外文翻譯--在獨自領(lǐng)域最佳多功能夾具布置的設(shè)計

1、<p><b>　　外文翻譯</b></p><p>　　專 業(yè) 機械設(shè)計制造及其自動化 </p><p>　　學(xué) 生 姓 名 </p><p>　　班 級 </p><p>　　學(xué) 號

2、 </p><p>　　指 導(dǎo) 教 師 </p><p>　　MULTI-OBJECTIVE OPTIMAL FIXTURE LAYOUT</p><p>　　DESIGN IN A DISCRETE DOMAIN</p><p>　　Diana Pelinescu and Michael Yu Wang</p&g

3、t;<p>　　Department of Mechanical Engineering</p><p>　　University of Maryland</p><p>　　College Park, MD 20742 USA</p><p>　　E-mail: yuwang@eng.umd.edu</p><p><b

4、>　　Abstract</b></p><p>　　This paper addresses a major issue in fixture layout design:to evaluate the acceptable fixture designs based on several quality criteria and to select an optimal fixture app

5、ropriate with practical demands. The performance objectives considered are related to the fundamental requirements of kinematic localization and total fixturing (form-closure) and are defined as the workpiece localizatio

6、n accuracy and the norm and distribution of the locator contact forces. An efficient interchange algorithm </p><p>　　I. INTRODUCTION</p><p>　　Proper fixture design is crucial to product quality

7、in terms of precision and accuracy in part fabrication and assembly. Fixturing systems, usually consisting of clamps and locators, must be capable to assure certain quality performances, besides of positioning and holdin

8、g the workpiece throughout all the machining operations. Although there are a few design guidelines such as 3-2-1 rule, automated systems for designing fixtures based on CAD models have been slow to evolve. </p>&

9、lt;p>　　This article describes a research approach to automated design of a class of fixtures for 3D workpieces. The parts considered to be fixtured present an arbitrary complex geometry, and the designed fixtures are

10、limited to the minimum number of elements required, i.e. six locators and a clamp. Furthermore, the fixels are modeled as non-frictional point contacts and are restricted to be applied within a given collection of discre

11、te candidate locations. In general, the set of fixture locations avail</p><p>　　the exterior surfaces of the workpiece. The goal of the fixture design is to determine first, from the proposed discrete domain

12、, the feasible fixture configurations that satisfy the form-closure constraint. Secondly, the sets of acceptable fixture designs are evaluated on several criteria and optimal fixtures are selected. The performance measur

13、es considered in this work are the localization accuracy, and the norm and distribution of the locator contact forces. These objectives cover the most cr</p><p>　　The optimal fixture design approach is based

14、 on a concept of optimum experiment design. The algorithm developed evaluates efficiently the admissible designs exploiting the recursive properties in localization and force analysis. The algorithm produces the optimal

15、fixture design that meets a set of multiple performance requirements.</p><p>　　II. RELATED WORK</p><p>　　Literature on general fixturing techniques is substantial, e.g., [1]. The essential requi

16、rement of fixturing is the century-old concept of form closure [2], which has been</p><p>　　extensively studied in the field of robotics in recent years [3, 4]. There are several formal methods for analyzing

17、 performance of a given fixture based on the popular screw theory, dealing with issues such as kinematic closure [5], contact types and friction effects [6]. A different analysis approach based on the geometric perturbat

18、ion technique was reported in [7]. An automatic modular fixture design procedure based on this method was developed in [8] to include geometric access constraints in</p><p>　　rigidity [6], tool accessibility

19、 and path clearance [7]. The problem of fixture synthesis has been largely studied for the case of a fixed number of fixture elements (or fixels) [8, 10], particularly in the application to robotic manipulation and grasp

20、ing for its obvious easons [3, 4]. This article aims to be an extension of the results on the fixture design issues previously reported in [14].</p><p>　　III. FIXTURE MODEL</p><p>　　The fundamen

21、tal performance of a fixture is characterized by the kinematic constraints imposed on the workpiece being held by the fixture. The kinematic conditions are well understood [3, 4, 5, 7, 12]. For a fixture of n locators (i

22、 = 1, 2, … , n), the fixture can be represented by:</p><p><b>　　y=GTq</b></p><p>　　where define small perturbations in the locator positions and the location of the workpiece respect

23、ively. The fixture design</p><p>　　is defined by the locator matrixi where and ni and ri denote the surface normal and position at the ith contact point on the workpiece surface. The problem of fixture desi

24、gn requires the synthesis of a fixturing scheme to meet a given set of performance requirements.</p><p>　　IV. QUALITY PERFORMANCE CRITERIA FOR A FIXTURE</p><p>　　A. Accurate Localization</p&g

25、t;<p>　　An essential aspect of fixture quality is to position with precision the workpiece into the fixturing system. In general the workpiece positional errors are due to the geometric variability of the part and

26、 the locators set-up errors. This paper will focus only on the workpiece positional errors due to the locator positioning errors. As an extension of the fixture model equation (eq.1), the locator positioning errors y can

27、 be related with the workpiece localization error q as follows:</p><p>　　Clearly, for given source errors the workpiece positional accuracy depends only on the locator locations being independent from the cl

28、amping system, the Fisher information matrix M ??GGT characterizing completely the system errors. It has been shown [12] that a suitable criterion to achieve high localization accuracy is to maximize the determinant of

29、the information matrix (Doptimality), i.e., max?det M?.</p><p>　　B. Minimal Locator Contact Forces</p><p>　　Another objective in planning a fixture layout might be to minimize all support forces

30、 at the locator contact regions throughout all the operations with complete kinematic restraint or force-closure. Locator contact forces in response to the clamping action are given as:</p><p>　　Normalizing

31、these forces with respect to the clamping intensity we obtain:</p><p>　　The force-closure condition requires these forces to be always positive for each locator i of a set of n locators:</p><p>

32、　　Computing the norm of the locator contact forces:</p><p>　　leads to an appropriate design objective, i.e. min</p><p>　　Note that this objective indicates both locator and clamp positions to b

33、e determined in the optimization process.</p><p>　　C. Balanced Locator Contact Forces</p><p>　　Another significant issue in designing a fixture is that the total force acting on the workpiece ha

34、ve to be distributed as uniformly as possible among the locator contact</p><p>　　regions. If p represents the mean reactive force in response to the clamp action, then we define the dispersion of the locator

35、 contact forces as:</p><p>　　Therefore, minimizing the defined dispersion represents an objective for a balanced force-closure: min(d).</p><p>　　V. OPTIMAL FIXTURE DESIGN WITH INTERCHANGE ALGORI

36、THMS</p><p>　　As mentioned earlier, by generating on the exterior surface of the workpiece to be fixtured a set of discrete locations defined as position and orientation, we create a potential collection for

37、 the fixture elements. For example, using the information contained in the part CAD model, a discrete vector collection (unitary, normal vectors) can be generated as uniformly as possible on those surfaces accessible to

38、the fixture components (fig.1).</p><p>　　Figure 1: Part CAD model and global collection of candidate locations for the fixture elements.</p><p>　　The fixture design layout will select from this

39、collection optimal candidates for locators and clamps with respect to the performance objectives and to the kinematic closure condition. Dealing with a large number of candidate locations the task of selecting an appropr

40、iate set of fixels is very complex.</p><p>　　As already introduced in [12, 14] an effective method for finding the desired fixture with regard to one of the previous quality objectives is the optimal pursuit

41、 method with an interchange algorithm. Due to its own limitations and to the fact that the objectives are functions with many extremes, the exchange procedure may not end up to a unique optimized fixture configuration, b

42、ut to several improved designs depending on the initial layout. Therefore the solution offered by the multiple interch</p><p>　　Phase 1: Random generation of initial sets of locators.</p><p>　　T

43、he starting layout is generated by a random selection of distinct sets, each consisting from 6 locators out of the list of N candidate locations. If the clamp is pre-determined, a</p><p>　　valid selection is

44、 obtained through a simultaneous check for all kinematic constraints. A big initial set of proposed ocators is preferred, giving the opportunity of finding a convergent optimal solution. However from the efficiency point

45、 of view the designer has to balance the algorithm between the accuracy of the final solution and the computation time.</p><p>　　Phase 2: Improvement by interchange.</p><p>　　The interchange alg

46、orithm's goal is to pursue for an improvement of the initial sets of locators with respect to one of the objectives. Basically, this is done iteratively by exchanging one by one the proposed locators with candidate l

47、ocations from the global collection. It is also essential to consider the form-closure restraint during the exchange procedure. The process will continue as long as an improvement of the objective function is registered.

48、 Studying the effect of interchange on the pr</p><p>　　Thus, at each interchange the pair is selected such that the significant term that controls the function evolution is improving, e.g. max p 2jk and min

49、Δpc , easing the iterative process.</p><p>　　Phase 3: Selecting the optimal solution.</p><p>　　Applying the interchange algorithm for each initial set of locators we will end up with several dis

50、tinct solutions on the configuration scheme of the fixture, the best fixture design corresponds evidently to the maximum improvement of the objective function. It should be emphasized that this algorithm can be used sequ

51、entially for different objective functions. Depending on the objective pursued the best solution can be evident (for a single objective) or might need the designer's final decision </p><p>　　VI. MULTI-OB

52、JECTIVE FIXTURE LOCATOR OPTIMIZATION</p><p>　　In many applications the clamp is already fixed given some practical considerations. Then with the clamp predefined, the best fixture with respect to a certain p

53、erformance criterion is constructed by selecting a suitable set of locators such that a significant improvement of the objective-function is registered. Using the random interchange algorithm we can analyze the impact of

54、 the optimization process on the fixture characteristics, as well as we can select the best optimized fixture solution </p><p>　　A. Multi-objective trade-offs</p><p>　　In some applications both

55、localization quality and a minimum force dispersion are important. In this case we may have to use a 2-step algorithm: first max(det M) and secondly min(d). The proposed order is a consequence of the above observations.

56、First, maximizing the determinant will automatically decrease the dispersion. Next, a decreasing in dispersion leads in a decreasing in determinant value. Therefore, during the second phase of the algorithm tradeoffs bet

57、ween the two objectives occur. To </p><p>　　A following set of plots present the results when the design requirements of precision localization and uniform contact forces are considered simultaneously. Fig.

58、2 and Fig. 3 illustrate the global changes of the fixture characteristics during the 2-step algorithm performed on an initial collection of distinct random sets of locators, with the clamp pre-fixed. It can be noticed th

59、e advantages of using max(det M) objective as a first step: while the determinant is increasing, the norm and the dis</p><p>　　Figure 2: Changes upon the fixture characteristics applying the 2-step optimizat

60、ion algorithm on an initial collection of random sets of locators.</p><p>　　Figure 3: Behavior during a 2-step random interchange algorithm for a collection of locator sets.</p><p>　　As an examp

61、le, the behavior of a single initial set of locators is studied during the interchange processes of the 2-step algorithm (Fig. 4), confirming the previous remarks. The trade-off zone is decisive in the multiobjective des

62、ign. The resultant configurations of the fixture after each successive phase are presented in Fig. 5. It can be noticed that the first objective moves the locators close to the boundaries as far as possible from each oth

63、er, while the second one reorients them to the su</p><p>　　Figure 4: General behavior of a 2-step interchange.</p><p>　　Figure 5: Fixture configurations during a 2-step algorithm: (a) initial, (

64、b) after max(det M), and (c) after min(d) respectively.</p><p>　　B. Designer decision in finalizing the fixture</p><p>　　During the second phase of the algorithm a fairly significant decrease in

65、 the determinant value is registered, so few solutions will be acceptable for the multi-objective problem. In order to overcome these problems, an active designer control during min(d) interchange procedure is recommende

66、d. Essentially, the modifications consist in controlling the exchange procedure, such that the determinant of the improved locators must be permanently greater than a certain bound, simultaneously with the c</p>&

67、lt;p>　　As an example, the behavior of a single set of locators is studied during the interchange process of a 2- step algorithm controlled for two different bounds of the determinant value, emphasizing the fact that i

68、n the trade off zone the designer decision is decisive in finalizing the fixture configuration (fig. 7).</p><p>　　Figure 6: Second phase of a 2-step random interchange algorithm: uncontrolled min(d); control

69、led min(d).</p><p>　　Figure 7: General behavior during a 2-step algorithm applied on a single set of locators. (a) for B1 and (b) for B2.</p><p>　　VII. OPTIMAL FIXTURE CLAMPING</p><p&

70、gt;　　This section deals with a more complicated problem: to search simultaneously for the optimal clamp and locators in order to achieve a required fixture quality. Varying the</p><p>　　clamp, it is obvious

71、that the number of combinations for possible clamp-locators candidates is increasing very much. It will be shown that this problem is manageable</p><p>　　for the precise localization objective. For the other

72、 objectives we will have to restrain the search of the optimal clamp inside of a small set of proposed locations, such that the optimization procedure could be handled.</p><p>　　A. Optimal Clamp from a Set o

73、f Clamps</p><p>　　In some applications the clamps have certain preferred locations, therefore the need to choose the best clamp from a proposed collection might be raised. For example, let's consider tha

74、t a collection of preferred clamps is given, and an optimal fixture design with respect to the highly precise localization objective is needed. It is obvious that applying a random interchange procedure successively for

75、each clamp, we find optimal fixture configurations for each specified clamp. Comparing the dete</p><p>　　Figure 8: Clamp selection from a collection of clamps for single-objective design.</p><p>

76、;　　Figure 9: The initial collection of proposed clamps; the best clamp and the corresponding locators.</p><p>　　B. Optimal Clamp from a Set of Clamps</p><p>　　Furthermore, by extension, the sele

77、ction of the optimal clamp from a set of proposed locations with regard to the multi-objective design problem can be considered. It consists of mainly applying the random 2-step interchange algorithm consecutively for ea

78、ch proposed clamp.</p><p>　　By collecting the results after applying this procedure for all the clamps, we can compare their different behavior, and select the most appropriate one. It is obvious that an opt

79、imal clamp allows only small fluctuations of the determinant while the force dispersion is decreasing significantly (fig. 10). As an example, Fig. 11 illustrates the final fixture design consisting of the best clamp sele

80、cted from a proposed collection with respect to the multi-objectives and the corresponding optimal lo</p><p>　　Figure 11: The initial collection of proposed clamps; the best clamp and the corresponding locat

81、ors.</p><p>　　VIII. CONCLUSIONS</p><p>　　This article focuses on optimal design of fixture layout for 3D workpieces with an optimal random interchange algorithm. The quality objectives considere

82、d include accurate workpiece localization, minimal and balanced contact forces. The paper focuses on multi-criteria optimal design with a hierarchical approach and a combined-objective approach. The optimization processe

83、s make use of an efficient interchange algorithm. Examples are used to illustrate empirical observations with respect to the de</p><p>　　The work described here is yet complete. Since the inter-relationship

84、between the locators and the clamps has a determinant role on the fixture quality measures, a more coherent and complete approach to study the influence of the clamp and search of the optimal clamp position is needed in

85、future works.</p><p>　　IX. REFERENCES</p><p>　　[1] P. D. Campbell, Basic Fixture Design. New York: Industrial Press, 1994. </p><p>　　[2] F. Reuleaux, The Kinematics of Machinery. D

86、over Publications, 1963.</p><p>　　[3] B. Mishra, J. T. Schwartz, and M. Sharir, "On the existence and synthesis of multifinger positive grips", Robotics Report 89, Courant Institute of Mathematical

87、 Sciences, New York University, 1986.</p><p>　　[4] X. Markenscoff, L. Ni, and C. H. Papadimitriou, "The geometry of grasping", International Journal of Robotics Research, vol. 9, no. 1, pp. 61-74,

88、1990.</p><p>　　[5] Y.-C. Chou, V. Chandru, and M. M. Barash, "A mathematical approach to automated configuration of machining fixtures: Analysis and synthesis", Journal Engineering for Industry, vo

89、l. 111, pp. 299-306,1989. </p><p>　　[6] E. C. DeMeter, "Restraint analysis of fixtures which rely on surface contact", Journal of Engineering for Industry, vol. 116, no. 2, pp. 207-215, 1994.</p

90、><p>　　[7] H. Asada and A. B. By, "Kinematics analysis of workpart fixturing for flexible assembly with automatically reconfigurable fixtures", IEEE Journal Robotics and Automation, vol. RA1, pp. 86-9

91、3, 1985.</p><p>　　[8] R. C. Brost and K. Y. Goldberg, "A complete algorithm for designing modular fixtures for polygonal parts", Tech. Rep. SAND93-2028, Sandia National Laboratories, 1994.</p>

92、;<p>　　[9] Y. Zhuang, K. Goldberg, and Y.-C. Wong, "On the existence of solutions in modular fixturing", International Journal of Robotics Research, vol. 15, no. 5, pp. 5-9, 1996.</p><p>　　[

93、10] W. Cai, S. J. Hu, and J. Yuan, "A variational method of robust fixture configuration design for 3-d workpieces", Journal of Manufacturing Science and Engineering, vol. 119, pp. 593-602, November 1997.</p

94、><p>　　[11] D. Baraff, R. Mattikalli, and P. Khosla, "Minimal fixturing of frictionless assemblies", CMU-RI TR-94-08, The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 1994.</p>

95、;<p>　　[12] M. Y. Wang, "An optimal design approach to 3D fixture synthesis in a point set domain", IEEE Trans. on Robotics and Automation, December 2000.</p><p>　　[13] A. Atkinson and A. Do

96、ney, Optimum Experimental Designs. New York: Oxford University Press, 1992.</p><p>　　[14] M. Y. Wang and D. Pelinescu, "Precision localization and robust force closure in fixture layout design for 3D wo

97、rkpieces", IEEE Int'l Conf. on Robotics and Automation (CD-ROM), San Francisco, April 2000.</p><p>　　在獨自領(lǐng)域最佳多功能夾具布置的設(shè)計</p><p>　　Diana Pelinescu and Michael Yu Wang 馬里蘭大學(xué)機械工程系</p>

98、<p>　　College Park, MD 20742 USA</p><p>　　摘要：本文論及一個在夾具布置設(shè)計的重要問題: 根據(jù)實用要求來選擇一套優(yōu)化的裝置，并評估可接受的裝置設(shè)計。主要宗旨是要考慮與根本要求有關(guān)的運動學(xué)方面和總的夾具形式(形式閉)， 還要考慮作為工件定位的準(zhǔn)確性和標(biāo)準(zhǔn)以及定位布置的聯(lián)系。 高效率的互換算法被使用在多標(biāo)準(zhǔn)優(yōu)化過程有很多不同的實用案件, 因此合適的交換平臺能執(zhí)

99、行綜合裝置。</p><p>　　關(guān)鍵詞：夾具 定位器 互算法 目標(biāo)函數(shù)</p><p><b>　　1介紹</b></p><p>　　適當(dāng)?shù)膴A具設(shè)計對產(chǎn)品質(zhì)量方面精確度和準(zhǔn)確性在部份制造和裝配是關(guān)鍵的. 夾具 系統(tǒng), 通常包括鉗位和定位器, 必須是可勝任保證成品質(zhì)量 包括安置和保證在機器生產(chǎn)中的加工過程.雖然有幾個設(shè)計指南如3-2-1

100、規(guī)則, 自動化的系統(tǒng)為設(shè)計夾具提供的CAD 模型在演變。這是一篇描述自動設(shè)計夾具之類的3D研究方法文章. 這部分被認(rèn)為是固定當(dāng)前任意復(fù)雜幾何, 并且被設(shè)計的夾具必需限制在對元素的最小數(shù)字, 即六臺定位器和鉗位。此外,固定器被限制在無非摩擦點接觸并且實用的位置. 總之, 夾具之類必需放在假定的潛在準(zhǔn)確的位置; 例如, 位置也許由可分辨的工件外表面決定的。首先確定夾具設(shè)計的目的, 從被提出的的特殊領(lǐng)域,在這個領(lǐng)域可行的夾具設(shè)計必需滿足形式關(guān)