shè)計(jì)。計(jì)算機(jī)輔助夾具設(shè)計(jì)在柔性制造系統(tǒng)中和計(jì)算機(jī)集成制造系統(tǒng)起著很重要的作用。設(shè)備的設(shè)計(jì)在機(jī)械加工系統(tǒng)中，計(jì)算出主程序數(shù)據(jù)主要包括下面三方面：客觀的裝備設(shè)計(jì)主要決定于零件的需求，工件的定位分析，每個(gè)零件的表面粗糙度。夾具的設(shè)計(jì)主要取決于工件的定位方式，支撐方式，夾緊位置及工件的表面情況。夾具結(jié)構(gòu)的設(shè)備選取和安裝設(shè)計(jì)主要取決于工件的定位和夾緊方式。自動化的模塊夾具結(jié)構(gòu)設(shè)計(jì)系統(tǒng)已經(jīng)發(fā)展到設(shè)備表面和位置能隨工件的變化而變化。夾具單位自動生成和放到正確的位置和輔助夾具有很緊密的關(guān)系。在自動夾具設(shè)計(jì)發(fā)展中，夾具的表面和位置關(guān)于工件表面需要自動化。工程師必須考慮到好多影響夾具設(shè)計(jì)因素，如工件的表面幾何形狀，加工時(shí)候的震動等因素。準(zhǔn)確關(guān)系和工件表面粗糙度的分析。夾具的穩(wěn)定性和工件夾裝方式的簡單可靠都必須驗(yàn)證。在這篇文章中，就是研究關(guān)于自動夾具裝夾表面影響的。
很少能找到相應(yīng)的文學(xué)報(bào)告。為了工件的裝夾方式和驗(yàn)證夾具的設(shè)計(jì)，一種分析方法已經(jīng)產(chǎn)生來驗(yàn)證工件安裝在夾具上和工件在夾具上的拆卸的容易度。一種從不同角度的方式用來評價(jià)夾具設(shè)計(jì)裝夾表面影響性。它限制于一個(gè)簡單的表面影響性例子。
夾具可包括兩方面：夾具屋面的易用性和工件裝卸易用性。前者是一種在混合的設(shè)計(jì)中緩解了表面性質(zhì)的評估程度，如下，在表面放置一個(gè)夾具元件(定位或夾子)是很容易的。con- tact表面是一個(gè)非常重要的選擇標(biāo)準(zhǔn)的固定準(zhǔn)備表面。后者是用來判定當(dāng)夾具被設(shè)計(jì)和建造好了，一個(gè)工件是否能容易得放進(jìn)去。迄今為止，在文獻(xiàn)中還沒有找到一種廣泛應(yīng)用的夾具可分析方法。在這篇文章中， 提出了一個(gè)準(zhǔn)確評估夾具可表面的方法。這種方法只能用在那些經(jīng)常應(yīng)用的夾具表面。第二部分，討論了一些夾具表面的基本要求。第三部分，提出了一個(gè)廣泛接受的夾具表面。一個(gè)離散化造型方法用來判定分析夾具表面發(fā)展的實(shí)施性問題和分布特性。最后，一個(gè)分析的例子被提出來了。
2.對夾具表面的基本要求
夾具表面是在工件定位和夾具工件時(shí)夾具元件(定位器的功能及夾子)所接觸的這些表面。本研究的焦點(diǎn)是分析夾具的設(shè)計(jì)，卡具表面上的工件，首先，文章以工件表面被初步評定為“合格候選人”的夾具的表面的基本要求開始的，主要定位的方向在設(shè)置的規(guī)劃中決定了。這些被評定為“合格候選人”的夾具表面的容易得到的性質(zhì)應(yīng)該用來作為評定滿足夾具表面和點(diǎn)分布的最佳選擇。在這項(xiàng)研究中，被接受的分析是在工件的簡要純幾何信息基礎(chǔ)上的簡要考察和從CAD模型中被提取的表面。另外的信息例如表面的光潔和公差是不用考慮的，因?yàn)樗鼈兪亲鳛榫确治鰥A具的計(jì)劃要考慮在內(nèi)的因素。
在一個(gè)復(fù)雜的工件，一些表面明顯的不合格去成為工件表面候選應(yīng)首先被去除。在我們最近的研究中，只有那些符合基本要求的表面能夠選作最初的候選表面:1、未加工的表面；2、平面表面；3、接近正常方向的表面；4、足夠大的表面。識別這些要求的主要目的，挑選出那有些明顯的資質(zhì)的工件表面并且假象所有的表面作為初步的候選人夾具的表面。
2.1未加工的表面
在真正的夾具設(shè)計(jì)中，那些在裝備中加工過的表面不能作為夾具表面是眾所周知的，因此絕對無法應(yīng)用于任何夾具元件。因此，一個(gè)合格的夾具表面必須是一個(gè)未加工的夾具表面。
2.2平面表面
夾具表面的模型備分為平面表面類型和圓柱體表面類型。然而，研究中接受的類型只有平面表面類型。不過這種放發(fā)對于圓柱體表面類型還是適用的。在一些方案中，平面表面類型選作夾具表面在夾具設(shè)計(jì)中帶有高優(yōu)越性。
2.3接近正常方向的表面
在眾多的設(shè)備中， 主要定位表面與定位表面是相垂直的。定位表面是那些底和邊被定位的定義。通常的夾緊形式是頂夾緊和變夾緊。當(dāng)模塊化的夾具被雇傭來生產(chǎn)時(shí)，這些設(shè)想是尤其正確的。對于那些夾緊和定位形式，一個(gè)人約束條件是有效的，邊定位和邊夾緊的方向垂直于底定位的方向，頂夾緊的方向與底定位的方向是相對的。國家安全委員會規(guī)定所有的歸一化向量并且能夠作為一種設(shè)備的可接受的方向。一般的，NBL總是設(shè)為主要的定位方向。不像彎曲的表面，平面表面有獨(dú)一無二的正規(guī)方向，稱為nr。如果nr與前面提到的那些被認(rèn)定接受的方向不相符和，這些表面就不能成為合格的候選夾具表面。換句話說，夾具表面應(yīng)該有一個(gè)被普遍接受的方向。
2.4足夠大的表面
那些太小的和形狀太細(xì)長的表面是不能作為夾具表面候選是夾具設(shè)計(jì)的常識。粗略估計(jì)一下這個(gè)表面是否足夠大去做為一個(gè)夾具表面，一個(gè)簡單的規(guī)則就出來了。這個(gè)規(guī)則表明了，表面的邊框的邊緣長度比入口門檻大那它在形狀方面是合格的。 IT 的價(jià)值是建立在夾具設(shè)計(jì)的被使用者指定和修改的夾具零元件上的。根據(jù)前面的要求過濾顯然無資格的表面之后，這些剩余的工件表面成為初步的合格的夾具表面。并且它們的那些容易得到的性質(zhì)需要被評價(jià)。
3.表面影響性分析
自動夾具設(shè)計(jì)裝夾表面影響性是一個(gè)模糊的理論,它與用于設(shè)計(jì)固定裝置的固定裝置組成成分緊密相關(guān)。要確定某普通固定裝置的組成成分是否可行,要看該備選零件的表面情況并計(jì)算出表面影響性值。以下幾家公司設(shè)計(jì)情況如下：
A是包含裝置表面面積和形狀方面信息的固定裝置表面的幾何圖；
B可能的圍繞固定裝置表面普通方向或表面周邊幾何區(qū)域的阻礙性零件幾何圖；
C有效固定裝置組成成分的大小和形狀。
公司A僅僅考慮到該固定裝置表面的幾何再現(xiàn)圖。在一個(gè)可行的固定裝置設(shè)計(jì)里,被選固定裝置點(diǎn)通常安裝在固定裝置的內(nèi)部區(qū)域,接觸區(qū)在該區(qū)域之間,該固定裝置組成成分應(yīng)該在該裝置相關(guān)作用表面的半上方。實(shí)際上,影響性分析的結(jié)果應(yīng)該能反映固定裝置表面的真正有效接觸區(qū),尤其是當(dāng)存在沿著該裝置表面普通方向或表面周邊區(qū)域的阻礙性零件幾何圖時(shí)。公司B也從很大程度上考慮到了固定裝置表面的實(shí)際影響性。因?yàn)檠刂撗b置表面普通方向或表面周邊區(qū)域的可能性的阻礙性零件幾何圖很可能阻礙固定裝置表面的一些次要區(qū)域的固定裝置組成成分接觸裝置表面,從而導(dǎo)致有效接觸區(qū)的減少。對于一個(gè)像數(shù)據(jù)4所展現(xiàn)的零件,盡管F面足夠大,并且形狀也不復(fù)雜,但由于零件本身的幾何結(jié)構(gòu)障礙,它與一般固定裝置組成成分的結(jié)合能力大大降低了。很明顯,表面影響性分析不可不考慮作用尺寸和固定裝置組成成分的特征。為了獲得一個(gè)更準(zhǔn)確的表面影響性評估從而更好的指導(dǎo)接下來的固定裝置結(jié)構(gòu)設(shè)計(jì),公司必須要進(jìn)行綜合性分析。然而,實(shí)際情況下,在固定裝置結(jié)構(gòu)設(shè)計(jì)圖完成之前,從庫存里選出來的固定裝置組成成分在裝置設(shè)計(jì)過程中是不知道的。為了避免這個(gè)問題,至少要通過組合尺寸,T是用來代替固定裝置組成成分的最小作用尺寸,它能被使用者特殊化和修改,它暗含如果一個(gè)固定裝置表面是可接受的,至少固定裝置組成成分和相關(guān)的作用表面要是TX，T能被相關(guān)表面確定。
要建立一個(gè)固定裝置表面影響性模型，要適當(dāng)?shù)乜紤]以下幾個(gè)基本的評估事實(shí):
1)同樣的形狀，零件表面的周邊沒有阻礙，更大面積的表面將會有更好的接觸性
2)同樣的面積且無周邊阻礙,簡單形狀的表面將會有更好的接觸性。
3)同樣的面積和形狀，表面周邊的阻礙越少，接觸性越高。
?? ? 在復(fù)雜的祗園，事實(shí)很可能是，平面工件有形狀和完全或部分阻力沿其正常的方向或繞著它的幾何形狀，從而要求上述日期必須表面鍍錫。這種適當(dāng)?shù)哪Ｐ蛻?yīng)該合理可比無障礙地全面反映人的需求,它可以適用于每個(gè)工件，無論多么復(fù)雜的金屬扣眼表面都有可能。
阿離散建模方法是首選，因?yàn)樗且话阍瓌t而且該算法容易在計(jì)算機(jī)上實(shí)現(xiàn)。這種方法包括三個(gè)步驟：1）表面取樣到一套離散點(diǎn)；2）對單獨(dú)和易于關(guān)聯(lián)的相鄰樣點(diǎn)進(jìn)行評估；3）無障礙環(huán)境的表面總體評價(jià)的結(jié)果基于所有采樣點(diǎn)。
3.1 表面離散
作為輔助分析之前的夾具規(guī)劃，如果夾具點(diǎn)未定，無障礙模式之間的任意平面和夾具元件表面是很難確定。在最終定位前，工件基板是固定下來的，可能的表面候選裝夾點(diǎn)可能是數(shù)量巨大的而且難以用連續(xù)模型處理。因此，我們的做法是在表面取樣到網(wǎng)格離散點(diǎn)一排平等間隔長度T。為了使采樣算法通用，外一包圍矩形表面被用作抽樣區(qū)域，而不是表面區(qū)域本身。當(dāng)某一套夾具元件用于夾具設(shè)計(jì)，T可以合理地從最小的功能表面尺寸中選擇夾具元件。
外一包圍矩形平面是非常有益的幾何約束提供的抽樣地區(qū)，它可以簡明扼要地提供外部形狀的限制信息，使采樣算法更加地通用。提取外包圍矩形的規(guī)則是非常簡單的。由于以自下而上定位/頂端夾緊表面法線方向是一致的納秒/負(fù)向兩個(gè)邊緣外一包圍矩形，所以它必須與X軸平行，而底部定位的方向是一致的消極載體的Z軸的工件坐標(biāo)系，因此其他兩個(gè)邊與Y軸平行，如圖所示。對于一方一定位/夾緊表面下ns上n，必須有兩個(gè)邊與Z軸平行，而其他兩個(gè)邊應(yīng)平行于向量積的NS和NBL，以這種方式可以在表面取樣到一組離散點(diǎn)的外一包圍矩形，采樣的某些點(diǎn)在外一包圍矩形之外。在此方法中，這些問題并不過分，因?yàn)樗麄兛赡苡兄跈z查裝夾表面周圍可能的障礙物。
3.2 點(diǎn)無障礙（ PA ）的樣品夾具點(diǎn)
在我們的模型中，表面是一個(gè)無障礙的統(tǒng)計(jì)值點(diǎn)基于無障礙（ PA ）的每一個(gè)有效的采樣點(diǎn)。PA由兩部分組成：孤立的點(diǎn)自我無障礙（ STA ）和點(diǎn)周圍相關(guān)無障礙（NRA）。SIA主要是對應(yīng)于孤立的無障礙的裝夾百分點(diǎn)，而NRA反映了延長無障礙的裝夾點(diǎn)。樣本點(diǎn)駕駛室被視為有效，如果是測試，至少不會無法獲得功能表面大小為T x T的固定元件。SIA和NRA的定義和計(jì)算方法如下。
新航虛擬采樣點(diǎn)的定義的基礎(chǔ)上，三個(gè)屬性標(biāo)記分別指定由S ，代表的立場地位的采樣點(diǎn)在表面上，代表梗阻地位表面的法線方向的采樣點(diǎn)，阿富汗國家發(fā)展戰(zhàn)略，代表接觸面積匹配程度的文本區(qū)。該標(biāo)記的S ，是用來說明是否平方米測試電網(wǎng)的中心，目前的樣本榮坐標(biāo)白元組合夾具元建模和裝配關(guān)系分析自動夾具配置設(shè)計(jì)。