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)】【CAD圖紙和文檔終稿可編輯】
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)】【CAD圖紙和文檔終稿可編輯】,三自由度 圓柱坐標(biāo)式氣壓驅(qū)動(dòng),CAD圖紙和文檔終稿可編輯,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)】【CAD圖紙和文檔終稿可編輯】,工業(yè),機(jī)器人,設(shè)計(jì),自由度,圓柱,坐標(biāo),氣壓,驅(qū)動(dòng),cad,圖紙
編號(hào)
無(wú)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(wú)錫太湖學(xué)院
畢業(yè)設(shè)計(jì)（論文）
開(kāi)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(lái)源
自擬
科學(xué)依據(jù)（包括課題的科學(xué)意義；國(guó)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(lèi)最偉大的發(fā)明之一，人類(lèi)對(duì)于機(jī)器人的研究由來(lái)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(mén)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(guó)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(guò)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(guò)程中發(fā)展起來(lái)的一種新型裝置。近年來(lái)，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(lái)的一門(mén)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(lèi)完成危險(xiǎn)、重復(fù)枯燥的工作，減輕人類(lèi)勞動(dòng)強(qiáng)度，提高勞動(dòng)生產(chǎn)率。機(jī)械手越來(lái)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(xiāo)對(duì)路的品種，提高產(chǎn)品質(zhì)量，更好地適應(yīng)市場(chǎng)競(jìng)爭(zhēng)的需要。
此外，醫(yī)療機(jī)器人是目前國(guó)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(lái),醫(yī)療機(jī)器人技術(shù)引起美、法、德、意、日等國(guó)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(guó)際先進(jìn)機(jī)器人計(jì)劃已召開(kāi)過(guò)的多屆醫(yī)療外科機(jī)器人研討會(huì)己經(jīng)立項(xiàng),開(kāi)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(guó)國(guó)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(guó)家已經(jīng)出現(xiàn)醫(yī)療，外科手術(shù)機(jī)器人市場(chǎng)化產(chǎn)品，并在臨床上開(kāi)展了大量病例研究。韓國(guó)和新加坡的機(jī)器人密度(即制造業(yè)中每萬(wàn)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(guó)、英國(guó)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?jī)?nèi)容
（1） 了解工業(yè)機(jī)械人的工作原理，國(guó)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(shuō)明書(shū)的撰寫(xiě)，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(guó)家工業(yè)自動(dòng)化的水平。
本課題屬工程設(shè)計(jì)類(lèi)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(guò)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(shū)要求查閱論文相關(guān)參考資料。填寫(xiě)畢業(yè)設(shè)計(jì)開(kāi)題報(bào)告書(shū)。
2013年1月11日-2013年3月5日：填寫(xiě)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(kāi)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(xiě)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(chē)車(chē)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](méi)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(wèn)題
（1）通過(guò)參考大量的文獻(xiàn)，掌握課題研究的背景，調(diào)研國(guó)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(wèn)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
指導(dǎo)教師意見(jiàn)
指導(dǎo)教師簽名：
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教研室（學(xué)科組、研究所）意見(jiàn)
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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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