外文翻譯-連接機(jī)械裝置的缺點(diǎn)和糾正解決方案

1、外文翻譯-連接機(jī)械裝置的缺點(diǎn)和糾正解決方案 河南理工大學(xué)本科畢業(yè)設(shè)計(jì)(論文)外文資料翻譯 題目:Defects in link mechanisms and solution rectification 連接機(jī)械裝置的缺點(diǎn)和糾正解決方案學(xué)院: 機(jī)械與動(dòng)力工程學(xué)院專(zhuān)業(yè): 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班級(jí): 機(jī)制專(zhuān)升本05-1 姓名: 陳 志 明 學(xué)號(hào): 0503050112 指導(dǎo)老師:焦 鋒 連接機(jī)械裝置的缺點(diǎn)和糾正解決方案1、緒論 從Grashof為四桿機(jī)構(gòu)的識(shí)別和分類(lèi)給出規(guī)那么以及Burmester提出中心點(diǎn)和圓點(diǎn)曲線開(kāi)始,連桿機(jī)構(gòu)的缺陷就成為一些研究的主題。即便在1883和1960之間發(fā)表過(guò)很

2、少一局部成果,一直到1967年Filemon提出了一個(gè)圖解設(shè)計(jì)方法來(lái)除去缺陷的時(shí)候,在這方面才出現(xiàn)這個(gè)突破性的成就。從那時(shí)以后每年都會(huì)有許多有關(guān)缺陷的論文發(fā)表。六十年代約25篇,在七十年代大約41篇, 在八十年代大約54篇然而在九十年代只有40篇論文。如此40年來(lái)這個(gè)專(zhuān)業(yè)研究已經(jīng)在全世界展開(kāi),涉及研究人員超過(guò)70個(gè),以論文形式,M.S. 和Ph.D.的論題,論文,專(zhuān)利,公告和其他發(fā)布形式,記錄超過(guò)170項(xiàng),它們以圖解、數(shù)字和計(jì)算等方法研究這些問(wèn)題。這個(gè)課題的持續(xù)穩(wěn)定的開(kāi)展說(shuō)明了它在機(jī)構(gòu)綜合領(lǐng)域的重要性。Filemon是第一個(gè)討論缺陷的人。Waldron,Barker,Gupta 等人是主要的奉

3、獻(xiàn)者。 Chase和Mirth精確的區(qū)分了回路和支路,這是有記錄的缺陷研究方面的重要成果。 在使用 Burmester 曲線進(jìn)行綜合的時(shí)候, 發(fā)現(xiàn)一些解理論上完全能滿足規(guī)定的幾何條件,但是不能滿足真實(shí)的裝配條件。原因是這些機(jī)構(gòu)雖然在規(guī)定的4個(gè)位置是可安裝的,但:1 不能夠在四個(gè)規(guī)定的位置之間連續(xù)地運(yùn)動(dòng)或2 運(yùn)動(dòng)是連續(xù)的,但是位置的次序是錯(cuò)誤的或3 它們?cè)趶囊粋€(gè)位置運(yùn)動(dòng)到另一個(gè)位置時(shí)需要拆開(kāi)才能完成在不拆開(kāi)重新裝配的情況下不能完成這一運(yùn)動(dòng)或4它們變換運(yùn)動(dòng)的方向。 出現(xiàn)這樣一些情況的原因是機(jī)構(gòu)中存在一種或較多的類(lèi)型的缺陷,這些在綜合時(shí)沒(méi)有考慮到。對(duì)機(jī)構(gòu)中這類(lèi)缺陷的研究在40多年來(lái)已經(jīng)引起許多研究者

4、的注意而且它正在繼續(xù)吸引他們。 在這一篇論文中,把關(guān)于這個(gè)課題的能得到的文獻(xiàn)進(jìn)行了回憶。 它在嘗試追尋該領(lǐng)域的歷史,突出其主要開(kāi)展趨勢(shì)并討論重大的奉獻(xiàn)。 文中列出的參考文獻(xiàn)所涉及到的大都為平面連桿機(jī)構(gòu),還一定程度涉及了的空間球面機(jī)構(gòu)。 它是具有相當(dāng)?shù)拇硇?能被廣泛理解的,但并不完整。2. 機(jī)構(gòu)中缺陷的類(lèi)型機(jī)械機(jī)構(gòu)的缺陷可以被分為: Grashof (曲柄)缺陷 順序缺陷 回路缺陷 分支缺陷(變換點(diǎn)或死點(diǎn)位置缺陷) 差的傳動(dòng)角。 回路,支路,順序, Grashof機(jī)構(gòu) 和非Grashof 機(jī)構(gòu)和傳動(dòng)角等知識(shí)對(duì)成功綜合一個(gè)可行機(jī)構(gòu)是根本的知識(shí)。 它對(duì)機(jī)構(gòu)分析也是有用的。 許多動(dòng)力學(xué)家對(duì)設(shè)計(jì)中傳動(dòng)

5、角標(biāo)準(zhǔn)方面作了詳細(xì)的工作。在66這本書(shū)中對(duì)和傳動(dòng)角有關(guān)的工作作了一個(gè)大體回憶 。 因此,這一論文只限于介紹前四類(lèi)缺陷。 方案校正意味著(如果有的話)從方案中消除任一缺陷,以下幾點(diǎn)要求方案校正:?為獲得一個(gè)完全沒(méi)有缺陷的機(jī)構(gòu)。多重缺陷校正的連桿機(jī)構(gòu)可以通過(guò)把Burmester曲線分成多段,使每段都沒(méi)有各種缺陷來(lái)獲得。?減少機(jī)構(gòu)的解空間這樣可以減少得到一個(gè)可行的設(shè)計(jì)的迭代次數(shù)。 如此就減少了綜合所需的時(shí)間。?在某一些情況下是沒(méi)有滿足條件的方案,所以應(yīng)該放棄進(jìn)一步的嘗試和防止尋找解決方案的不必要的時(shí)間浪費(fèi)。?減少功率損失和增加力與運(yùn)動(dòng)傳輸?shù)男省?將過(guò)程編入電腦程序以減少計(jì)算時(shí)間。對(duì)一個(gè)可調(diào)四桿機(jī)構(gòu)

6、,使其一個(gè)或兩個(gè)參數(shù)可自由選擇能夠得到比沒(méi)有自由選擇參數(shù)更好的結(jié)果。這是因?yàn)檫B桿設(shè)計(jì)不僅要滿足根本的方程,同時(shí)它還要滿足如分支、順序問(wèn)題、傳動(dòng)角和效率等要求。4. Grashof 校正 眾所周知,不可能所有的連桿機(jī)構(gòu)都具有能轉(zhuǎn)整周的曲柄。人們常?？释羞@樣一個(gè)曲柄因?yàn)檫B桿機(jī)構(gòu)可以被一個(gè)連續(xù)不斷的旋轉(zhuǎn)電機(jī)驅(qū)動(dòng)。因此在任何綜合過(guò)程中,區(qū)分開(kāi)擁有整轉(zhuǎn)曲柄的方案是非常重要的。這個(gè)問(wèn)題被稱(chēng)為Grashof問(wèn)題,因?yàn)镚rashof準(zhǔn)那么被用來(lái)區(qū)分機(jī)構(gòu)是否具有旋轉(zhuǎn)的曲柄。4.1 Grashof 準(zhǔn)那么(I) 如果l是最長(zhǎng)的連桿,s是最短的連桿,p和q是剩下的平面四桿機(jī)構(gòu)的另外兩桿如果 l+sp+q 那么機(jī)構(gòu)

7、僅有一個(gè)整轉(zhuǎn)的曲柄。(II)最短的桿件必須是曲柄或機(jī)架。如果是曲柄,那么機(jī)構(gòu)是一個(gè)最短連桿為整轉(zhuǎn)曲柄的曲柄搖桿機(jī)構(gòu)。如果最短桿為機(jī)架,這個(gè)機(jī)構(gòu)是一個(gè)輸出和輸入構(gòu)件都轉(zhuǎn)整周的雙曲柄機(jī)構(gòu)。基于Groshof準(zhǔn)那么,機(jī)構(gòu)稱(chēng)為: Grashof 機(jī)構(gòu) 最短桿是整轉(zhuǎn)的曲柄或機(jī)架 非Grashof 機(jī)構(gòu)機(jī)構(gòu)中沒(méi)有整轉(zhuǎn)構(gòu)件。4.2 Grashof (曲柄)缺陷 如果在機(jī)構(gòu)中的沒(méi)有可能轉(zhuǎn)整周的構(gòu)件,那么機(jī)構(gòu)稱(chēng)為具有 Grashof 缺陷的機(jī)構(gòu)。當(dāng)最短的連桿既不是一個(gè)主動(dòng)件也不是機(jī)架構(gòu)件的時(shí)候 , 會(huì)有這種缺陷。舉例來(lái)說(shuō);所有的三搖桿機(jī)構(gòu)除了機(jī)架之外全是搖桿。4.3 Grashof 校正 Grashof 校正意

8、味著Grashof缺陷的除去或選擇只有那些滿足Grashof準(zhǔn)那么的連桿機(jī)構(gòu)。除去Burmester曲線上沒(méi)有Grashof機(jī)構(gòu)局部和識(shí)別出曲線上的滿足Grashof的不等式準(zhǔn)那么的一局部,就可以消除缺陷。為了決定弧線段的Grashof的類(lèi)型,在圓點(diǎn)曲線上找到連桿機(jī)構(gòu)的最短桿是非常必要的。 4.4 Grashof 校正的文獻(xiàn)回憶 Grashof給出了一組準(zhǔn)那么來(lái)把四桿機(jī)構(gòu)識(shí)別并分類(lèi)為雙曲柄、搖桿曲柄和雙搖桿機(jī)構(gòu)。Hain,Beggs和Hartenberg沒(méi)有證明地提到了這些,然而 Blaschke和Muller,Harding和Midha給出了不完全的證明。Filemon和Paul確定了區(qū)別兩

9、種雙搖桿機(jī)構(gòu)的方法。也就是,區(qū)分那些有完全回轉(zhuǎn)的連桿和那些擺動(dòng)的連桿。 他們依以下各項(xiàng)重新表達(dá)了 Grashof準(zhǔn)那么:1 有兩種不同類(lèi)型的雙搖桿機(jī)構(gòu),因此連桿機(jī)構(gòu)共有四種根本類(lèi)型。 2Grashof's 的不等式的滿足對(duì)至今存在一個(gè)回轉(zhuǎn)的曲柄是一個(gè)充分必要條件。 3Grshof判據(jù)的等式形式是機(jī)構(gòu)存在變換點(diǎn)的一個(gè)必要充分條件。 Gupta藉由檢測(cè)傳動(dòng)角的極值直接發(fā)現(xiàn)了相同的等式條件。Kohli和Khonji由分析得到了球面五桿機(jī)構(gòu)組的可轉(zhuǎn)性判據(jù)。他們對(duì)一個(gè)球面的五桿機(jī)構(gòu)推導(dǎo)出了個(gè)別輸入可轉(zhuǎn)性條件及全部可轉(zhuǎn)性條件。 Ting和Tsai為五桿桿組提供了一個(gè)有效簡(jiǎn)單的 Grashof型可動(dòng)

10、性判據(jù)而且把他們分類(lèi)為(i)雙曲柄機(jī)構(gòu)和ii非雙曲柄機(jī)構(gòu)。對(duì)這二種類(lèi)型的工作區(qū)域也進(jìn)行了研究。 Ting提出了五桿機(jī)構(gòu)的Grashof準(zhǔn)那么并證明了與四桿機(jī)構(gòu)Grashof準(zhǔn)那么是相同的。他也把它們分類(lèi)為:i、一級(jí)五桿機(jī)構(gòu): a雙曲柄或三曲柄,b一個(gè)有條件的雙曲柄或單曲柄機(jī)構(gòu)組,c零曲柄機(jī)構(gòu)和 ii 二級(jí)五桿機(jī)構(gòu)-非雙或非三曲柄機(jī)構(gòu),a有條件的雙曲柄機(jī)構(gòu);b單曲柄機(jī)構(gòu); c與輸入和固定構(gòu)件條件有關(guān)的零曲柄機(jī)構(gòu)。 Tting提出了N桿 N連桿數(shù)活動(dòng)性準(zhǔn)那么,用來(lái)控制裝配性和旋轉(zhuǎn)性i以決定任何的單一閉環(huán)N桿運(yùn)動(dòng)鏈的整轉(zhuǎn)性,ii 預(yù)知在任何二個(gè)毗連的構(gòu)件間的可轉(zhuǎn)性,iii 說(shuō)明而且識(shí)別特殊位形的存在

11、 ,iv 分類(lèi)連桿機(jī)構(gòu)v 說(shuō)明在不同的等級(jí)連桿機(jī)構(gòu)之間的特殊位形的差異或識(shí)別他們的之間不能旋轉(zhuǎn)角的差異。Barker給平面四桿機(jī)構(gòu)一個(gè)完全和系統(tǒng)的分類(lèi)由 Grashof,非 Grashof和變換點(diǎn)類(lèi)型所組成。其重要的特性作為解空間的特征外表給出。這些可能被用來(lái)創(chuàng)立設(shè)計(jì)線圖,這些線圖可用來(lái)選擇具有期望特性的機(jī)構(gòu)。 Barker和Shu提出了一個(gè)方法,那個(gè)方法中三個(gè)設(shè)計(jì)位置方程序與無(wú)量綱構(gòu)件長(zhǎng)度的相等偏差狀條件相結(jié)合,得到一個(gè)三次多項(xiàng)式。這個(gè)多項(xiàng)式的根產(chǎn)生可能的解決方案,它們必須進(jìn)行評(píng)估。在缺陷被消除后,剩余的方案產(chǎn)生無(wú)缺陷的 Grashof-曲柄-搖桿- 搖桿和 Grashof- 曲柄- 曲柄-

12、 曲柄機(jī)構(gòu),這些機(jī)構(gòu)在傳動(dòng)角上相等偏差。 Zhao 等人用數(shù)值的方式對(duì)平面機(jī)構(gòu)的可動(dòng)性區(qū)域進(jìn)行了研究。 Williams和Reinholtz給予了Grashof準(zhǔn)那么的證明;使用多項(xiàng)式的 s 定律區(qū)別。Angeles和Callejas提出了Grashof可動(dòng)性準(zhǔn)那么的一個(gè)代數(shù)公式;并采用梯度法對(duì)平面連桿機(jī)構(gòu)進(jìn)行優(yōu)化。 Norton等人 給出了三角形不等式概念用來(lái)證明如果可動(dòng)性角給定,那么存在機(jī)架的鉸鏈點(diǎn)位置解空間的兩個(gè)不同區(qū)域,即 Grashofian 和非Grashofian區(qū)域。Kimbrell 和Hunt討論Grashof和Non-Grashof四桿結(jié)構(gòu)的漸近位形。 Rastegar對(duì)空

13、間機(jī)構(gòu)的可動(dòng)條件引出提出了一個(gè)一般的方法,包括傳動(dòng)角限制。 沒(méi)有這些限制,這些條件必須對(duì)機(jī)構(gòu)的每一對(duì)相似的位形分別導(dǎo)出。Rastegar提出幾何學(xué)的近似值技術(shù)過(guò)去在缺少傳動(dòng)角限制一直為獲得空間RSSR機(jī)構(gòu)的閉環(huán)Grashof- 型可動(dòng)性條件。Sen 和 Mruthyunjaya 以為機(jī)構(gòu)應(yīng)該最好有限制的可轉(zhuǎn)性。整轉(zhuǎn)性不但減少奇異而且給工作空間較好的運(yùn)轉(zhuǎn)精度。如果機(jī)構(gòu)不能整轉(zhuǎn), 首先,他們建議丟棄在模擬試驗(yàn)期間產(chǎn)生沒(méi)有完整的旋轉(zhuǎn)的所有機(jī)構(gòu)。如果機(jī)構(gòu)部份地是旋轉(zhuǎn)的, 全部接受 局部旋轉(zhuǎn)機(jī)構(gòu)直到獲得一個(gè)整轉(zhuǎn)機(jī)構(gòu)。 Gupta等人進(jìn)行了平面和空間機(jī)構(gòu)的可動(dòng)性分析,通過(guò)機(jī)械手手腕設(shè)計(jì)應(yīng)用對(duì)球面的四桿機(jī)構(gòu)

14、可轉(zhuǎn)性準(zhǔn)那么進(jìn)行了靈活性分析。 Angeles和Bernier對(duì)平面四桿機(jī)構(gòu)也做了一樣的工作。 Waldron確定出具有整轉(zhuǎn)曲柄的Burmester綜合方案而且討論了消除掉不需要的 Grashof 位形。Davitasvili設(shè)計(jì)了五桿鉸鏈機(jī)構(gòu)。Ting用證據(jù)證明N- 桿可動(dòng)性定律。Fox和Willmert通過(guò)不等式考慮了角驅(qū)動(dòng)結(jié)束優(yōu)化了曲線生成機(jī)構(gòu)的設(shè)計(jì)。 Alizade 和 Sandor 確定了空間四桿機(jī)構(gòu)的完全轉(zhuǎn)動(dòng)曲柄的存在條件。 Nolle研究了 RSSR 機(jī)構(gòu)運(yùn)動(dòng)的范圍傳遞轉(zhuǎn)移。 Skreiner 識(shí)別了空間四桿機(jī)構(gòu)的可動(dòng)性區(qū)域。 Pamidi 和 Freudenstein 討論了五

15、桿 RCRCR 空間機(jī)構(gòu)的運(yùn)動(dòng)。 Freudenstein 和 Primirose對(duì)變形四桿機(jī)構(gòu)提出了曲柄的標(biāo)準(zhǔn)。Harrisberger 作了空間四桿機(jī)構(gòu)的活動(dòng)型分析,Sticher用橢圓線圖法對(duì)RSSR機(jī)構(gòu)作了同樣的結(jié)構(gòu)分析。Savage和 Soni 對(duì)所有的球面四桿機(jī)構(gòu)作了獨(dú)特的描述。 Paul給出了約束度的統(tǒng)一標(biāo)準(zhǔn)。 Duffy 和 Gilmartin 給出了具有不同運(yùn)動(dòng)列的空間四桿機(jī)構(gòu)的位置限制。 他們也繼續(xù)對(duì)球面四桿機(jī)構(gòu)的可動(dòng)性作了分析。 Jenkin等人研究了空間機(jī)構(gòu)的總體運(yùn)動(dòng)。 Khonji 討論了球面的五桿機(jī)構(gòu)的可轉(zhuǎn)性準(zhǔn)那么。4.5 Grashof類(lèi)型和回路的關(guān)系 Svobo

16、da做了Grashof類(lèi)型校正同時(shí)包括回路校正, Filemon , Waldron ,Barker, Jeng ,Chase和Mirth討論了同樣的問(wèn)題。 Grashof 型四桿機(jī)構(gòu)非變換點(diǎn)機(jī)構(gòu),有二個(gè)回路。非Grashof四桿只有一個(gè)回路。因此任何的非 Grashof解方案保證無(wú)回路缺陷。當(dāng)且僅當(dāng)測(cè)試角 改變?cè)诰_位置之間時(shí) , Grashof 四桿機(jī)構(gòu)變更回路。測(cè)試角是兩個(gè)內(nèi)角之一,在連桿機(jī)構(gòu)最短邊的對(duì)面,在每一個(gè)精確位置都要測(cè)試。它是從最短邊的對(duì)邊到最短邊的相鄰邊逆時(shí)針測(cè)量,在范圍內(nèi)。 Defects in link mechanisms and solution rectificat

17、ion1.Introduction Since from Grashof set the rules for indentifying and classifying the four-bar mechanisms and Burmese presented the center point and circle point curves, the defects in the mechanisms have been the subject of several studies. Even though a very few works are published between 1883

18、and 1960, the break through took place when Filemon proposed a graphical construction to eliminate the defects in 1967 Since then no year went without the publication of a paper on defects. In sixties about 25, in seventies about41, in eighties about54 whereas in nineties as good as 40 works were re

19、ported. Thus the major study has been stretched over 40 years by more than 70 researchers all over the world and recorded in the form of papers, M.S. and Ph.D. theses, reports, patents, bulletins and other publications numbering more than 170 in all graphical, numerical and computational methods. Th

20、e constant growth of the subject shows its importance in the field of syntheses. Filemon appears to be the first person to address many of the defects. Waldron et al., Barker et al., and Gupta et al. are the major contributors. Chase and Mirth distinguished circuit precisely from branch placing the

21、critical study of the defects on records When using the Burmester curves for synthesis, it is discovered that some of the solutions fulfill the prescribed geometrical conditions theoretically but the constructional reality is not met with the cause for this is that these mechanisms-altough mountable

22、 in the four prescribed positions:1 Are not able to move continuously between the four prescribed positions or2 The movement is continuous but the order of positions is wrong or3 They need to be disconnected while moving from one position to the other cannot move without disconnecting and reassembli

23、ng or4 Change the direction of motion The reasons for such situations are the presence of one or more types of the defects in the mechanisms that are not taken care of while synthesizing the mechanisms. Study of such defects in the mechanisms has drawn the attention of many researchers for over four

24、 decades and still it is continuing to attract them In this paper, a review of the literature available on the subject is made. An attempt is made to trace out the history highlighting major trends and discussing significant contributions. The references listed concerned largely to planar link mecha

25、nisms and to some extent spatial spherical mechanisms also. It is fairly representative and comprehensive rather than being complete.2. Types of defects in the mechanism The defects in the mechanisms may be identified as:Grashofs crank defect,order defect,circuit defect,branch defect change point or

26、 dead center position defect,poor transmission angle The knowledge of circuit, branch, order, Grashof and non-Grashof linkages and transmission angle is essential for successful synthesis of a feasible mechanism. It is also useful for analyzing the mechanism. Many kinematicians in detail have dealt

27、with the work on the transmission angle criteria of design. A broad review of works pertaining to the transmission angle is found in. Hence, this paper constrains to the first four types of defects only.3.Need for the solution rectification Solution rectification means the elimination of defects if

28、any from the solution The need for the solution rectification arises also from the following requirements:To get a mechanism completely free from defects. Linkages rectified for multiple defects are obtainable by intersecting the Burmester curve segments free of each defect individually To reduce so

29、lution space of mechanism that tends to reduce the iterations to arrive at a feasible design. Thus to reduce the time required for the synthesis To show that in some cases there are no solutions, which fulfill the conditions so as to give up further trial and to avoid the unnecessary waste of time i

30、n the course of finding the solution To reduce power losses and increase the efficiency of force/motion transmission To make the procedure codable into a computer program and to reduce the computing timeUsually one gets better results by having one or two free choices of parameters for an adjustable

31、 four-bar linkage, than solution without any free choice of parameter. This is because the design of linkage has to satisfy not only the basic equations but also the conditions like branch and order problem. Transmission angle and efficiency.4. Grashof rectificationIt is a known fact that all the li

32、nkages may not posses fully rotatable crank. It is usually desirable to have such a crank so that the linkage can be driven by a continuously rotating motor Therefore in any synthesis procedure it is important to be able to separate solutions, which do possess fully rotating cranks. This problem has

33、 been referred as the “Grashof problem because Grashofs rules areeused to distinguish linkages with fully rotating cranks.4.1. The Grashofs rule ? If l is the length of the longest link, s is the length of the shortest link and p and q are the lengths of the remaining two sides of a planar four-bar

34、mechanism, the linkage can only have a fully rotatable crank if, l + s p + q ? The shortest link must either be a crank or the base. If it is a crank, the linkage is a crank-rocker with the shortest link as fully rotatable crank. If the shortest link is the base, the linkage is a drag link with both

35、 in put and out put links fully rotatable. Based on the rules the mechanisms are named as follows:Grashofs MechanismLinkages in which the shortest link is fully rotatable or the base fixed link Non-Grashofs Mechanism Linkages in which no link is fully rotatable.4.2. Grashof;s crank defect If no link

36、 in the mechanism is capable of rotating fully, the linkage is said to have Grashof defect. This happens when the shortest link is neither a driving link nor a ground link. For example; the triple rocker mechanism in which all the links except the ground links except the ground link are the rockers.

37、4.3. Grashof rectification Grashof rectification means the elimination of Grashof defect or selecting only those linkages , that satisfy the Grashof rule. Deleting the portions of the Burmester curves, which do not give the Grashof mechanism and identifying the segments of curve on which the Grasof

38、inequality is satisfied can de this It is necessary only to locate the shortest link of the linkage given by any circle point on that segment in order to determine the Grashof type everywhere on the segment.4.4. Review of literature on Grashof rectification Grashof gave a set of rules to identify an

39、d classify the four-bar mechanisms into double cranks, rocker cranks and double rockers. Hain, Beyer, Begs and Hartenberg referred these without proof whereas Blaschke and Muller, Harding and Midha et al. published incomplete proofs. Filemon and Paul identified the lacuna to distinguish between the

40、two types of double rockers, i.e., those with fully revolving couplers and those with oscillating couplers. They restated the Grashofs rules as follows; 1 There are tow distinct types of double rockers and therefore four basic types of four-bar linkages. 2 Satisfaction of Grashofs inequality is a su

41、fficient as well as necessary condition for existence of minimum of one revolving crank. 3 Equality form of Grashofs criterion is a necessary and sufficient condition for the existence of change point mechanism Gupta found the same equality conditions more directly by examining the extreme values of

42、 the transmission angle. Kohli and Khonji derived rotatability criteria of spherical five-bar linkages analytically. They developed the conditions of individual input revolvability and the conditions of full rotatability for a spherical five-bar linkage. Ting and Tsai presented an effective and simp

43、le Grashofs type mobility criterion for five-bar linkages and classified them into i double-crank linkages and ii non-double-crank linkages. The working area of two types is also investigated. Ting proposed five-bar Grashofs criterion and proved the same through the use of four-bar Grashofs criterio

44、n. He also classified them into i Class-I five-bar mechanisms: a double crank or triple crank, b a conditional double- or single-crank linkage, c a zero-crank linkage and ii Class-II five-bar mechanisms-non-double-or non-triple-crand linkage;a double crank or triple crand, b single-crank linkage, c

45、a zero-crank linkage depending on the condition of the input and fixed links Ting proposed N-bar N number of links mobility criteria which govern the assemblability and rotatability i to determine the full rotatability of any single-closed-loop N-bar chains,ii to predict the revolvability between an

46、y two adjacent links,iii to explain and identify the existence of singular positions ,iv to classify the linkages and v to explain the difference of singular positions between the linkages of different classes or to identify the difference between their non-revolvable angles Barker gave a complete a

47、nd systematic classification of planar four-bar linkages consisting of Grashofs, non-Grashofs and change point types. The significant properties are presented as characteristic surfaces within the solution space. These can be used to construct design charts permitting the selection of mechanisms wit

48、h desirable properties. Barker and Shu presented a method in which three design position equations are combined with equal deviation condition on the non-dimensional link lengths to produce a third-order polynomial. The roots of this polynomial produce potential solutions, which must be evaluated fo

49、r defets. After the defects are removed, the remaining solutions yield defect-free Grashof-Crand-Rocker-Rocker and Grashof-Crank-Crank-Crank mechanisms, which have equal deviation on the transmission angle. Zhao et al., dealt with mobility region of planar linkage by numerical approach Williams and

50、Reinholtz gave the proof of Grashof;s law using polynomial discriminates.Angeles andCallejas presented an algebraic formulation of Grashof;s mobility criteris with application to planar linkage optimization using gradient-dependent methods. Norton et al. gave the triangle inequality concept used to

51、prove that if the mobility angle is given, two distinct regions of base pivot locations solution space exist, the Grashofian and no-Grashofian region. Kimbrell and Hunt discuss the asymptotic configurations of Grashof and non-Grashof four-bar linkages Rastegar presented a general method for the deri

52、vation of movability conditions for spatial mechanisms that may include transmission angle limitations. In the absence of these limitations, such conditions must be derived separately for each pair of similar configurations of the mechanism. Rastegar presented a geometrical approximation technique u

53、sed to derive closed-form Grashof-type movability conditions for spatial RSSR mechanisms in presence and absence of transmission angle limitations Sen and Mruthyunjaya opine that the mechanism should preferably have finite rotatability. Complete rotatability not only reduces the singularities but also gives workspace of better accuracy of performance. If the mechanism is not fully rotatable, to start with, they suggest