關節(jié)型機器人腰部結(jié)構設計（含11張CAD圖紙）
關節(jié)型機器人腰部結(jié)構設計（含11張CAD圖紙）,關節(jié),機器人,腰部,結(jié)構設計,11,CAD,圖紙
設計任務
題目： 關節(jié)型機器人腰部結(jié)構設計
一、設計內(nèi)容
題目來源于生產(chǎn)實際。設計一個用于焊接的關節(jié)型機器人，進行機器人的總體
方案設計、腰部結(jié)構設計以及其零件設計。
二、設計依據(jù)
焊接機器人具有六個自由度，腰關節(jié)回轉(zhuǎn)，臂關節(jié)俯仰，肘關節(jié)俯仰，
腕關節(jié)仰腕、擺腕和旋腕，腕部最大負荷6kg，最大速度2m/s，最大工作空間半徑
1500mm。
三、技術要求
1、機器人應能滿足工作要求，保證焊接精度；
2、工作可靠，結(jié)構簡單；
3、裝卸方便，便于維修、調(diào)整；
4、盡量使用通用件，以便降低制造成本。
四.設計物化成果的具體內(nèi)容及要求
1、圖紙工作量及要求
設計圖樣全部用AutoCAD繪制，總的繪圖量達3張A0以上，具體要求：
（1）機器人外形尺寸圖一張；
（2）腰部及底座裝配圖一張；
（3）設計的所有零件的零件圖。
主要參考文獻：
1、殷際英.何廣平.關節(jié)型機器人：北京:化學工業(yè)出版社，2003.
2、馬香峰.工業(yè)機器人的操作機設計.北京：冶金工業(yè)出版社，1996.
3、費仁元.張慧慧.機器人機械設計和分析.北京：北京工業(yè)大學出版社，1998.
4、周伯英.工業(yè)機器人設計.北京：機械工業(yè)出版社，1995.
5、蔡自興.機器人學.北京：清華大學出版社，2000.
6、宗光華,劉海波譯.機器人技術手冊. 北京：科學出版社，1996.
7、徐衛(wèi)良，錢瑞明譯.機器人操作的數(shù)學導論. 北京：機械工業(yè)出版社，1998.
8、孫迪生，王炎.機器人控制技術.北京：機械工業(yè)出版社，1998.
9、徐灝.機械設計手冊.第二版.北京：機械工業(yè)出版社，2000.
10、成大先.機械設計手冊.第4版. 北京：化學工業(yè)出版社，2002.
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文 獻 資 料
[1] 薛安克，汪新中，蔡宗耀．HDJ003平面關節(jié)型裝配機器人微機實時控制系統(tǒng)[J] ．機械工業(yè)自動化,1997，19(2)：30-32，40
[2] 熊臘森,彭振國,陳一堅,曹東杰．IR761/125型點焊機器人在平頭駕駛室總裝生產(chǎn)線上的應用[M]．武漢：華中理工大學,1998(5):10—12,35
[3] 楊宜明,章云,林漢榮,柯燕嬌．MR—2型微機器人的研究[M]．廣州：廣東工學院機器人研究室, 1994,13-14
[4] 湯祥州,謝存禧,于江．SMA微型機器人的結(jié)構設計與分析[J]．機械科學與技術, 1997, 16(6):992-996
[5] 徐錦康,群濤,劉啟芬． XZ—I型弧焊機器人[J]．機械工業(yè)自動化,1994, 16(3):24-27
[6] 劉啟芬,黃虎．弧焊機器人控制功能的實現(xiàn)[J]．南京氣象學院學報,1995,18(3):410-415
[7] 張勇德,劉廷榮,李華敏．機器人多指靈巧手的結(jié)構型式的優(yōu)化分析[M]．黑龍江: 哈爾濱工業(yè)大學,1999(7):9-13,48
[8] 李樹軍,李德錫,權太國．一種3自由度串并聯(lián)平臺型機器人結(jié)構[J]．東北大學學報(自然科學版) , 1996,17(6):641-644
[9] 鐘春敏．異形石材加工雙臂機器人結(jié)構設計[J]．陜西工學院學報, 2000,16(4):12-14
[10] 陳炯．便攜式關節(jié)型弧焊機器人的研制[M]．四川油氣田建設工程總公司，
2001(10):23-26
[11] 崔文旭．機器人在汽車焊接生產(chǎn)線柔性化中的應用[J]．焊接技術，2003，32(5):36-37
開題論證報告
題目名稱：關節(jié)型機器人腰部結(jié)構設計
一、題目來源、題目研究的主要內(nèi)容及國內(nèi)外現(xiàn)狀綜述
（一）題目來源：
本題目來源于生產(chǎn)實際，手工電弧焊接效率低，操作環(huán)境差，而且對操作員技術熟練程度要求較高，因此采用機器人技術，實現(xiàn)焊接生產(chǎn)操作的柔性自動化，以提高生產(chǎn)效率。而且,現(xiàn)在對許多構件的焊接精度和速度等提出越來越高的要求,一般工人已難以勝任這一工作；此外,焊接時的火花及煙霧等,對人體造成危害,因此,焊接過程的完全自動化已成為重要的研究課題。其中,十分重要的就是要應用焊接機器人。
（二）題目研究的主要內(nèi)容：
設計一個用于焊接的關節(jié)型機器人，進行機器人的總體方案設計、腰結(jié)構設計及其零件設計。
關節(jié)型機器人的機械本體部分一般為由各種關節(jié)串接起若干連桿組成的開鏈式機構。由于結(jié)構上的原因，其關節(jié)通常只有轉(zhuǎn)動型和移動型。關節(jié)型機器人主要特點是模仿人類腰部到手臂的基本結(jié)構，因此本體結(jié)構通常包括關節(jié)型機器人的機座結(jié)構及腰部關節(jié)轉(zhuǎn)動裝置、手腕結(jié)構及手腕關節(jié)轉(zhuǎn)動裝置和末端執(zhí)行器。我所做的課題偏重與機座和腰部的結(jié)構設計。
弧焊機器人多采用占地面積小，動作范圍較大的關節(jié)型操作機，其靈活性大，能以最佳狀態(tài)決定焊槍的位置。
（三）國內(nèi)外現(xiàn)狀綜述：
目前，對機器人技術的發(fā)展有最重要影響的國家是日本和美國。美國在機器人技術的綜合性水平上仍處于領先地位，日本生產(chǎn)的機器人數(shù)量和種類則居世界首位。我國發(fā)展機器人技術起步于20世紀70年代末。1995年9月，6000m水下機器人試驗成功.近年來,在步行機器人、精密裝配機器人及多自由度關節(jié)型機器人研制等前沿領域內(nèi)逐步縮短與世界水平的差距。
自從第一臺工業(yè)機器人問世以來，機器人的應用領域從汽車工業(yè)逐漸向其他行業(yè)滲透，機器人的種類也從操作手逐漸衍生出各種各樣的機器人，如今機器人已經(jīng)深入到人類生活的方方面面。人類科技的進步、文明的發(fā)展已經(jīng)和機器人產(chǎn)生了密切的關系。人類社會的發(fā)展已經(jīng)離不開機器人技術，而機器人技術的進步必然對推動科技發(fā)展產(chǎn)生不可忽視的作用。當前和今后的機器人技術正逐漸向著具有行走能力、對環(huán)境的自主性強、具有多種感覺能力的方向發(fā)展。機器人也正在逐漸具有智能。美國貝爾科爾公司已成功地將神經(jīng)網(wǎng)絡裝配在芯片上，其智能分析速度比普通計算機要快數(shù)千倍，能更好地完成識別語言和圖像處理等工作。
華中理工大學的熊臘森、彭振國、陳一堅和曹東杰教授合著的一篇論文，題為《IR761/125型點焊機器人在平頭駕駛室總裝生產(chǎn)線上的應用》，它主要介紹了IR761/125型點焊機器人的機械結(jié)構和控制系統(tǒng)；重點討論了該機器人的焊接生產(chǎn)應用；提出了機器人的使用維護和故障處理建議。
南京機械?？茖W校的徐錦康、邵群濤和劉啟芬合著的論文《XZ-I型弧焊機器人》主要介紹了XZ-I型機器人操作機結(jié)構和機構設計，位置交流伺服控制系統(tǒng)及計算機控制軟件特點，給出了主要算法。
二、本題目擬解決的問題
焊接機器人具有6個自由度：① 腰關節(jié)回轉(zhuǎn)；② 臂關節(jié)俯仰；③ 肘關節(jié)俯仰；④ 腕關節(jié)仰腕；⑤ 擺腕；⑥旋腕。其中要詳細地設計機器人基座和腰部的結(jié)構。整體機器人要實現(xiàn)腕部最大負荷6kg，最大速度2m/s，最大工作空間半徑1500mm 。
在設計過程中要考慮到很多問題：① 機器人的六個關節(jié)采用何種驅(qū)動器；② 傳動比的選擇要合理；③ 同一軸上的軸承要保證很好的同軸度；④基座采用何種材料如何制造；⑤ 立柱與大臂如何聯(lián)接；⑥ 要有足夠大的安裝基面，以保證機器人工作時的穩(wěn)定性；⑦ 腰座承受機器人全部重量和工作載荷，應保證足夠的強度、剛度和承載能力；⑧ 腰座軸系及傳動鏈的精度對末端執(zhí)行器的運行精度影響最大。因此腰座與手臂的聯(lián)接要有可靠的定位基準面。
三、 解決方案及預期效果
（一）解決方案：
機器人大體采用PUMA型
1. 操作機的驅(qū)動系統(tǒng)設計；
關節(jié)型機器人本體驅(qū)動系統(tǒng)包括驅(qū)動器和傳動機構，它們常和執(zhí)行機構聯(lián)成一體，驅(qū)動臂桿和載荷完成指定的運動。常用的驅(qū)動器有電機和液壓、氣動驅(qū)動裝置等。其中采用電機驅(qū)動是最常用的驅(qū)動方式。電極驅(qū)動具有精度高，可靠性好，能以較大的變速范圍滿足機器人應用要求等特點。所以在這次設計中我選擇了直流電機作為驅(qū)動器。
2. 速度和位置檢測；
3. 伺服控制系統(tǒng)選擇；
4. 工作空間的確定；
5. 機器人本體結(jié)構設計；
①內(nèi)部鋁鑄件形狀復雜，既用作內(nèi)部齒輪安裝殼體與軸的支承座，又兼作承力骨架，傳遞集中載荷。這樣不僅節(jié)省材料，減少加工量，又使整體質(zhì)量減輕。手臂外壁與鑄件骨架采用膠接，使連接件減少，工藝簡單，減輕了質(zhì)量。
② 軸承外形環(huán)定位簡單。一般在無軸向載荷處，載荷外環(huán)采用端面打沖定位的方法。
③ 采用薄壁軸承與滑動銅襯套，以減少結(jié)構尺寸，減輕質(zhì)量。
④ 有些小尺寸齒輪與軸加工成一體，減少連接件，增加了傳遞剛度。
⑤ 大、小臂，手腕部結(jié)構密度大，很少有多余空隙。如電機與臂的外壁僅有0.5mm間隙，手腕內(nèi)部齒輪傳動安排亦是緊密無間。這樣使總的尺寸減少，質(zhì)量減少。
⑥ 工作范圍大，適應性廣。PUMA除了自身立柱所占空間以外，它的工作空間幾乎是他的長臂所能達到的全球空間。再加之其手腕軸的活動角度大，因此使它工作時位姿的適應性強。譬如用手腕擰螺釘，手腕關節(jié)4，6配合，一次就能轉(zhuǎn)1112°。
⑦ 由于結(jié)構上采用了剛性齒輪傳動，調(diào)整齒輪間隙機構，彈性萬向聯(lián)軸器，工藝上加工精密，多用整體鑄件，使得重復定位精度高。
⑧ 機器人手臂材料的選擇：
機器人手臂的材料應根據(jù)手臂的工作狀況來選擇。根據(jù)設計要求，機器人手臂要完成各種運動。因此，對材料的一個要求是作為運動的部件，它應是輕型材料。而另一方面，手臂在運動過程中往往會產(chǎn)生振動，這將大大降低它的運動精度。因此，在選擇材料時，需要對質(zhì)量、剛度、阻尼進行綜合考慮，以便有效地提高手臂的動態(tài)性能。
機器人手臂材料首先應是結(jié)構材料。手臂承受載荷時，不應有變形和斷裂。從力學角度看，即要具有一定的強度。手臂材料應選擇高強度材料，如鋼、鑄鐵、合金鋼等。機器人手臂是運動的，又要具有很好的受控性，因此，要求手臂比較輕。綜合而言，應該優(yōu)先選擇強度大而密度小的材料做手臂。其中，非金屬材料有尼龍6、聚乙烯和碳素纖維等；金屬材料以輕合金為主。
⑨腰關節(jié)采用齒輪二級傳動?？倐鲃颖葹?8，第一級傳動傳動比為4，第二級傳動比為12，主軸的角速度為3.82 rad/s。
（二）預期效果：
工作可靠，結(jié)構簡單；裝卸方便，便于維修、調(diào)整；能很好的實現(xiàn)自動電弧焊的功能。
3
關節(jié)型機器人腰部結(jié)構設計
摘要: 為了提高生產(chǎn)效率和產(chǎn)品的焊接質(zhì)量,滿足實際工作需要,本課題設計了用于焊接的關節(jié)型機器人。根據(jù)機器人的工作要求和結(jié)構特點，進行了機器人的總體設計，確定了機器人的外形尺寸和工作空間，擬定了機器人各關節(jié)的總體傳動方案，對機器人腰關節(jié)結(jié)構進行了詳細設計，合理布置了電機和齒輪，確定了各級傳動參數(shù)，進行了齒輪、軸和軸承的設計計算和校核。利用齊次變換矩陣法建立了六自由度關節(jié)機器人的正運動學模型，求出機器人末端相對于各自參考坐標系的齊次坐標值，建立了在直角坐標空間內(nèi)機器人末端執(zhí)行器的位置和姿態(tài)與關節(jié)變量值的對應關系?；趲缀瓮队霸硗茖С鱿鄳哪孢\動學模型，求出了各個關節(jié)的角度值，建立了機器人關節(jié)空間與世界空間的映射關系。該機器人具有剛性好，位置精度高、運行平穩(wěn)的特點。
關鍵詞：關節(jié)型機器人；位姿分析；總體設計；腰部結(jié)構設計
The waist structural design of articulated robot
Abstract : In order to improve the efficiency of production and welding quality of products and meet real work's needs, this subject has designed the articulated robot used for welding . According to the job requirements for the robot and structure characteristic , I have carried on the overall design of the robot, confirmed the external dimension and workspace of the robot, drafted the overall transmission scheme of every joint of the robot. I have designed the waist structure of the robot in detail, assigned the electrical machinery and gear wheel rationally, confirmed at all level transmission parameters , carried on the design and calculating of gear wheels , shafts and bearings and checking them.The kinematic model of robot system has been built up by means of the homogenous transformation of matrix in this thesis and deduces the robot's homogenous coordinate which is relative to its reference coordinate. We also make up the position relationship between the robot's end effector and the variable friable of every joint. The inverse kinematic model is deduced which based on the projection principle of geometry and the value of angle is worked out. What’s more, the relationship is built up between the joint space of robot and the world space. This robot has the characteristics of fine rigidity , position precision high , that operate steadily.
Key words: Articulated robot; Appearance analysis in the location; Design overallly; Waist articulated structural design of the robot
目 錄
1 前言…………………………………………………………………………………1
1.1 題目來源及分析…………………………………………………………………1
1.2 研究目的…………………………………………………………………………2
1.3國內(nèi)外發(fā)展及研究現(xiàn)狀…………………………………………………………2
2 關節(jié)型機器人總體設計……………………………………………………………4
2.1 確定基本技術參數(shù)………………………………………………………………4
2.1.1機械結(jié)構類型的選擇…………………………………………………………4
2.1.2 額定負載………………………………………………………………………5
2.1.3 工作范圍………………………………………………………………………5
2.1.4 操作機的驅(qū)動系統(tǒng)設計………………………………………………………5
2.1.5 控制系統(tǒng)的選擇………………………………………………………………6
2.1.6 確定關節(jié)型機器人手臂的配置形式…………………………………………6
2.2 關節(jié)型機器人本體結(jié)構設計……………………………………………………7
3 關節(jié)型機器人腰部結(jié)構設計…………………………………………………… 10
3.1 電動機的選擇…………………………………………………………………10
3.2 計算傳動裝置的總傳動比及分配各級傳動比………………………………12
3.3 軸的設計計算…………………………………………………………………12
3.3.1 計算各軸轉(zhuǎn)速、轉(zhuǎn)矩和輸入功率……………………………………………12
3.3.2 確定三根軸的具體尺寸……………………………………………………13
3.4 確定齒輪的參數(shù)………………………………………………………………17
3.4.1 選擇材料……………………………………………………………………17
3.4.2 壓力角的選擇………………………………………………………………17
3.4.3 齒數(shù)和模數(shù)的選擇…………………………………………………………17
3.4.4 齒寬系數(shù)的確定……………………………………………………………17
3.4.5 確定齒輪傳動的精度………………………………………………………18
3.4.6 齒輪的校核…………………………………………………………………19
3.5 殼體設計………………………………………………………………………22
4 關節(jié)型機器人的位姿分析………………………………………………………23
4.1 機器人的位姿與運動的描述…………………………………………………23
4.2 關節(jié)型機器人的廣義連桿變換矩陣…………………………………………23
4.3 關節(jié)型機器人運動方程………………………………………………………26
4.3.1 關節(jié)型機器人運動分析……………………………………………………26
4.3.2 關節(jié)型機器人運動反解……………………………………………………29
5 結(jié)論………………………………………………………………………………34
參考文獻……………………………………………………………………………35
附錄…………………………………………………………………………………36
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 IndustrialRobots and Robotics 7, Vol. 2, pp. 31-46, 1983.
5. Paul, R.P.: Robot Manipulators: Mathematics, Pro-gramming, and Control. MIT Press, Cambridge,1982.
6. Lee,. C.G.S.: Fundamentals of Robotics. Addison-Wesley, New York, 1983.
7. Warnecke, H.J., Schraft, R.D.: Industrial Robots. IFS,Bedford, 1982.
8. Pieper, D.L.: The kinematics of manipulators undercomputer control. AIM 72, Stanford, CA. StanfordUniversity Artificial Intelligence Laboratory.
9. Coiffet, P., Chirouze, M.: An Introduction to RobotTechnology. Kogan Page, London, 1983.
10. Wang, K., Lien T.K.: Closed form solution for theinverse kinematics of a PUMA robot man-ipulator--II. Demonstration. Robotics Comput.-Integr. Mfg. 5: 159-163, 1989.
中文原文
一個機器人結(jié)構設計及運動學
機械臂毫升.理論
KESHENG WANG and TERJE K . LIEN
生產(chǎn)工程實驗室，NTH-SINTEF，N-7034，挪威特隆赫姆
六自由度機器人可以分為兩個部分：與前三個關節(jié)為主要定位，最后三個關節(jié)為主要面向腕臂。如果我們考慮連續(xù)的鏈接是平行或垂直的，只有12的臂和兩個手腕結(jié)構可能是有用的而且不同于對機器人機械手的機械設計。這種簡化可以導致對手臂和手腕的不同組合配置相應的逆運動學算法。對于一個機器人逆運動學是非常有效和簡單的計算方法。
簡介
一個機器人由若干環(huán)節(jié)通過接頭連接在一起。在機器人的機械手設計，對運動鏈的選擇是器人一個最重要的決定在機械和控制器的設計過程。
為了定位和定向的機器人末端執(zhí)行器的任意，六自由度的要求：方向三度的位置和三自由度的自由。每個機械手關節(jié)可以提供一個自由度的機械手，因此必須要提供在六個自由度的位置和方向正交的至少有六的接頭。
機械手的結(jié)構取決于節(jié)點的不同組合。對工業(yè)機器人的結(jié)構的可能變化的數(shù)量可以確定如下。
V=6DF；那么V=數(shù)量的變化；DF=自由度
這些因素表明，不同鏈可建數(shù)量非常大，例如六軸46656鏈是可能的。然而，這是大量不適合運動的原因。
我們可以將一個機器人六自由度分為兩部分：臂由前三個關節(jié)和相關鏈接;與手腕由過去的三節(jié)點和相關鏈接。然后運動鏈的變化將極大地減少。即留置了手臂和手腕的結(jié)構。20種不同的手臂和8種手腕設計。
在文本中，我們有20種不同的手臂，有12中手臂是不同的，很有用的。我們得出這樣的結(jié)論：五種手臂和兩種手腕是商業(yè)工業(yè)機器人的基本結(jié)構。這種簡化可能導致對手臂和手腕的不同組合的相應配置逆運動學算法。
機器人的結(jié)構設計機械手
在本文中，最佳的工作空間和簡單，
我們假設：
（一）具有六個自由度的機器人可以分為兩部分：連接組成的前三個關節(jié)和相關的鏈接被稱為ARM；剩余的關節(jié)聯(lián)動相關鏈接是所謂的手腕。
（二）兩個環(huán)節(jié)由一個聯(lián)合低副連接。旋轉(zhuǎn)和直線連接中使用的機器人機械手。
（三）接頭的軸線是垂直或相互平行。
據(jù)作者所知，這種假設是適用于大多數(shù)的商業(yè)工業(yè)機器人。我們可以考慮結(jié)構的手臂和手腕的分別。
對機器人的手臂結(jié)構
（一） 圖形表示。畫一個機器人在側(cè)視圖或透視是復雜的和不放棄的各個環(huán)節(jié)中的相互關系，如何清晰的照片。在一個平面上畫一個機器人繪圖過于簡單，并沒有給出一個明確的施工圖。我們妥協(xié)的這個問題的一個簡單的三維圖表示的機器人機械手的結(jié)構和動作。對不同關節(jié)表示的一種典型形式顯示在表：
表1 一個機器人的圖形表示
類型 運動 自由度 符號
1. 固定梁 固定 0
2. 轉(zhuǎn)動 旋轉(zhuǎn) 1
3 線性 翻譯 1
1 2 3 4 5 6 7 8
RRR RRL RLR RLL LRR LRL LLR LLL
（二）相結(jié)合的關節(jié)。我們使用R來表示一個轉(zhuǎn)動關節(jié)和L代表一個線性聯(lián)合。接頭不同的組合可以得到如下：
根據(jù)與平行或垂直的軸的不同組合，每一組合有四種亞相結(jié)合。因此，32的組合可以到達：
(1) RRR R⊥R⊥R (2)RRL R⊥R⊥L
R⊥R‖R R⊥R‖L
R‖R⊥R R‖R⊥L
R‖R‖R R‖R‖L
(3) RLR R⊥L⊥R (4)RLL R⊥L⊥L
R⊥L‖R R⊥L‖L
R‖L⊥R R‖L⊥L
R‖L‖R R‖L‖L
(4) LRR L⊥R⊥R (5)LRL
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