【正文】 1 pp, 7183 (1994).[4] HERVE , “Intrinsic formulation of problems of geometry and kinematics of mechanism”, Mech, Mach, Theory 17, pp 179184 (1994).[5] SUGIMOTO K, DUFFY J, “Application of linear Algebra to Screw Systems”, Mech, Mach, Theory 17, pp, 7383 (1994).[6] HERVE , SPARACINO F, “Structural Synthesis of Parallel Robots Generating Spatial Translation” 5th Int. Conf, on Adv, Robotics, IEEE n186。placements”, Mech, Mach, Theory 13, pp, 437450 (1978).[2] FRANGHELLA P, “Kinematics of Spatial Linkage by Group Algebra: a strucrure based approach”, Mech, Mach, Theory 23, n186。 relative to the first two axes. The third prismatic pair will be perpendicular to the third axis. The mobile platform is able to undergo pure translation in a wide volume with no jamming effect.Conclusions The importance of Lie group theory, expecially for kinematics is recognized from various source [10], [11], [12], [13], [14], [15]. Investigation of new parallel robots generating pure translation led us to the construction of several prototypes. Increasing performances and the low cost of fabrication make these robots attractive for modern industry. They are presented as an alternative to the DELTA robot and have the classical parallel robot advantages for positioning, precision, rapidity and fixed motor location.References [1] HERVE , “Analyse structurelle des m233。 there is no passive mobility.The displacement operator for the {X {w}} subgroup, acting on point M is: M → N + ａu + bv + cw +exp(hw^) N M^ is the symbol of the vector product.Point N and the vectors u, v, w make up an orthogonal frame of reference in the space and a, b, c, h are the four parameters of the subgroup which has the dimension 4.Parallel robots for spatial translation To produce spatial translation it is sufficient to place two mechanical generators of the subgroups {X(w)} and {X(w’)},w≠w’, in parallel, between a mobile platform and a fixed motors then three generators of the three subgroups {X(w)},{X(w’)},{X(w’’)},w≠w’, is needed. Any series of P, R or H pairs which constitute a mechanical generator of the {X (w)} subgroup can be implemented. Morever, these three mechanical generators may be different or the same depending on the desired kinematics results. This wide range of binations gives rise to an entire family of robots capable of spatial translation. Simulation of the most interesting architectures can easily be achieved and the choice of the robot to be constructed can therefore meet the needs of the missioner. Clavel’s Delta robot belongs to this family as it is based on the same kinematics principles [7].The parallel manipulator YSTARSTAR [16] is made up by three cooperating arms which generate the subgroups {X (u)}, {X (u’)}, {X(u’’)}, (fig 1). The three arms are identical and each one generates a subgroup {X(u)} by the series RHPaR where Pa represents the circular translation liaison determined by the two opposite bars of a planar hinged parallelogram. The axes of the two revolute pairs and of the screw pair must be parallel in order to generate a {X (u)}, subgroup. For each arm, the first two pairs, . the coaxial revolute pair and the screw pair, constitute the fixed part of the robot and form at the same time the mechanical structure of an axes lie on the same plane and divide it into three identical parts thus forming a Y shape. Hence the angle between any two axes is always 2/3. The mobile part of the robot is made up by three PaR series that all converge to a mon point below which the mobile platform is located. The platform stays parallel to the reference plane and cannot rotate about the axis perpendicular to this plane. Any kind of appropriate end effectors can be placed on this mobile platform. The derivation of the {T} subgroup, which proves the mobile platform can only translate in the space, is given in [8].The H – Robot For a great majority of parallel robots including the Delta Robot and the Y Star, the working volume of the end effectors is small relative to the bulkiness of the whole device. It is the essential drawback of such a kind of manipulator. In order to avoid this native narrowness of the working volume, it can be imagine to implement three input electric jacks with three parallel axes instead of converging axes. Three arms similar to those of the Y Star cannot be employed: the intersection set of three equal set {X (v)} will be equal to {X (v)} instead of {T}. Hence, designing the new HRobot [16], we have chosen two arms of the Y Star type and a third pattern which may be pared with the Delta arms.This third mechanism begins from the fixed frame with a motorized prismatic pair parallel to the first two electric jacks. It is followed by a hinged planar parallelogram which is free to rotate around an axis perpendicular to the P pair thanks to a bar of the parallelogram. The opposite bar is connected to the mobile platform via a revolute pair R of parallel axis. This property is maintained when the parallelogram changes of shape (with one degree of freedom).In a first prototype built at “IUT de Ville D’Avray ”(France) by a team a students directed by the professor Pastor233。 {D} 綜合剛體運(yùn)動(dòng)。{S(N)} 在點(diǎn)N周圍的額球狀的旋轉(zhuǎn)裝置。{G(P)} 對(duì)平面P的平行平面運(yùn)動(dòng)。{t(P)} 對(duì)平面 P 的平移。,和 NN 的 u39。{t(D)} 對(duì)直線 D 的平移。這種新機(jī)器人具有通用并行機(jī)器人在定位、靈敏性和馬達(dá)定位安裝方面的優(yōu)點(diǎn)，可代替DELTA機(jī)器人。通過對(duì)偶新的并行機(jī)器人的查證能夠?qū)ε嘉覀冞M(jìn)行機(jī)器人原型的構(gòu)造有很大幫助。移動(dòng)平臺(tái)在不需要人為調(diào)節(jié)的條件下在較大工作空間內(nèi)自行移動(dòng)。兩柱狀對(duì)偶偶相對(duì)偶于前兩軸呈45度角。第三個(gè)電動(dòng)千斤頂為垂直安裝。柱狀機(jī)器人的草圖見圖3。軸C必須在每次排列中與R軸平行。因此，利用柱狀對(duì)偶偶代替平行四邊形（Star機(jī)器人）進(jìn)行機(jī)器人設(shè)計(jì)是一個(gè)經(jīng)濟(jì)可行的方法。柱狀機(jī)器人滑動(dòng)對(duì)偶偶P較好的性有能在在工業(yè)機(jī)械元件上得到應(yīng)用的可能。移動(dòng)平臺(tái)與半氣缸相似，其自由度為3。邊螺旋桿允許沿著其軸轉(zhuǎn)動(dòng)和移動(dòng)。三個(gè)絞接的平行四邊形位于（4）的兩端，在（5）的中間將螺母與水平平臺(tái)（3）連接。此H型機(jī)器人安裝了具有3種系統(tǒng)的螺桿(1)／大間距的螺母(2)，能允許快速移動(dòng)。此機(jī)器人的第一個(gè)樣機(jī)有一個(gè)團(tuán)隊(duì)的學(xué)生在Pastor233。與此桿相對(duì)偶的桿經(jīng)由平行軸的旋轉(zhuǎn)對(duì)偶R被連結(jié)到移動(dòng)平臺(tái)上。這第三條機(jī)械臂開始形成帶有與第一個(gè)兩電動(dòng)千斤頂平行的機(jī)動(dòng)化柱狀對(duì)偶的固定框架。與Y Star相似的機(jī)器人臂不能使用：三個(gè)相同集{X (v)}的交集等于{X (v)}而不是{T}。這是此類機(jī)器人的一個(gè)缺陷。 所得到的反應(yīng)移