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canismes par group des d233。 Design of parallel manipulators via the displacement groupJacques ECELE CENTRALE PARIS92295 CHATENAY MALABRY CEDEXFRANCE Abstract: Our aim is to give a plete presentation of the application of Life Group Theory to the structural design of manipulator robots. We focused our attention on parallel manipulator robots and in particular those capable of spatial translation. This is justified by many industrial applications which do not need the orientation of the endeffectors in the space. The advantage of this method is that we can derive systematically all kinematics chains which produce the desired displacement subgroup. Hence, an entire family of robots results from our investigation. The TSTAR manipulator is now a working device. HROBOT, PRISMROBOT are new possible robots. These manipulators respond to the increasing demand of fast working rhythms in modern production at a low cost and are suited for any kind of pick and place jobs like sorting, arranging on palettes, packing and assembly.Keywords: Kinematics, Parallel Robot.IntroductionThe mathematical theory of groups can be applied to the set of displacements. If we can call {D} the set of all possible displacements, it is proved, according to this theory, that {D} have a group structure. The most remarkable movements of a rigid body are then represented by subgroups of {D}. This method leads to a classification of mechanism [1]. The main step for establishing such a classification is the derivation of an exhaustive inventory of the subgroups of the displacement group. This can be done by a direct reasoning by examining all the kinds of products of rotations and translations [2]. However, a much more effective method consists in using Lie Group Theory [3] , [4].Lie Groups are defined by analytical transformations depending on a finite number of real parameters. The displacement group {D} is a special case of a Lie Group of dimension six. Lie’s TheoryWithin the framework of Lie’ Theory, we associate infinitesimal transformations makingup a Lie algebra with finite operations which are obtained from the previous ones by exponentiation. Continuous analytical groups are described by the exponential ofdifferential operators which correspond to the infinitesimal transformations of the group.Furthermore, group properties are interpreted by the algebraic structure of Lie algebra of the differential operators and conversely. We recall the main definition axiom of a Lie algebra: a Lie algebra is a vector space endowed with a bilinear skew symmetric closed product. It is well know [5] , that the set of screw velocity fields is a vector space of dimension six for the natural operations at a given point N.By following the steps indicated in [3] we can produce the exhaustive list of the Lie subgroup of Euclidean displacements {D} (see synoptical list 1). This is done by first defining a differential operator associated with the velocity field. Then, by exponentiation, we derive the formal Lie expression of finite displacements which are shown to be equivalent to affine direct orthonormal transformations. Lie subalgebras of screw velocity fields lead to the description of the displacement subgroups.The {X (w)} subgroupIn order to generate spatial translation with parallel mechanisms, we are led to look for displacements subgroups the intersection of which is the spatial translation subgroup {T}.We will consider only the cases for which the intersection subgroup is strictly included in the two “parallel” subgroups. The most important case of this sort is the parallel association of two {X (w)} subgroups with two distinct vector directions w and w’. It is easy to prove: {X(w)}{X(w’)}={T},w≠w’The subgroup {X (w)} plays a prominent role in mechanism design. This subgroup bines spatial translation with rotation about a movable axis which remains parallel to given direction w , well defined by the unit vector w. Physical implementations of {X(w)} mechanical liaisons can be obtained by ordering in series kinematics pairs represented by subgroups of {X(w)}. Practically only prismatic pair and a revolute pair P, R, H are use to build robots (the cylindric pair C bines in a pact way a prismatic pair and a revolute pair). A plete list of all possible binations of these kinematics pairs generating the {X (w)} subgroup is given in [6].Two geometrical conditions have to be satisfied in the series: the rotation axes and the screw axes are parallel to the given vector w。{Y(w,p)} 平面垂直平移到 w 所允許的平移旋轉(zhuǎn)和沿任何軸平行到 w 的旋轉(zhuǎn)動(dòng)作。^u=O){H(N,u,p)} 轉(zhuǎn)軸 (N ,u,p)= 2 k 的螺旋運(yùn)動(dòng)。簡(jiǎn)寫列表 1置換組的子群{E} 恒等。結(jié)論很多資料[10], [11], [12], [13], [14], [15]表明了假設(shè)群論的,特別是其動(dòng)力學(xué)的重要性。實(shí)際上,這些軸都是水平的。P對(duì)偶偶的方向可以是任意的。一個(gè)平行四邊形能夠利用四轉(zhuǎn)動(dòng)對(duì)偶偶R得到一個(gè)移動(dòng)自由度。中心螺母則不允許平行四邊形構(gòu)架的轉(zhuǎn)動(dòng)。它由軸承(6)通過(guò)執(zhí)行機(jī)構(gòu)M控制。當(dāng)平行四邊形形狀變化時(shí),這個(gè)性質(zhì)被保持(自由度為一)。因此,在計(jì)新的H機(jī)器人[16]時(shí),我們選擇與YSta相同的兩條手臂,第三條手臂可與Delta手臂相比。H型機(jī)器人 大部分并型機(jī)器人包括Delta機(jī)器人和Y Star機(jī)器人,其末端執(zhí)行器的工作空間與整個(gè)裝置相比較小。機(jī)器人的移動(dòng)部分由PaR系列組成,都能集中于移動(dòng)平臺(tái)做指定的某點(diǎn)位置。3只機(jī)械臂是相同且每只都能通過(guò)一系列的RHPaR生成一個(gè)子群{X (u)},其中Pa代表循環(huán)平移協(xié)作,此平移協(xié)作由一塊絞接的平行四邊形的兩對(duì)偶立的桿控制決定。這種組合范圍很廣,使得整個(gè)能進(jìn)行空間平移的機(jī)器人家族成員得到了增加??臻g平移的并聯(lián)機(jī)器人當(dāng)兩子群組{X(w)} 和{X(w’)},w≠w’,滿足w≠w’,但矢量平行時(shí),在移動(dòng)平臺(tái)和固定馬達(dá)之間,其機(jī)械生成元就足以能產(chǎn)生空間平移。同時(shí)它們必須連續(xù)的滿足兩種幾何情況:旋轉(zhuǎn)軸與螺旋軸要與給定的矢量w平行;不是被動(dòng)運(yùn)動(dòng)。該子群由帶有旋轉(zhuǎn)運(yùn)動(dòng)的空間平移組成,其旋轉(zhuǎn)主軸方向與所給定的矢量w的方向始終平行。{X (w)}子群為了利用平行機(jī)理得到空間平移,我們需要找到所有位移子群的交集——空間平移子群{T}。該列表是通過(guò)首先定義一個(gè)與速度場(chǎng)有關(guān)的微分運(yùn)算符得到的。另外,群體特性通過(guò)微分運(yùn)算及其逆運(yùn)算所得到的李代數(shù)的代數(shù)結(jié)構(gòu)而得到了解釋。假設(shè)群論是在取決于許多有限實(shí)參數(shù)的全純映射的基礎(chǔ)上定義的。這方法導(dǎo)致機(jī)械裝置的分類 [1]。這些機(jī)器人能滿足現(xiàn)代生產(chǎn)快節(jié)奏工作中價(jià)格低以及符合挑選的工作環(huán)境,如選料、安排、包裝、裝配等發(fā)日益增長(zhǎng)的需求。這個(gè)方法的優(yōu)點(diǎn)是我們能系統(tǒng)地導(dǎo)出能預(yù)期得到位移子群的所有運(yùn)動(dòng)學(xué)鏈。在此我對(duì)導(dǎo)師付出的辛勤勞動(dòng)和提供的良好學(xué)習(xí)環(huán)境表示衷心的感謝。在壓榨過(guò)程中,采用套裝式變導(dǎo)程二級(jí)壓榨,這比傳統(tǒng)的榨油機(jī)在性能上有了很大的改進(jìn)。,取=15第六章 結(jié)束語(yǔ)1.在設(shè)計(jì)螺旋榨油機(jī)的過(guò)程中,設(shè)計(jì)的對(duì)象主要是大豆等油料作物,適用于中小油廠,因此所需要得零件的精度要求不高,但榨螺軸的成本比較高,為了提高榨油機(jī)的工作壽命,要求配合精度高一些。計(jì)算系數(shù) e= ,Y1= ,Y2= ,YO= .(2)Ⅰ軸和Ⅱ軸的軸承選用相同型號(hào)的軸承,圓錐滾子軸承,型號(hào)為32905 。軸的深度 t= mm .5芯軸上的鍵Ⅱ,