工業(yè)機(jī)器人設(shè)計(jì)【三自由度 圓柱坐標(biāo)式氣壓驅(qū)動(dòng)】【11張CAD圖紙+PDF圖】
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無錫太湖學(xué)院
畢業(yè)設(shè)計(jì)(論文)
題目: 工業(yè)機(jī)器人設(shè)計(jì)
機(jī)電 系 機(jī)械工程及自動(dòng)化 專業(yè)
學(xué) 號(hào): 0923195
學(xué)生姓名: 白文杰
指導(dǎo)教師: 黃敏 (職稱:副教授 )
2012年5月25日
7
無錫太湖學(xué)院本科畢業(yè)設(shè)計(jì)(論文)
誠 信 承 諾 書
本人鄭重聲明:所呈交的畢業(yè)設(shè)計(jì)(論文) 工業(yè)機(jī)器人設(shè)計(jì) 是本人在導(dǎo)師的指導(dǎo)下獨(dú)立進(jìn)行研究所取得的成果,其內(nèi)容除了在畢業(yè)設(shè)計(jì)(論文)中特別加以標(biāo)注引用,表示致謝的內(nèi)容外,本畢業(yè)設(shè)計(jì)(論文)不包含任何其他個(gè)人、集體已發(fā)表或撰寫的成果作品。
班 級(jí): 機(jī)械94
學(xué) 號(hào): 0923195
作者姓名:
2013 年 5 月 25 日
無錫太湖學(xué)院
機(jī)械 系 機(jī)電一體化 專業(yè)
畢 業(yè) 設(shè) 計(jì)論 文 任 務(wù) 書
一、題目及專題:
1、題目 工業(yè)機(jī)器人設(shè)計(jì)
2、專題
二、課題來源及選題依據(jù)
工業(yè)機(jī)器人對(duì)于人類來說是當(dāng)今世界最為突出的發(fā)明之一,人類對(duì)機(jī)器人深入的進(jìn)行研究。在上個(gè)世紀(jì)的70年代以后,計(jì)算機(jī)技術(shù)、控制技術(shù)、傳感技術(shù)和人工智能技術(shù)的迅速發(fā)展,工業(yè)機(jī)器人的研究也進(jìn)入了高速發(fā)展的階段,成為綜合了計(jì)算機(jī)、控制論、機(jī)構(gòu)學(xué)、信息和傳感技術(shù)、人工智能、仿生學(xué)等多門學(xué)科而形成的高新技術(shù)。其本質(zhì)是感知、決策、行動(dòng)和交互四大技術(shù)的綜合,是當(dāng)代研究十分活躍,應(yīng)用日益廣泛的一項(xiàng)技術(shù)。機(jī)器人應(yīng)用水平是一個(gè)國家工業(yè)自動(dòng)化水平的重要標(biāo)志。
本課程通過對(duì)工業(yè)機(jī)器人設(shè)計(jì),幫助自身加深對(duì)的理解和提高對(duì)其專業(yè)知識(shí)機(jī)械原理、機(jī)械設(shè)計(jì)、材料力學(xué)機(jī)器人、傳動(dòng)、實(shí)體建模、有限元分析等方面的相關(guān)內(nèi)容的運(yùn)用能力。
三、 本設(shè)計(jì)(論文或其他)應(yīng)達(dá)到的要求:
①了解工業(yè)機(jī)器人設(shè)計(jì)原理,國內(nèi)外的研究發(fā)展現(xiàn)狀;
② 完成工業(yè)機(jī)器人設(shè)計(jì)的總體方案設(shè)計(jì);
③完成有關(guān)零部件的選型計(jì)算、結(jié)構(gòu)強(qiáng)度校核及氣動(dòng)系統(tǒng)設(shè)計(jì);
④熟練掌握有關(guān)計(jì)算機(jī)繪圖軟件,并繪制裝配圖和零件圖紙,折合A0不少于2.5張;
⑤完成設(shè)計(jì)說明書的撰寫,并翻譯外文資料1篇 。
四、接受任務(wù)學(xué)生:
機(jī)械94 班 姓名 白文杰
五、開始及完成日期:
自2012年11月12日 至2013年5月25日
六、設(shè)計(jì)(論文)指導(dǎo)(或顧問):
指導(dǎo)教師 簽名
簽名
簽名
教研室主任
〔學(xué)科組組長研究所所長〕 簽名
系主任 簽名
2013年11月12日
摘 要
在生產(chǎn)過程工業(yè)機(jī)械手是模擬人手動(dòng)作的機(jī)械設(shè)備,它可以替代人工搬運(yùn)重物或單調(diào),在高粉塵,高溫,有毒,易燃,放射性和其他相對(duì)較差的工作環(huán)境。機(jī)器人可用于在生產(chǎn)過程中的自動(dòng)化抓住并移動(dòng)工件自動(dòng)化設(shè)備,它是在生產(chǎn)過程的機(jī)械化和自動(dòng)化,開發(fā)出一種新的類型的設(shè)備。近年來,隨著電子技術(shù),特別是計(jì)算機(jī)的廣泛使用機(jī)器人的開發(fā)和生產(chǎn)的高科技領(lǐng)域已成為迅速發(fā)展起來的一項(xiàng)新興技術(shù),它更促進(jìn)機(jī)器人的發(fā)展,使得機(jī)械手能更好地實(shí)現(xiàn)與機(jī)械化和自動(dòng)化的有機(jī)結(jié)合。機(jī)械手能夠代替人類完成危險(xiǎn)、減輕人類勞動(dòng)強(qiáng)度、重復(fù)枯燥的工作,提高勞動(dòng)生產(chǎn)力。
本設(shè)計(jì)是關(guān)于三自由度的圓柱形機(jī)械手。利用Auto CAD軟件對(duì)制件進(jìn)行設(shè)計(jì)繪圖。其包括夾持器、小臂、大臂和底座。明確合理的設(shè)計(jì)思路,確定了機(jī)械手工作原理并對(duì)然夾持器、氣缸、步進(jìn)電機(jī)、軸承進(jìn)行了校核計(jì)算并附帶了簡圖并對(duì)零件的質(zhì)量、重心、慣性主軸和慣性力矩進(jìn)行輔助設(shè)計(jì)計(jì)算,可以大大減輕在設(shè)計(jì)過程中繁瑣計(jì)算及校核步驟。
關(guān)鍵字:機(jī)械手,氣缸,校核。
Abstract
Industrial manipulator is the mechanical equipment which is used in the production process and simulate to the behave of hands with electrical integration. It can carry heavy objects and work in the harsh environment which is high temperature, poisonous ,full of dust, flammable and combustible monotonous and full of radioactive substance instead of people. Manipulator is a automatic device which is used in the automatic production process and it can carry and move things. It is a new device which is developed in the mechanization and automatic production process. In recent years , with the widely used of electronic technique especially the electronic computer. The research and production of robot has became a new technology which is developing rapidly in the high-tech industry . It promotes the development of manipulator. It makes the combination of the manipulator with mechanization and automation become easier . Manipulator can complete the dangerous and boring work instead of people. It can reduce labour intensity of people and raise the labour productivity .
This design is a cylindrical manipulator which is related to delta degrees of freedom. It designs and draws the picture with Auto cad software ,it includes holder, a small arm, the big arm and the base. The clear and reasonable thinking determines the working principle of the manipulator . This also checks and calculates the holder, cylinder, stepper motor and bearing. Apart from this , it contains some pictures and design and measure the quality , barycentre principal axis of inertia and force of parts. It can greatly reduce the complicated calculation and check in the design process.
Keywords: robot, cylinder, checking
目錄
摘 要 III
ABSTRACT IV
目錄 V
1 緒論 1
1.1 本課題研究的內(nèi)容和意義 1
1.2 國內(nèi)外發(fā)展概況 1
1.3 工業(yè)機(jī)械手設(shè)計(jì)內(nèi)容 2
1.4 機(jī)械手設(shè)計(jì)的作用 2
1.5 工業(yè)機(jī)械手的分類和組成 2
2 手部的設(shè)計(jì) 5
2.1 機(jī)械手設(shè)計(jì)參數(shù)和運(yùn)動(dòng)方案 5
2.1.1 運(yùn)動(dòng)方案 5
2.1.2 驅(qū)動(dòng)系統(tǒng)和位置檢測裝置的選擇: 5
2.2 手部設(shè)計(jì)的結(jié)構(gòu)和計(jì)算 6
2.2.1 機(jī)械手的基本要求 6
2.3 手部力的計(jì)算 7
2.3.1 夾緊力的計(jì)算 7
2.3.2 手爪驅(qū)動(dòng)氣缸的設(shè)計(jì) 8
2.3.3 手部誤差的分析 10
3 機(jī)械手臂的設(shè)計(jì) 12
3.1 機(jī)械小臂設(shè)計(jì) 12
3.1.1 小臂驅(qū)動(dòng)力的計(jì)算 12
3.1.2 小臂驅(qū)動(dòng)氣缸的設(shè)計(jì) 13
3.1.3 氣缸筒壁厚的計(jì)算 14
3.1.4 氣缸的選用 14
3.1.5 校核活塞的穩(wěn)定性 14
3.1.6 小臂剛度校核 15
3.1.7 端蓋的連接方式及強(qiáng)度計(jì)算 15
3.2 大臂的結(jié)構(gòu)設(shè)計(jì) 17
3.2.1 大臂的結(jié)構(gòu)和要求 17
3.2.2 驅(qū)動(dòng)力的計(jì)算 17
3.2.3 大臂驅(qū)動(dòng)氣缸的設(shè)計(jì) 17
3.2.4 氣缸的選擇 18
3.2.5 校核活塞的穩(wěn)定性 18
3.2.6 大臂剛度校核 19
4 驅(qū)動(dòng)系統(tǒng)設(shè)計(jì) 20
4.1 軸承的設(shè)計(jì) 20
4.1.1 軸承的選擇 20
4.1.2 軸承的計(jì)算: 20
4.1.3 軸承的壽命校核: 21
4.2 電機(jī)的基本情況和選擇 22
4.2.1 電機(jī)的選則與計(jì)算 22
4.2.2 注意事項(xiàng) 23
4.2.3 工作原理 24
4.2.4 步進(jìn)電機(jī)的特點(diǎn) 24
4.3 諧波減速器 24
4.3.1 諧波減速器的簡介 24
4.3.2 諧波減速器的設(shè)計(jì) 25
4.4 腰座的結(jié)構(gòu) 26
5 總 結(jié) 28
致 謝 29
參考文獻(xiàn) 30
附 錄 31
1 緒論
1.1 本課題研究的內(nèi)容和意義
機(jī)械工業(yè)是國民的基本部分。工業(yè)機(jī)械手的設(shè)計(jì)是一項(xiàng)綜合設(shè)計(jì)與機(jī)械制造,機(jī)電工程等專業(yè)聯(lián)系一起。通過這次設(shè)計(jì)提高學(xué)生的機(jī)構(gòu)分析能力,機(jī)電一體化機(jī)械結(jié)構(gòu)設(shè)計(jì)的設(shè)計(jì)能力提升。來學(xué)習(xí)一些生產(chǎn)時(shí)的設(shè)計(jì)方法。
工業(yè)機(jī)械手是近十年來發(fā)展起來的,一種高科技自動(dòng)生產(chǎn)。這體現(xiàn)了人類智能和適應(yīng)性,機(jī)械手能在各個(gè)環(huán)境下完成作業(yè)能力,在國民經(jīng)濟(jì)發(fā)展中起著重要的作用,具有很廣闊的前景。近20年來,氣動(dòng)技術(shù)的運(yùn)用領(lǐng)域迅速拓寬,尤其在各個(gè)生產(chǎn)線上的應(yīng)用??删幊炭刂坪蜌鈩?dòng)驅(qū)動(dòng)相結(jié)合,使整個(gè)自動(dòng)化系統(tǒng)更高級(jí)??刂聘拥撵`敏,性能更佳的可靠。
工業(yè)機(jī)械手設(shè)計(jì)是機(jī)械設(shè)計(jì),機(jī)電一體化,機(jī)械制造等我們學(xué)習(xí)的專業(yè)中一個(gè)重要的環(huán)節(jié),是學(xué)完有關(guān)專業(yè)課和教學(xué)基礎(chǔ)課程的一次專業(yè)的綜合設(shè)計(jì)。學(xué)生的機(jī)械結(jié)構(gòu)設(shè)計(jì)和分析綜合能力都得到了有效的提高。通過這次學(xué)習(xí)得到了掌握生場自動(dòng)化的設(shè)計(jì)技能。
經(jīng)過這次設(shè)計(jì),可以把有聯(lián)系的課程(氣動(dòng)技術(shù),機(jī)械設(shè)計(jì),機(jī)械原理,測試技術(shù),危機(jī)計(jì)算機(jī)原理等)中我們所知道的理論性知識(shí)加以運(yùn)用,從而得到鞏固和發(fā)展,讓理論和實(shí)際得到了更好的結(jié)合。所以說機(jī)械手設(shè)計(jì)是一門比較綜合的設(shè)計(jì)。
經(jīng)過這次設(shè)計(jì),培養(yǎng)了學(xué)生獨(dú)立分析機(jī)械設(shè)計(jì)的能力,樹立了正確的設(shè)計(jì)思想和思維,掌握了機(jī)電一體化一些機(jī)電產(chǎn)品的步驟和基本設(shè)計(jì)方法,這樣為今后自動(dòng)化的設(shè)計(jì)打下了良好的基礎(chǔ)。
通過本次的機(jī)械手的設(shè)計(jì),讓學(xué)生熟練的去掌握和運(yùn)用一些相關(guān)的知識(shí),比如參考資料還有范文章結(jié)構(gòu)。是學(xué)生具有一個(gè)設(shè)計(jì)人員應(yīng)該具有的基本設(shè)計(jì)技能[1]。
1.2 國內(nèi)外發(fā)展概況
現(xiàn)在對(duì)于國內(nèi)的情況,機(jī)械手大部分的使用在各個(gè)領(lǐng)域。比如:在冷加工工業(yè)里還有在機(jī)床的加工上。當(dāng)然我們?cè)谏a(chǎn)過程中會(huì)有很多的困難。比如說:形式復(fù)雜和環(huán)境溫度過于高這些都影響著生產(chǎn)。但我們可以提供這方面的技術(shù)解決困難,讓機(jī)械手更好的工作為了更好的得機(jī)械手的能力,我們要提高它的性能和速度。在其它行業(yè)和工業(yè)部門,也隨著工業(yè)技術(shù)水平的不斷提高,而逐步擴(kuò)大機(jī)械手的使用。
現(xiàn)在對(duì)于國外在行業(yè)中運(yùn)用機(jī)械手有很多。美國首先把機(jī)械手運(yùn)用于搬運(yùn)一些對(duì)人體具有傷害的放射性物質(zhì)。國外實(shí)質(zhì)上是使用的是定位控制機(jī)械手,他沒有視覺上和觸覺上的反饋。世界各地正在積極地研究視覺和觸覺上有反饋的機(jī)械手,讓他能夠準(zhǔn)確的來定位工件的位置和準(zhǔn)確的夾持工件。為了判斷機(jī)械手抓取的是否是工件,她有視覺傳感器輸入
三個(gè)方向的視覺的信息,因此,在計(jì)算機(jī)圖形分析,以確定是否抓取工件。目前主要運(yùn)用在機(jī)床,壓力機(jī)的下料和橫斷壓力機(jī)的下料,以及噴漆和點(diǎn)焊等作業(yè)。在國外發(fā)展機(jī)械手的趨勢(shì)是加大力度研制具有某種智能能力的機(jī)械手。讓其具有一定的傳感的能力,對(duì)于外界的變化能夠反饋,并相應(yīng)的做出反應(yīng)和變更。如果有一個(gè)位置稍有偏差,即是能夠自我糾正,但也可以檢測,強(qiáng)調(diào)視覺功能和觸覺功能的研究。已經(jīng)取得了一些成果。世界高端工業(yè)機(jī)器人,高精密,高速,多軸,輕量級(jí)的趨勢(shì)。符合要求的微米和亞微米級(jí)的定位精度,它的運(yùn)行速度可達(dá)到3M/S的新產(chǎn)品,以實(shí)現(xiàn)六軸負(fù)載2KG生產(chǎn)系統(tǒng)量已超過總重量為100KG。更重要的是,機(jī)器人手的柔性制造系統(tǒng)和柔性制造單元相結(jié)合,從根本上改變當(dāng)前系統(tǒng)的手動(dòng)操作的機(jī)械制造狀態(tài)。同時(shí),隨著機(jī)器人和小型化再小型化,其應(yīng)用將超過傳統(tǒng)的機(jī)械領(lǐng)域,向電子,生物,生命及科學(xué),航空和航天等高端產(chǎn)業(yè)方向上發(fā)展。
1.3 工業(yè)機(jī)械手設(shè)計(jì)內(nèi)容
機(jī)電一體化技術(shù)是集合機(jī)械工程、傳感技術(shù)、信息處理技術(shù)等形成的一種綜合的技術(shù)。盡管機(jī)電一體化的產(chǎn)品種類比較多,但由于他們形式和復(fù)雜程度還有功能的不同,做工的機(jī)械本體部分是最基本的,必不可少的因素。工業(yè)機(jī)械手的設(shè)計(jì)在內(nèi)容和知識(shí)還有深度上都是適中的。
我們所要設(shè)計(jì)的是擬定整體的方案,驅(qū)動(dòng)裝置和傳動(dòng)裝置的方案。根據(jù)自由度選擇和合適的參數(shù)選擇合適的手部和腕部還有臂和機(jī)身的結(jié)構(gòu)。完成各部分的計(jì)算。工業(yè)機(jī)械手工作裝配圖的設(shè)計(jì)與繪制。氣壓系統(tǒng)的設(shè)計(jì)。機(jī)械手的運(yùn)動(dòng)分析。最后寫上說明書。
1.4 機(jī)械手設(shè)計(jì)的作用
機(jī)械手的廣泛運(yùn)用可以歸納為以下幾方面:
1)建造軸類、盤類、環(huán)類的自動(dòng)線。一般采用的都是機(jī)械手在傳送帶之間或機(jī)床之間傳送工件。深井泵廠自動(dòng)生產(chǎn)線在沈陽和大連軸承4軸和5軸加工自動(dòng)馬達(dá)線軸等,已成為國內(nèi)汽車生產(chǎn)線。
2)在實(shí)現(xiàn)單機(jī)自動(dòng)化方面。各種的半自動(dòng)化機(jī)床都有夾緊、進(jìn)刀、切削、退刀和松開等反面的功能。不過還需要人去上下料。如果實(shí)現(xiàn)自動(dòng)化只需要一個(gè)人去看管機(jī)器?,F(xiàn)在機(jī)械手在這方面運(yùn)用的有很多。一些國產(chǎn)機(jī)在出廠時(shí)附帶機(jī)械手,安裝機(jī)器人的用戶提供了條件。
3)國內(nèi)大規(guī)模生產(chǎn)3T,5T,10T鍛造錘,轉(zhuǎn)一轉(zhuǎn)爐下部,兩個(gè)機(jī)器人放置在爐子前有一定的角度,從而使材料的自動(dòng)化。
總的來說:對(duì)環(huán)境的適應(yīng)性強(qiáng),能代替危險(xiǎn)的事物和對(duì)人有害的操作,長時(shí)間工作對(duì)人有害的場所,對(duì)于機(jī)械手是沒有影響的。只要合理的設(shè)計(jì),合理的選材就可以在高溫、有害氣體、放射性物質(zhì)、滅火等環(huán)境中都能自如的工作。
機(jī)械手的持久度和耐勞性能強(qiáng),可以把人們從單調(diào)的勞動(dòng)中解救出來。甚至擴(kuò)大了人的功能,他進(jìn)行適當(dāng)?shù)木S修、檢修即能實(shí)現(xiàn)長時(shí)間的單調(diào)重復(fù)的工作,有與機(jī)械手工作精確度高,可以避免認(rèn)為的操作錯(cuò)誤。
機(jī)械手靈活性好,能適應(yīng)產(chǎn)品的變化。因?yàn)闄C(jī)械手的運(yùn)動(dòng)程序和運(yùn)動(dòng)位置能夠十分靈活的改變。因?yàn)樗淖杂啥?,又能提供迅速改變作業(yè)內(nèi)容。在小批量生產(chǎn)中,起著重要的作用。采用機(jī)械手能明顯提高勞動(dòng)生產(chǎn)效率和生產(chǎn)成本。
存檔編碼:無無錫錫太太湖湖學(xué)學(xué)院院 2013 屆屆畢畢業(yè)業(yè)作作業(yè)業(yè)周周次次進(jìn)進(jìn)度度計(jì)計(jì)劃劃、檢檢查查落落實(shí)實(shí)表表 系別:信機(jī)系 班級(jí):機(jī)械94 學(xué)生姓名:白文杰 課題(設(shè)計(jì))名稱:工業(yè)機(jī)器人設(shè)計(jì) 開始日期:2012年11月12日周次起止日期工作計(jì)劃、進(jìn)度每周主要完成內(nèi)容存在問題、改進(jìn)方法指導(dǎo)教師意見并簽字備 注1-32012年11月12日-2012年12月2日教師下達(dá)畢業(yè)設(shè)計(jì)任務(wù),學(xué)生初步閱讀資料,完成畢業(yè)設(shè)計(jì)開題報(bào)告。按照任務(wù)書要求查閱論文相關(guān)參考資料,填寫畢業(yè)設(shè)計(jì)開題報(bào)告書存在問題:書寫格式有錯(cuò)誤,對(duì)課題理解程度不夠,分析有所欠缺。改進(jìn)方法:在指導(dǎo)老師的幫助下,對(duì)課題有較深的了解。4-102012年12月3日-2013年1月20日指導(dǎo)專業(yè)實(shí)訓(xùn)機(jī)械設(shè)計(jì)綜合實(shí)訓(xùn)存在問題:機(jī)械部件設(shè)計(jì)不夠完善,缺少經(jīng)驗(yàn)。改進(jìn)方法:了解機(jī)械設(shè)計(jì)的詳細(xì)過程。11-122013年1月21日-3月1日指導(dǎo)畢業(yè)實(shí)習(xí)相關(guān)機(jī)械制造廠實(shí)習(xí),了解本專業(yè)的實(shí)踐知識(shí)存在問題:沒有實(shí)習(xí)實(shí)訓(xùn)的經(jīng)驗(yàn),無法將課本知融會(huì)貫通。改進(jìn)方法:認(rèn)真參與工作,虛心求教。132013年3月4日-3月8日查閱參考資料查閱與設(shè)計(jì)有關(guān)的參考資料不少于10篇,其中外文不少于5篇存在問題:查閱資料相關(guān)度小,無法滿足要求。改進(jìn)方法:利用空余時(shí)間,去圖書館查找相關(guān)資料,在網(wǎng)上查找相關(guān)文獻(xiàn)。142013年3月11日-3月15日翻譯外文資料翻譯機(jī)械方面的外文資料存在問題:專業(yè)英文水平較低,無法正確翻譯專業(yè)詞匯。改進(jìn)方法:借助一些翻譯軟件、專業(yè)字典幫助翻譯提高翻譯準(zhǔn)確性性。152013年3月18日-3月22日工業(yè)機(jī)械手設(shè)計(jì)的整體分析分析各種結(jié)構(gòu)的設(shè)計(jì)存在問題:缺乏設(shè)計(jì)經(jīng)驗(yàn),零件選擇不確定。改進(jìn)方法:通過比較決定最后方案。162013年3月25日-4月1010日繪制裝配圖初步繪制裝配圖存在問題:零部件配合有錯(cuò)誤。改進(jìn)方法:重新設(shè)計(jì)并繪制相關(guān)部件。172013年4月10日-4月1919日繪制裝配圖修改完成裝配圖存在問題:不能完全體現(xiàn)沖模細(xì)節(jié)。改進(jìn)方法:繪制局部視圖,體現(xiàn)細(xì)節(jié)。182013年4月2020日-4月2525日零件部設(shè)計(jì)對(duì)機(jī)械夾持器、電機(jī)等的設(shè)計(jì)和選擇存在問題:夾持器尺寸計(jì)算選擇方案。改進(jìn)方法:選擇滑槽桿夾持器進(jìn)行計(jì)算。19-202013年4月25日-4月3030日繪制零件圖繪制底座、活塞、夾持器等存在問題:標(biāo)注尺寸不全,圖紙表示不全面。改進(jìn)方法:檢查標(biāo)注,繪制局部剖圖。212013年4月3131日-5月5 5日設(shè)計(jì)說明書(論文)、摘要和小結(jié)編寫完成設(shè)計(jì)說明書(論文)、摘要和小結(jié)存在問題:說明書的格式不規(guī)范,摘要不合理要求等。改進(jìn)方法:根據(jù)畢業(yè)設(shè)計(jì)的規(guī)范要求更改,重新按要求編寫摘要。222013年5月6日-5月10日修改設(shè)計(jì)說明書(論文)格式修改設(shè)計(jì)說明書開題報(bào)告格式存在問題:附錄格式不規(guī)范,摘要英文不合理要求等。改進(jìn)方法:根據(jù)畢業(yè)設(shè)計(jì)的規(guī)范要求更改。232013年5月13日-5月17日上交資料、準(zhǔn)備答辯整理所有資料,打印后上交,準(zhǔn)備答辯按學(xué)院要求整理并裝訂 說明:1、“工作計(jì)劃、進(jìn)度”、“指導(dǎo)教師意見并簽字”由指導(dǎo)教師填寫,“每周主要完成內(nèi)容”,“存在問題、改進(jìn)方法”由學(xué)生填寫。2、本表由各系妥善歸檔,保存?zhèn)洳?。周次起止日期工作?jì)劃、進(jìn)度每周主要完成內(nèi)容存在問題、改進(jìn)方法指導(dǎo)教師意見并簽字備 注編號(hào)
無錫太湖學(xué)院
畢業(yè)設(shè)計(jì)(論文)
相關(guān)資料
題目: 工業(yè)機(jī)器人設(shè)計(jì)
機(jī)電 系 機(jī)械工程及自動(dòng)化專業(yè)
學(xué) 號(hào): 0923195
學(xué)生姓名: 白文杰
指導(dǎo)教師: 黃敏(職稱:副教授)
2013年5月25日
無錫太湖學(xué)院
畢業(yè)設(shè)計(jì)(論文)
開題報(bào)告
題目: 工業(yè)機(jī)器人設(shè)計(jì)
機(jī)電 系 機(jī)械工程及自動(dòng)化 專業(yè)
學(xué) 號(hào): 0923195
學(xué)生姓名: 白文杰
指導(dǎo)教師: 黃敏 (職稱:副教授)
2012年11月25日
課題來源
自擬
科學(xué)依據(jù)(包括課題的科學(xué)意義;國內(nèi)外研究概況、水平和發(fā)展趨勢(shì);應(yīng)用前景等)
機(jī)器人是二十世紀(jì)人類最偉大的發(fā)明之一,人類對(duì)于機(jī)器人的研究由來已久。上世紀(jì)70年代之后,計(jì)算機(jī)技術(shù)、控制技術(shù)、傳感技術(shù)和人工智能技術(shù)迅速發(fā)展,機(jī)器人技術(shù)也隨之進(jìn)入高速發(fā)展階段,成為綜合了計(jì)算機(jī)、控制論、機(jī)構(gòu)學(xué)、信息和傳感技術(shù)、人工智能、仿生學(xué)等多門學(xué)科而形成的高新技術(shù)。其本質(zhì)是感知、決策、行動(dòng)和交互四大技術(shù)的綜合,是當(dāng)代研究十分活躍,應(yīng)用日益廣泛的領(lǐng)域。機(jī)器人應(yīng)用水平是一個(gè)國家工業(yè)自動(dòng)化水平的重要標(biāo)志。
機(jī)器人技術(shù)的研究在經(jīng)歷了第一代示教再現(xiàn)型機(jī)器人和第二代感知型機(jī)器人兩個(gè)階段之后進(jìn)入第三代智能機(jī)器人的發(fā)展階段。
機(jī)械手是在自動(dòng)化生產(chǎn)過程中使用的一種具有抓取和移動(dòng)工件功能的自動(dòng)化裝置,它是在機(jī)械化、自動(dòng)化生產(chǎn)過程中發(fā)展起來的一種新型裝置。近年來,隨著電子技術(shù)特別是電子計(jì)算機(jī)的廣泛應(yīng)用,機(jī)器人的研制和生產(chǎn)已成為高技術(shù)領(lǐng)域內(nèi)迅速發(fā)展起來的一門新興技術(shù),它更加促進(jìn)了機(jī)械手的發(fā)展,使得機(jī)械手能更好地實(shí)現(xiàn)與機(jī)械化和自動(dòng)化有機(jī)結(jié)合。機(jī)械手能代替人類完成危險(xiǎn)、重復(fù)枯燥的工作,減輕人類勞動(dòng)強(qiáng)度,提高勞動(dòng)生產(chǎn)率。機(jī)械手越來越廣泛地得到了應(yīng)用,在機(jī)械行業(yè)中它可用于零部件組裝 ,加工工件的搬運(yùn)、裝卸,特別是在自動(dòng)化數(shù)控機(jī)床、組合機(jī)床上使用更普遍。目前,機(jī)械手已發(fā)展成為柔性制造系統(tǒng)FMS和柔性制造單元FMC中一個(gè)重要組成部分。把機(jī)床設(shè)備和機(jī)械手共同構(gòu)成一個(gè)柔性加工系統(tǒng)或柔性制造單元,它適應(yīng)于中、小批量生產(chǎn),可以節(jié)省龐大的工件輸送裝置,結(jié)構(gòu)緊湊,而且適應(yīng)性很強(qiáng)。當(dāng)工件變更時(shí),柔性生產(chǎn)系統(tǒng)很容易改變,有利于企業(yè)不斷更新適銷對(duì)路的品種,提高產(chǎn)品質(zhì)量,更好地適應(yīng)市場競爭的需要。
此外,醫(yī)療機(jī)器人是目前國外機(jī)器人研究領(lǐng)域中最活躍、投資最多的方向之一,其發(fā)展前景非??春?。近年來,醫(yī)療機(jī)器人技術(shù)引起美、法、德、意、日等國家學(xué)術(shù)界的極大關(guān)注, 研究工作蓬勃興起。二十世紀(jì)九十年代起,國際先進(jìn)機(jī)器人計(jì)劃已召開過的多屆醫(yī)療外科機(jī)器人研討會(huì)己經(jīng)立項(xiàng),開展基于遙控操作的外科研究,用于戰(zhàn)傷模擬手術(shù)、手術(shù)培訓(xùn)、解剖教學(xué)。歐盟、法國國家科學(xué)研究中心也將機(jī)器人輔助外科手術(shù)及虛擬外科手術(shù)仿真系統(tǒng)作為重點(diǎn)研究發(fā)展的項(xiàng)目之一在發(fā)達(dá)國家已經(jīng)出現(xiàn)醫(yī)療,外科手術(shù)機(jī)器人市場化產(chǎn)品,并在臨床上開展了大量病例研究。韓國和新加坡的機(jī)器人密度(即制造業(yè)中每萬名雇員占有的工業(yè)機(jī)器人數(shù)量)居世界第1-3位,包攬了前三名。西歐的意大利、法國、英國和東面的匈牙利、波蘭等,機(jī)器人制造業(yè)及應(yīng)用機(jī)器人的情況都有很大發(fā)展
研究內(nèi)容
(1) 了解工業(yè)機(jī)械人的工作原理,國內(nèi)外的研究發(fā)展現(xiàn)狀。
(2) 完成工業(yè)機(jī)器人的總體方案設(shè)計(jì)(包括行走機(jī)構(gòu),回轉(zhuǎn)機(jī)構(gòu)、夾持結(jié)構(gòu))等。
(3) 完成有關(guān)零部件的選型計(jì)算、結(jié)構(gòu)強(qiáng)度校核計(jì)算;
(4) 熟練掌握有關(guān)計(jì)算機(jī)繪圖軟件,并繪制裝配圖和零件圖紙,折合A0不少于2.5張。
(5) 完成設(shè)計(jì)說明書的撰寫,并翻譯外文資料1篇。
擬采取的研究方法、技術(shù)路線、實(shí)驗(yàn)方案及可行性分析
工業(yè)機(jī)器人目前已成為大規(guī)模制造業(yè)中作自動(dòng)化生產(chǎn)線上的重要成員。工業(yè)機(jī)器人的技術(shù)水平和應(yīng)用程度在一定程度上反映了一個(gè)國家工業(yè)自動(dòng)化的水平。
本課題屬工程設(shè)計(jì)類課題,要求完成工業(yè)機(jī)器人的總體和零部件結(jié)構(gòu)設(shè)計(jì)。通過本設(shè)計(jì),可以幫助學(xué)生加深對(duì)本專業(yè)的相關(guān)知識(shí)理解和提高綜合運(yùn)用專業(yè)知識(shí)能力。
研究計(jì)劃及預(yù)期成果
研究計(jì)劃:
2012年11月12日-2012年12月25日:按照任務(wù)書要求查閱論文相關(guān)參考資料。填寫畢業(yè)設(shè)計(jì)開題報(bào)告書。
2013年1月11日-2013年3月5日:填寫畢業(yè)實(shí)習(xí)報(bào)告。
2013年3月8日-2013年3月14日:按照要求修改畢業(yè)設(shè)計(jì)開題報(bào)告。
2013年3月15日-2013年3月21日:學(xué)習(xí)并翻譯一篇與畢業(yè)設(shè)計(jì)相關(guān)的英文材料。
2013年3月22日-2013年4月11日:分析全自動(dòng)機(jī)械手中“臂”機(jī)構(gòu)的基本原理,基本理論及方法;全自動(dòng)機(jī)械手中“臂”機(jī)構(gòu)的傳動(dòng)設(shè)計(jì)及基本設(shè)計(jì)計(jì)算。
2013年4月12日-2013年4月25日:全自動(dòng)機(jī)械手中“臂”機(jī)構(gòu)的設(shè)計(jì)、結(jié)構(gòu)圖、裝配圖設(shè)計(jì);全自動(dòng)機(jī)械手中“臂”機(jī)構(gòu)傳動(dòng)分析研究。
2013年4月26日-2013年5月21日:畢業(yè)論文撰寫和修改工作。
特色或創(chuàng)新之處
(1)結(jié)構(gòu)緊湊,工作范圍大而安裝占地小。
(2)具有很高的可達(dá)性??梢允蛊涫植窟M(jìn)入像汽車車身這樣一個(gè)封閉的空間內(nèi)
進(jìn)行作業(yè),而直角坐標(biāo)型的機(jī)器人就不行。
(3)因?yàn)闆]有移動(dòng)關(guān)節(jié),所以不需要導(dǎo)軌。轉(zhuǎn)動(dòng)關(guān)節(jié)容易密封,由于軸承件是
大量生產(chǎn)的標(biāo)準(zhǔn)件,則摩擦小,慣量小,可靠性好。
(4)所需關(guān)節(jié)驅(qū)動(dòng)力矩小,能量消耗少
已具備的條件和尚需解決的問題
(1)通過參考大量的文獻(xiàn),掌握課題研究的背景,調(diào)研國內(nèi)外有關(guān)課題研究方面的現(xiàn)狀、發(fā)展和應(yīng)用情況,發(fā)現(xiàn)全自動(dòng)機(jī)械手中“臂”機(jī)構(gòu)設(shè)計(jì)中的問題,明確課題研究的目的、意義、任務(wù)及內(nèi)容。
(2)學(xué)習(xí)和掌握全自動(dòng)機(jī)械手實(shí)現(xiàn)手術(shù)的相關(guān)方法和技術(shù),并結(jié)合課題實(shí)際分析各種相關(guān)方法和技術(shù)的優(yōu)缺點(diǎn),以便確定方案和設(shè)計(jì)內(nèi)容
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英文原文
THE STRUCTURE DESIGN AND KINEMATICS OF A ROBOT
MANIPULATORml. THEORY
KESHENG WANG and TERJE K . LIEN
Production Engineering Laboratory, NTH-SINTEF, N-7034 Trondheim, Norway
A robot manipulator with six degrees of freedom can be separated into two parts: the arm with the first three joints for major positioning and the wrist with the last three joints for major orienting. If we consider theconsecutive links to be parallel or perpendicular, only 12 arm and two wrist configurations are potentially usefuland different for robot manipulator mechanical design. This kind of simplification can lead to a generalalgorithm of inverse kinematics for the corresponding configuration of different combinations of arm and wrist.The approaches for calculating the inverse kinematics of a robot manipulator are very efficient and easy.The approaches for calculating the inverse kinematics of a robot manipulator are very efficient and easy.
1. INTROUCTION
A robot manipulator consists of a number of linksconnected together by joints. In robot manipulatordesign, the selection of the kinematic chain of therobot manipulator is one of the most importantdecisions in the mechanical and controller designprocess.
In order to position and orient the end effector ofthe robot manipulator arbitrarily, six degrees offreedom are required: three degrees of freedom forposition and three degrees of freedom for orient-ation. Each manipulator joint can provide onedegree of freedom, and thus a manipulator musthave a minimum of six joints if it is to provide sixorthogonal degrees of freedom in position andorientation.
The construction of manipulators depends on thedifferent combination of joints. The number of poss-ible variations of an industrial robot structure can bedetermined as follows:
V =6
where
V= number of variations.
D F = n u m b e r of degrees of freedom
These considerations show that a very largenumber of different chains can be built, for examplesix axis 46,656 chains are possible. 6 However, alarge number is not appropriate for kinematicreasons.
We may divide the six degrees of freedom of arobot manipulator into two parts: the arm whichconsists of the first three joints and related links; andthe wrist which consists of the last three joints andrelated links. Then the variations of kinematic chainswill be tremendously reduced. Lien has developedthe constructions of arm and wrist, i.e. 20 differentconstructions for the arm and eight for the wrist.2
In this paper, we abbreviate the 20 different armsinto 12 kinds of arms which are useful and different.We conclude that five kinds of arms and two kinds ofwrists are basic constructions for commercial indus-trial robot manipulators. This kind of simplificationmay lead to a general algorithm of inverse kinema-tics for the corresponding configuration of differentcombinations of arm and wrist.
2.STRUCTURE DESIGN OF ROBOT MANIPULATORS
In this paper, for optimum workspace and sim-plicity, we assume that:
(a) A robot with six degrees of freedom may beseparated into two parts: the linkage consistingof the first three joints and related links is calledthe arm; the linkage of the remaining joints andrelated links is called the wrist.
(b) Two links are connected by a lower pair joint.Only revolute and linear joints are used in robotmanipulators.
(c) The axes of joints are either perpendicular or
According to the authors' knowledge, thisassumption is suitable for most commercially usedindustrial robot manipulators. We can consider thestructure of arm and wrist separately.
2.1. The structure o f the arm o f robot manipulator
(a) Graphical representation. To draw a robot inside view or in perspective is complicated and doesnot give a clear picture of how the various segmentsmove in relation to each other. To draw a robot in aplane sketched diagram is too simple and does notgive a clear construction picture. We compromisethis problem in a simple three-dimensional diagramto express the construction and movements of arobot manipulator. A typical form of representationfor different articulations is shown in Table 1.
(b) Combination of joints. We use R to representa revolute joint and L to represent a linear joint.Different combinations of joints can be obtained asfollows:
According to the different combinations with theparallel or perpendicular axes, each previous combin-ation has four kinds of sub-combination. Thus, 32combinations can be arrived at:
If the second joint is a linear joint and both the otherjoints are perpendicular to it, two choices in relationto the first and the third joints are considered paral-lel or perpendicular.
In all, there are 36 possible combinations of a simplethree-joint arm.
Nine of 36 possible combinations degenerate intoone or two degrees of freedom.
Seven of the remainder are planar mechanisms.Thus, there are 20 possible spatial simple arms.
Let us consider R1 [1 L2 I L3 in whichthe first joint permits rotation about the vertical axis,the second joint is a vertical linear joint (i.e. parallelto the first), and the third joint is a horizontal linearjoint (i.e. perpendicular to the second). This armdefines a typical cylindrical robot. Changing thesequential order of the joints so that either (a) thevertical linear joint precedes the rotary joint, or (b)the vertical linear joint follows the horizontal one,will result in no change in the motion of the arm. Inthis case there are two linkages which are both"equivalent" to the standard cylindrical linkage. Inall such cases where two or more equivalent linkagesexist, the representative of the group will be the onein which the linear joint that is parallel to a rotaryjoint is in the middle (joint No. 2). Counting onlyone linkage to represent the group of equivalentswill eliminate eight of the 20 combinations. Theremaining 12 categories of links are useful and dif-ferent shown in Fig. 1. We get the same results as inRef. 4.
(c) Five basic types o f manipulator arm. Althoughthere are 12 useful and different arm-configurationswhich can be used in the design of a robot man-ipulator arm, in practice only some of them arepractical and commonly used. We find that mostcommercially available industrial robots can bebroken down into only five groups according to the.
characteristics of their arm motion and geometricalappearance.The five groups can be defined as follows and areshown in Fig. 6.
1. Cartesian ( L I L I L)
2. Cylindrical (R II L 1 L)
3. Spherical (R I R I L)
4. Revolute (R I RII R)
5. Double cylindrical ( LII R II R).
2.2. The structure o f a manipulator wrist
(a) Joint type. We have used the first three joints,i.e. the arm of the robot manipulator, to completethe major task of positioning. Then we use the lastthree joints to provide the three degrees of freedomof orientation and refer to the related linkages as thewrist.
The wrist of a complete manipulator must containthree revolute joints, since the orientation of a rigidbody has three degrees of freedom, for example firstrotation about the X axis, then rotation about the yaxis, and finally rotation about the z axis.
(b) Combination or joints and links. Because theorientation of a wrist which only has three rotationaljoints is simplest, its combination is much simpFrom the combination R R R , we know that onlyone of the four configurations can be used for com-pleting the orientation of robot wrist. R II R II R is aplanar mechanism. R 1 R II R and R II R 1 R cannotexpress three degrees of freedom in the orientationof the robot wrist. So only the R 1 R 1 R construc-tion can be used to complete the orientation task.
If we have a different sequence of x, y, z axes, ofcourse we can get many kinds of wrist configuration.But many of them are "equivalent". We only con-sider the relationship between the first and the thirdjoint: parallel and perpendicular. Two differentcombinations can be arrived at, i.e. the Euler angleand r o l l - p i t c h - y a w angle expressions that are shownin Fig. 2. The sequence of x, y, z axes does, however,have an influence on the complexity of the inversekinematic solution.
2.3. Typical robot manipulator structure
We can use five categories of arm configurationand two kinds of wrist configuration to combine 10different kinds of robot manipulators with the sixdegrees of freedom which exist in industrial practice.Of course, we can also consider the other seven outof 12 arm categories with one out of two wristcategories to build a new robot manipulator. Butmost of them have not appeared in industrial prac-tice yet.
3. SOLUTION FOR INVERSE KINEMATICS OF ROBOT MANIPULATOR
3.1. General principlesTo find the inverse kinematic equations of a robotmanipulator at first appears to be a difficult task. Butwhen the manipulator is separated into two parts, itbecomes relatively simple.The relationship between the position and orien-tation of manipulator links connected together byrotational joints shown in Fig. 3, can be described by
Where
0i is the ith joint variable;
di is the ith joint offset;
ai is the ith link length; and
ai is the ith link twist angle.
The position and orientation of the end effector ofthe robot manipulator °T is the matrices product. 3,
T = A I A 2 A 3 A 4 A s A 6 . (2)
By the associative law the product of matrices can beregrouped into two subsets which represent the armand wrist respectively
Where
And
The superscripts designate the reference frame; arepresents the tip of the arm; and w represents thetip of wrist, i.e. the center of the end effector of themanipulator.°T given for the end effector can be written as a4 x 4 homogeneous matrix composed of a orienta-tion submatrix R and a position vector p5.6
We can obtain the vector OaPdirectly using a vectoranalysis method. The detail will be mentioned in thenext section.
from Eq. (4),
We can get 01, 02, 03, the first three joint variablesfrom the solution of the following equation:
The orientation of the end effector of the robotmanipulator can be considered as the product of theorientation of the arm and the orientation of the wrist:
From Eqs (12) and (5), we can obtain
where
We can get the last three joint variables 04, 05, 06 by solving Eq. (13).
3.2. Different methodsThere are two kinds of solutions for the robot
manipulator: closed form solutions and numericalsolutions. Because of their iterative nature, numeri-cal solutions are generally much slower than thecorresponding closed form solutions, so much so that for most uses, we are not interested in the numerical approach to solution of kinematics. But, in general, it is much easier to obtain the numerical algorithm
than to obtain the closed form solution.
In this paper we propose algorithms of both solu-tions.
(a) Closed form solution. In the closed form solu-tion, the key problem is to obtain the position of thetip of the arm P. It is simple to obtain the position ofthe arm tip for the wrist axis intersecting at onepoint. But it is complex for the wrists where there isan axis offset, because the movement of the wristwill greatly affect the position of end effector of themanipulator
In the following, we use the RRR + Euler angleand RRR + R - P - Y angle as examples to describehow to get the position of the tip of arm separately. RRR + Euler angleFigure 4 shows a sketch diagram of a
R R R + Euler angle
robot manipulator (PUMA 600) and the co-ordinate system which is represented by the D - Hexpression. The figure shows the relationship be-tween the arm and wrist vectors. ~r, is the positionvector from the base coordinate frame to the centerof the end effector of the robot manipulator. Arepresents the approach direction of the end effec-tor, °aPis the arm vector measured from the origin tothe connecting point of the arm and wrist, gP is thewrist vector having the same direction as the Avector and length measured from the connectionpoint of the arm and wrist to the center of the endeffector.
With reference to frame 0, the product ~R gP issimply gP, i.e. the position of the center of the endeffector of robot manipulator measured from the tipof the arm, all with respect to frame 0. We canobtain
This states that the total translation of the endeffector is the sum of the translation from the base to
the tip of the arm plus the transformation from thetip of the arm to the center of the end effector.
From Eq. (17), we can easily obtain the positionof the arm tip ~P as follows:
Then we can use Eqs (10) and (11) to obtain the firstthree joint variables 0:, 02, 03 and Eq. (13) to obtainthe last three joint variables 04, 05,06. The detailedsolution is shown in Part II. t0
Figure 5 shows a sketch diagram of a RRR +R - P - Y angle robot manipulator (Cincinatti Mila-
cran T 3) and the coordinate system. Euler anglesare different from R - P - Y angles because the vector0p is affected by the movement of joint 4. Here is anexample showing how to treat the wrist axis offset.gPt:is the wrist vector having the same direction asthe A vector and length measured from the point ofjoint 4 to the center of the end effector, i.e. d+. ~P2 isthe other wrist vector having length measured frompoint of joint 4 to point of joint 5, i.e. a4. oP, theposition of arm, can be computed from the se-quential solution of the following set of equations:
Then we can obtain 01, 02, 03 from Eqs (10) and (11)and obtain 0+, 05, 06 from Eq. (13).
? General closed form solution algorithm
Step 1. Finding the approach vector of the endeffector
Step 2.If there is some off-set in the wrist construc-tion, use the vector algebra to determine the
off-set gP, and get the arm vector, i.e. theposition of arm tip, then go to step 4.Otherwise go to Step 3. Compute the arm vector ~P directly usingapproach vector A.
Step 4. Compute the first three joint variables 01,02, 03, using the arm vector gP from Eqs
(10) and (11).
Step 5. Compute the last three joint variables 04, 05,06 from Eq. (13).This approach shows that the number of computa-tions is kept to a minimum by reducing the overallproblem into separate steps which in turn lowers thelikelihood of errors and helps to reduce the tedious-ness of the work.
(b) Numerical solution. The algorithm for thenumerical solution:
Step 1. Assume the last three joint variables 04, 05,06 by the best available approximation,perhaps from a previous computed point.
Step 2. Compute the arm joint variables 81, 02, 03from Eqs (10) and (11).
Step 3. Compute wrist joint variables 04, 05, 06 from
Eq. (13), using the values of the arm jointvariables obtained from step 2.
Step 4. Compute the position and orientation of theend effector of robot manipulator using the
values of all joint variables obtained fromstep 2 and step 3.
Step 5. If the errors between the given values andthe calculated values is less than a pre-
specified value, then the procedure stops.Otherwise go to step 2 to repeat the pro-
cedure.The physical interpretation of the above pro-cedure is alternately to move the arm and wrist, oneto satisfy the positional and other to satisfy theorientational specification of the end effector, eachtime moving only the arm (or the wrist) while hold-ing the wrist (or the arm) fixed.
This method has been implemented in a PUMA600 robot manipulator. It has been found that four is a sufficient number of iterations to reach therequired accuracy (A < 0.01 mm) and the number has been fixed in the inverse kinematic solution.This algorithm has the advantage of treating the different kinds of robots with the same algorithm.But this method needs so much more computing time than the closed form solution, that it is notsuitable for real-time control of robot manipulators.
4. CONCLUSIONS
The variety of possible robot configurations isvery large. A step towards generalization has been made by emphasizing that robot manipulators ofpractical importance are separable into primary sub-systems, the arm and the wrist. Mathematical treat-ment of various robots may be modularized and thusgreatly simplified by giving a separate description ofvarious arms and various wrists in common use.It has been discovered that only 12 useful and different categories of arm construction and twokinds of wrist construction exist. Using thehomogeneous transformation matrix method, theinverse kinematic solution is easily derived.The two algorithms which consist of the closedform and numerical solution of the inverse kine-matics have been given in this paper.
REFERENCES
1. Denavit, J., Hartenberg, R.S.: A kinematic notationfor law pair mechanisms based on matrices. J. Appl.Mech. Trans. ASME 77: 215-221, 1955.
2. Lien, T.K.: Banestyring for universelle handterings-automater. Trondheim, August 1980.
3. Lien, T.K.: Coordinate transformations in CNC sys-tem for automatic handling machines, llth CIRPSeminar on Manufacturing Systems, Nancy, France,June 1979.
4. Milenkovic,V., Huang, B.: Kinematicsof major robotlinkage. 13th International Symposium on Industria
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