三自由度并聯(lián)機構的平行機設計
三自由度并聯(lián)機構的平行機設計,三自由度并聯(lián)機構的平行機設計,自由度,并聯(lián),機構,平行,設計
編號
無錫太湖學院
畢業(yè)設計(論文)
相關資料
題目: 六自由度液壓運動平臺的自動控制
信機 系 機械工程及自動化專業(yè)
學 號: 0923280
學生姓名: 賴坤楠
指導教師: 龔常洪 (職稱:副教授)
(職稱: )
2013年5月25日
目 錄
一、畢業(yè)設計(論文)開題報告
二、畢業(yè)設計(論文)外文資料翻譯及原文
三、學生“畢業(yè)論文(論文)計劃、進度、檢查及落實表”
四、實習鑒定表
無錫太湖學院
畢業(yè)設計(論文)
開題報告
題目: 六自由度液壓運動平臺的自動控制
信機 系 機械工程及自動化 專業(yè)
學 號: 0923280
學生姓名: 賴坤楠
指導教師: 龔常洪 (職稱:副教授)
(職稱: )
2012年11月25日
課題來源
六自由度平臺的研制
科學依據(jù)(包括課題的科學意義;國內(nèi)外研究概況、水平和發(fā)展趨勢;應用前景等)
(1)課題科學意義
六自由度運動平臺是由六支油缸,上、下各六只萬向鉸鏈和上、下兩個平臺組成,下平臺固定在基礎上,借助六只油缸的伸縮運動,完成上平臺在空間六個自由度(X,Y,Z,α,β,γ)的運動,從而可以模擬出各種空間運動姿態(tài),可廣泛應用到各種訓練模擬器如飛行模擬器、艦艇模擬器、海軍直升機起降模擬平臺、坦克模擬器、汽車駕駛模擬器、火車駕駛模擬器、地震模擬器以及動感電影、娛樂設備等領域,甚至可用到空間宇宙飛船的對接,空中加油機的加油對接中。在加工業(yè)可制成六軸聯(lián)動機床、靈巧機器人等。由于六自由度運動平臺的研制,涉及機械、液壓、電氣、控制、計算機、傳感器,空間運動數(shù)學模型、實時信號傳輸處理、圖形顯示、動態(tài)仿真等等一系列高科技領域,因而六自由度運動平臺的研制變成了高等院校、研究院所在液壓和控制領域水平的標志性象征。
(2)六自由度運動平臺的研究狀況及其發(fā)展前景
目前世界上研制大型六自由度平臺的國家較多,主要有加拿大、美國、英國、法國、德國、日本、俄羅斯、荷蘭等國,大多用于飛機(包括戰(zhàn)斗機、運輸機和民航客機)模擬飛行訓練,在艦船、裝甲車輛、自行火炮等方面也有一些應用。近幾年來,六自由度平臺系統(tǒng)也被應用到工業(yè)甚至娛樂場所。隨著6-DOF并聯(lián)機構研究的深入,對于自由度少于六的空間并聯(lián)機構(稱為少自由度機構),也引起許多學者的注意,國外的專家學者們也對其進行了研究改進。而國外也已研制出虛擬軸機床。我國并聯(lián)機器人出現(xiàn)的較晚,起先出現(xiàn)在引進的6-DOF飛行模擬器上。近幾年來我國的一些高等院校和科研院所也相繼投入人力物力。在微動器或稱作微動機構研究方面,也取得了不小的發(fā)展。但在運動模擬器的相關技術方面,與國外還存在較大距離。
由于六自由度運動平臺的應用廣泛,未來還將不斷地往數(shù)字化和微動作方面改進發(fā)展。
研究內(nèi)容
(1)了解國內(nèi)外多自由度運動平臺的現(xiàn)狀和發(fā)展趨勢,了解近十幾年平臺的數(shù)字虛擬化發(fā)展。
(2)查閱六自由度運動平臺的相關圖形,熟悉其結構,和相關液壓伺服系統(tǒng)并能對其進行設計。
(3)掌握相關系統(tǒng)的數(shù)學模型的建立和使用。
(4)掌握PID控制方式,并了解如何使用以提高系統(tǒng)的運動性能。
(5)掌握虛擬樣機技術,并能用其對剛體進行運動學和動力學方面的仿真。
擬采取的研究方法、技術路線、實驗方案及可行性分析
(1)實驗方案
建立液壓控制系統(tǒng)的模型,使用常規(guī)的PID控制方式和基于BP神經(jīng)網(wǎng)絡的PID控制方式對其進行模擬仿真,比較優(yōu)劣;
運用虛擬樣機技術,對運動平臺進行運動學和動力學的模擬仿真。
(2)研究方法
(1)在常規(guī)的PID控制方式下,對運動平臺進行仿真研究。
(2)在基于BP神經(jīng)網(wǎng)絡的PID控制方式下,對運動平臺進行仿真研究。
(3)利用三維軟件畫出六自由度運動平臺的實物圖,設定參數(shù),使用軟件對其進行運動學和動力學的仿真。
研究計劃及預期成果
研究計劃:
2012年11月12日-2012年12月2日:按照任務書要求查閱論文相關參考資料,完成畢業(yè)設計開題報告書。
2012年12月3日-2013年3月1日:接受專業(yè)實訓,完成畢業(yè)實習報告。
2013年3月4日-2013年3月15日:查閱并翻譯與畢業(yè)設計相關的英文材料。
2013年3月18日-2013年4月12日:確定總體方案,設計運動平臺的相關尺寸。
2013年4月15日-2013年5月10日:繪制運動平臺相關工程圖并對平臺進行模擬。
2013年5月13日-2013年5月25日:畢業(yè)論文撰寫和修改工作。
預期成果:
達到預期的實驗結論:與常規(guī)的PID控制方式相比,基于BP神經(jīng)網(wǎng)絡的PID控制方式控制的曲線超調(diào)量小、調(diào)整時間短,穩(wěn)態(tài)誤差小。由此說明神經(jīng)網(wǎng)絡對電液伺服這類高階、非線性、動特性隨負載變化很大的系統(tǒng)就很好的實時控制能力。
特色或創(chuàng)新之處
(1)合理運用計算機進行幫忙,減輕了某些負擔,也提高了效率。
(2)采用對比的方法來研究問題,思路清晰,簡單明了,行之有效。
已具備的條件和尚需解決的問題
(1)可以輕松的實用軟件對平臺進行模擬仿真。
(2)液壓系統(tǒng)的振動和噪聲有待進一步降低。
指導教師意見
指導教師簽名:
年 月 日
教研室(學科組、研究所)意見
教研室主任簽名:
年 月 日
系意見
主管領導簽名:
年 月 日
外文資料
Closed-Form Direct Kinematics Solution of a New Parallel Minimanipulator
In recent years,many researchers have shown a great deal of interest in studying parallel manipulators.Such mechanisms are most suitable for applications in which the requirements for accuracy,rigidity,load-to-weight ratio,and load distribution are more important thanthe need for a large workspace.
The famous Stewart platform(Stewart,1965) is probably the first six-degree-of-freedom(six-DOF) parallel mechanism which has been studied in the literature.It consists of a moving platform and a base which are connected by means of six independent limbs.Many researchers have considered the Stewart platform as a robot manipulator(e.g.,Fichter and MacDowell,1980;Hunt,1983;Yang and Lee,1984;Fichter,1986).Other types of six-DOF parallel manipulators have been introduced and studied in literature(e.g.,Kohli et al.,1988;Hudgens and Tesar,1988;Tsai and Tahmasebi,1991a).
Waldron and Hunt(1987)demonstrated that kinematic behavior of parallel mechanisms has many inverse characteristics to that of serial mechanisms.For example,direct kinematics of a parallel manipulator is much more difficult than its inverse kinematics;whereas,for a serial manipulator,the opposite is true.Dieudonne et al.(1972)applied Newton-Raphson's method to solve direct kinematics of a motion simulator identical to the Stewart platform.Behi(1988) used a similar technique to numerically solve the direct kinematics problem of a parallel mechanism similar to the Stewart platform.Griffis and Duffy(1989)as well as Nanua et al.(1990)studied direct kinematics of special cases of Stewart platform,in which pairs of spherical joints are concentric on either the platform or both the base and the platform.They were able to reduce the problem to an eighth-degree polynomial in the square of a single variable(total degree of sixteen).However,as mentioned by Griffis and Duffy(1989),pairs of concentric spherical joints may very well present design problems.Lin et al.(1990)solved direct kinematics of anther class of Stewart platforms,in which there are two concentric spherical joints on the base and two more concentric spherical joints on the platform.The latter class of Stewart platforms suffer form lack of symmetry and concentric spherical joints are still needed in their construction.Other researcher have also been able to obtain closed-form solutions for other special forms of the Stewart platform(e.g.,Innocenti and Parenti-Castelli,1990;Parenti-Castelli and Innocenti,1990).It is worth mentioning that,to the best of our knowledge,no one has ye been able to obtain a closed-form direct kinematics solution for the general Stewart platform with six independent limbs.Recently,Raghavan(1991)used a numerical technique known as polynomial continuation to show that there are forty solutions for the direct kinematics of the Stewart platform of general geometry.Murthy and Waldron(1990a,1990b)have been able to relate the direct kinematics of some parallel mechanisms to the inverse kinematics of their serial dual mechanisms.
In this paper,closed-form direct kinematic solution for a six-DOF parallel minimanipulator is presented.The minimanipulator is one of the high-stiffness and high-resolution mechanisms introduced by Tsai and Tahmasebi(1991a,1991b)for fine position and force control in a hybrid serial-parallel manipulator system,It will be shown that direct kinematics of the minimanipulator involves solving an eighth-degree polynomial in the square of a single variable.
Let subscript i in this section and the rest of this work represent numbers 1, 2, and 3 in a cyclic manner. The minimanipulator contains three inextensible limbs,PiRi. The lower end of each limb is connected to a simplified five-bar linkage driver and can be moved freely on the base plate. The desired minimanipulator motion is obtained by moving the lower ends of its three limbs on its base plate. Two-DOF universal joints connect the limbs to the moving platform. The lower ends of the limbs are connected to the drivers through three more universal joints. Note that one of the axes of the upper universal joint is collinear with the limb, while the other axis of the upper universal joint as well as one of the axes of the lower universal joint are always perpendicular to the limb. This arrangement is kinematically equivalent to a limb with a spherical joint at its lower end and a revolute joint at its upper end. Point Ci is the output point of a driver. At point Di, there is an actuator on each side of the base plate to drive links DiAi and DiBi. The simplified five-bar drivers are completely symmetric. As a result, coordination between actuator rotations can be easily accomplished. Namely,angular displacement of an output point Ci is obtained by equal actuator rotations, and its radial displacement is obtained by equal and opposite actuator rotations.
Simplified five-bar linkages and inextensible limbs are used to improve positional resolution and stiffness of the minimanipulator. Since the minimanipulator actuators are base mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. In addition, to achieve even load distribution, the minimanipulator is made completely symmetric.
The equivalent limb configuration will be used for analysis, because the spherical-and-revolute limb is easier to analyze than the universal-and-universal limb. The lower ends of the limbs are connected to two-DOF drivers. The upper end of the limbs are connected to the platform through revolute joints. Note that the joint axes at points are parallel to lines.
Let us define the fixed base reference frame and the moving platform reference frame in detail. The origin of the base reference frame is placed at the centroid of triangle DiDZD3 .The positive X-axis is parallel to and points in the direction of vector DZD3. The positive Y-axis points from point 0 to point Dl.The Z-axis is defined by the right-hand-rule. Similarly, the origin of the platform reference frame is placed at the centroid of triangle P1PZP3. The positive U-axis is parallel to and points in the direction of vector PZP3. The positive V-axis points from point 0 to point P1. The W-axis is defined by the right-hand-rule. To keep the minimanipulator symmetric, both triangles D1DZD3 and P1PZP3 are made equilateral.
In this paper, closed-form solution for direct kinematics of a new three-limbed six-degree-of-freedom minimanipulator is presented. It is shown that the for direct kinematics of the minimanipulator is sixteen. To maximum number of solutions obtain these solutions, only an eighth-degree polynomial in the square of a single variable has to be solved. It is also proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs. The results of a numerical example are verified by an inverse kinematics analysis.
This research was supported in part by the NSF Engineering Research Center program, NSFD CDR 8803012. The first author gratefully acknowledges the support of NASA/Goddard Space Flight Center. Such supports do not constitute endorsements of the views expressed in the paper by the supporting agencies.
Workspace analysis and optimal design of a 3-leg 6-DOF parallel platform mechanism
A new class of six-degree-of-freedom (DOFs) spatial parallel platform mechanism is considered in this paper. The architecture consists of a mobile platform connected to the base by three identical kinematic chains using five-bar linkages. Recent investigations showed that parallel mechanisms with such a topology for the legs can be efficiently statically balanced using only light elastic elements. This paper follows up with a workspace analysis and optimization of the design of that parallel mechanism. More specifically, considering a possible industrial application of the architecture as a positioning and orienting device of heavy loads, an optimization procedure for the maximization of the volume of the three-dimensional (3-D) constant-orientation workspace of the mechanism is first presented. As the mechanism could also have great potential as a motion base for flight simulators, we develop here a discretization method for the computation and graphical representation of a new workspace with coupled translational and rotational DOFs. This workspace can be defined as the 3-D space which can be obtained when generalized coordinates x,y and torsion angle ψ in the tilt-and-torsion angles parametrization are constant. A second procedure is then presented for the maximization of the volume of this second subset of the complete workspace. For both approaches, our purpose is to attempt an optimal design of the mechanism by maximizing the volume of the associated 3-D Cartesian region that is free of critical singularity loci.
Determination of the wrench-closure workspace of 6-DOF parallel cable-driven mechanisms
A parallel cable-driven mechanism consists essentially of a mobile platform connected in parallel to a base by light weight links such as cables.the control of length of the cables allows the control of the pose of the platform.For instance,a mechanism driven by eight cables is shown in Fig.1.Parallel cable-driven mechanisms have several advantages over conventional rigid-link mechanisms(Barrette and Gosselin,2005,Merlet,2004,Roberts et al.,1998).The mass and inertia of the moving part is reduced and they are less expensive.Moreover,parallel cable-driven mechanisms are easier to build,transport and reconfigure and they have the possibility of working in a very large space.Consequently,parallel cable-driven mechanisms have been used in several applications such as ,for instance,robotic cranes(Dagalakis et al.,1989),high speed manipulation(Kawamura et al.,2000),active suspension devices(Lafourcade,2004)and virtual reality(Merlet,2004).
This paper deals with the determination of the workspace of six-DOF parallel cable-driven mechanisms.This workspace may be limited by the total length of each cable,by the interferences between the cables and between the cables and the mobile platform and by the unidirectional nature of the forces applied by the cables on the mobile platform.The limitations due to the total lengths of the cables can be determined by means of algorithms presented in(Gosselin,1990)and in(Merlet,1999).However,the workspace will usually not be limited by the total lengths of the cables since large total lengths can generally be used.For a constant orientation of the mobile platform,the problem of the influence on the workspace of the cables interferences is addressed in(Merlet,2004).The third limitation which is due to the unidirectional nature of the forces applied by the cables on the platform has been studied mainly in the case of planar parallel cable-driven mechanisms in(Barrette and Gosselin,2005,Fattah and Agrawal,2005,Gallina and Rosati,2002,Gouttefade Gosselin,2006,Roberts et al.,1998,Stump and Kumar,2004,Verhoeven and Hiller,2000,Verhoeven,2004,Williams et al.,2003).
中文翻譯
新的封閉式并聯(lián)迷你機器人的直接運動學正解
近年來,許多研究人員已經(jīng)對并聯(lián)式迷你機器人表現(xiàn)出了極大的興趣。這種結構在精度、剛度、載荷重量比和載荷分布方面比那些所占空間更大的更適合。
著名的斯圖爾特平臺(斯圖爾特,1965)可能是第一個已經(jīng)記錄在文獻中的六自由度(六度)并聯(lián)機構。它是由六個獨立的肢體將一個移動平臺和一個地基連接而成。許多研究者認為斯圖爾特平臺可以當作一個機器人機械臂(例如,菲克特·麥克道威爾,1980年,亨特,1983年,楊振寧與李政道,1984年,菲克特,1986)。其他類型的六自由度并聯(lián)機構已在文獻中被引入和研究(例如,Kohli等人,1988;哈金斯和特薩,1988;蔡和塔瑪塞比,1991a)。
沃爾德倫和狩獵(1987)表明,并聯(lián)機構的運動學行為有許多逆特性,串行機制。例如,并聯(lián)機構的直接運動學比它的逆運動學困難得多,而對于串行機械臂,事實正好相反。迪厄多內(nèi)等人。(1972)應用牛頓-拉夫遜方法解決同一個的運動模擬器的斯圖爾特平臺運動學正解。后(1988)采用了類似的技術來對一個類似斯圖爾特平臺的并聯(lián)機構進行直接運動學數(shù)值求解。格里菲斯和Duffy(1989)以及Nanua等人(1990)研究了斯圖爾特平臺的特殊情況下,在其中對球形接頭的基極和平臺的平臺或同心的正運動學。他們能夠減少在一個單變量的平方第八度多項式(共十六度)的問題。然而,由格里菲斯和杜菲所提到的(1989),同心球節(jié)點對很可能存在設計問題。林等人(1990)解決了另一類的斯圖爾特平臺直接運動學問題,其中有兩個同心球節(jié)點的基礎上,和兩個同心球節(jié)點平臺。后一種斯圖爾特平臺受對稱和同心球接頭形式缺乏仍需要建設。其他的研究人員也能獲得斯圖爾特平臺的其他特殊形式的封閉形式的解決方案(例如,因諾琴蒂帕倫蒂卡斯泰利,1990;帕倫蒂卡斯泰利和因諾琴蒂,1990)。值得一提的是,據(jù)我們所知,還沒有人就能夠得到一個封閉的形式的有六個獨立的肢體的廣義斯圖爾特平臺的直接運動學解決方案。最近,拉加萬(1991年)采用了數(shù)字技術,被稱為多項式延續(xù)表明,有40解決方案的直接斯圖爾特平臺運動學的一般幾何。穆爾蒂和沃爾德倫(1990a,1990b)已經(jīng)能夠涉及一些并聯(lián)機構直接運動學的串行雙機制的逆運動學。
在本文中,封閉式六自由度并聯(lián)迷你機器人的直接運動學現(xiàn)在已解決了。該迷你機器人是一種高剛度和高分辨率的機構由仔與塔瑪塞比介紹(1991a,1991b)在混合串并聯(lián)機器人系統(tǒng)優(yōu)良的位置和力控制,它將會顯示的迷你機器人直接運動學解決在一個單一的變量的第八次多項式的平方。
這段下標和這項工作的其他代表數(shù)字1,2,和3個循環(huán)的方式。該迷你機器人包含三個不可伸長的四肢,皮里。每個肢體下端連接一個簡化的五桿機構驅(qū)動,可在基板上自由移動。迷你機器人所需的運動是由其基板移動的三肢下端得到。兩個自由度的萬向節(jié)連接四肢的運動平臺。四肢的下端通過三個萬向節(jié)連接到驅(qū)動程序。請注意,一個上部萬向節(jié)軸與肢體共線,而上部萬向節(jié)軸等以及一個較低的萬向節(jié)軸始終垂直于肢體。這樣的安排是運動學等效與在其下端球形接頭和旋轉(zhuǎn)在其上端連接一個肢體。點是一個驅(qū)動器的輸出點。在點二,在底板各邊執(zhí)行驅(qū)動鏈接的轉(zhuǎn)動和迪比。簡化的五條司機是完全對稱的。作為一個結果,致動器的旋轉(zhuǎn)之間的協(xié)調(diào),可以很容易地完成。即,一個輸出點的角位移的致動器詞等旋轉(zhuǎn)得到的,其徑向位移是由大小相等、方向相反的致動器的旋轉(zhuǎn)得到的。
簡化的迷你機器人的五桿機構和不可伸長的四肢是用來提高位置精度和剛度的。由于迷你機器人的致動器是底座安裝;高載荷能力,小尺寸和低功耗的致動器,可以得到。此外,達到均勻的負荷分布,迷你機器人是完全對稱的。
等效的肢體配置將用于分析,由于球面和旋轉(zhuǎn)翼比通用和通用的肢體容易分析。四肢的下端連接到兩個自由度的驅(qū)動程序。四肢的上端通過旋轉(zhuǎn)接頭連接到平臺。請注意,在分接頭的軸線是平行線。
我們詳細的定義固定的基礎參考幀和參考幀的移動平臺。該基地的參考框架原點位于三角didzd3質(zhì)心。x正軸平行的向量和點dzd3方向。從點0到點DL y軸正向點。Z軸是由右手法則定義。同樣,該平臺的參考框架原點位于三角p1pzp3質(zhì)心。正是平行和點的方向矢量卵透明帶。從0點到點P1正軸點。W是由右手法則定義。保持迷你機器人對稱,兩個三角形是等邊d1dzd3和p1pzp3。
在本文中,為一個新的封閉形式三肢六自由度迷你機器人直接運動學提出了解法,。結果表明,對迷你機器人直接運動學有十六項。解決方案的最大數(shù)目獲得這些解決方案,只有一個第八度的多項式在一個單變量的平方是要解決。這也證明了十六個解決方案是八對反映結構相對于平面穿過的三肢下端。數(shù)值算例的結果是由一個逆運動學分析驗證。
支持這項研究部分由美國國家科學基金會工程研究中心項目,NSFD CDR 8803012。第一作者感謝美國宇航局/哥達德太空飛行中心的支持。這種支持不構成支持文中支撐機構表達的觀點。
一個三腿并聯(lián)六自由度平臺機構的工作空間分析及優(yōu)化設計
在本文中被認為是一類新的六度自由(自由度)空間并聯(lián)平臺機構。該架構由一個移動平臺連接到基座由三個相同的五連桿機構運動鏈。最近的研究表明,這樣的拓撲結構為腿的并聯(lián)機構可以有效地靜平衡只使用光彈性元件。本文提出了并聯(lián)機構的工作空間分析及優(yōu)化設計。更具體地說,考慮到可能的工業(yè)應用的體系結構作為定位和定向裝置的沉重的負荷,對三維體積最大化的優(yōu)化程序(三維)的機制不變的方位空間了。作為機構也可以有很大的潛力,作為運動基地的飛行模擬器,我們在這里開發(fā)的計算和平移和轉(zhuǎn)動自由度耦合的一個新的工作空間的圖形表示的離散化方法。此工作區(qū)可以被定義為三維空間時可以得到廣義坐標x,在傾斜和扭轉(zhuǎn)角度參數(shù)y和扭轉(zhuǎn)角的ψ不變。然后第二個程序?qū)υ摰诙蛹耐暾墓ぷ骺臻g體積最大化。對于這兩種方法中,我們的目的是通過最大化的相關的3-D直角區(qū)域,自由體積的臨界奇異性位點的嘗試機制的優(yōu)化設計。
六自由度并行電纜驅(qū)動機制的扳手關閉工作區(qū)的測定
一個并行電纜驅(qū)動機構主要包括并聯(lián)連接到由輕到重鏈接如電纜的電纜長度控制允許平臺的姿態(tài)控制底座移動平臺。并行電纜驅(qū)動機構有幾個優(yōu)點超過傳統(tǒng)的剛性連接的機構(Barrette,戈斯林,2005,墨赫萊,2004,羅伯茨等人,1998)。運動部件的質(zhì)量和慣性的減小使得它們更便宜。此外,并行電纜驅(qū)動機構更容易建立,運輸和重新配置,他們有可能工作在一個非常大的空間。因此,并行電纜驅(qū)動機構已被使用,例如在一些應用中,例如,機器人起重機(Dagalakis,等人,1989),高速操作(河村等人,2000),主動懸架裝置(拉富爾卡德,2004年)和虛擬現(xiàn)實(墨赫萊,2004年)。
本文論述了確定的六自由度工作空間并聯(lián)柔索驅(qū)動機構。此工作區(qū)的每根電纜的總長度可能是有限的,之間的電纜連接和電纜之間的移動平臺和移動平臺上的電纜所施加的力,由單向性的干擾。由于電纜的總長度的限制,可以通過算法確定(戈斯林,1990)和(墨赫萊,1999)。然而,工作區(qū)通常不受電纜的總長度影響,從大的總長度一般都可以用。對移動平臺一個恒定的方向,對斜拉索的空間干擾的影響問題已經(jīng)解決(墨赫萊,2004)。第三個限制是由于施加的力,由電纜平臺上的單向性主要是平面并行電纜驅(qū)動機制的案例研究(Barrette,和戈斯林,2005,法塔赫和Agrawal,2005,蓋琳娜和羅薩蒂,2002,茍?zhí)匕l(fā)德和戈斯林,2006,羅伯茨等人,1998,斯頓普和庫馬爾,2004,范霍文和希勒偉,2000,范霍文,2004,威廉姆斯等人,2003)。
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