新型六自由度平行機(jī)構(gòu)設(shè)計(jì)和運(yùn)動(dòng)學(xué)參數(shù)的優(yōu)化外文文獻(xiàn)翻譯、中英文翻譯

1、 MECHANICAL DESIGN AND KINEMATIC OPTIMIZATION OF A NOVEL SIX-DEGREE-OF-FREEDOM PARALLEL MECHANISM Antonio Frisoli, Fabio Salsedo, Diego Ferrazzin, Massimo Bergamasco PERCRO Simultaneous Presence, Telepresence and Virtual PresenceScuola Superiore S. AnnaVia Carducci, 40 56127 PISA, ItalyE-mail: anton

2、ysssup.it, bergamascopercro.sssup.itABSTRACT A six-degree-of-freedom hand controller with force feedback capabilities has been designed. The proposed mechanism new design is fully parallel and actuator redundant. Actuator redundancy refers to the addition of more actuators than strictly necessary to

3、 control the mechanism without increasing the mobility. A new cable transmission is used to drive each of the six degrees of freedom, allowing all actuators be fixed to ground. Kinematic optimization of the dexterity and redundant actuation analysis of the manipulator has been developed. The mechani

4、cal design of a prototype version is shown.KEYWORDS Haptic Interface, Tendon Transmission, Six Dof Parallel ManipulatorINTRODUCTION Parallel manipulators have been extensively studied for their favorable properties in terms of structural stiffness, position accuracy and good dynamic performance (Mer

5、let 1990). Their well-known counterbalance is lack in workspace dimensions and more complex direct kinematics law. Several parallel manipulators proposed in the literature are based on octahedral geometry kinematics (Fichter 1986, Albus et al. 1993) With the adoption of such a kinematics, the geomet

6、ric coincidence between two joints leads to a lack of the one-to-one correspondence between leg points on platform and base. The legs form a “zigzag triangulated pattern” (Hunt and McHaree 1998) that connect the base to the mobile platform. With this kinematics the manipulator can support external l

7、oads with increased stiffness and avoid the singularity configurations, with a consequent average improvement in kinematic performance. The novel manipulator, presented in this paper, has been devised to realize a six-degree of freedom haptic interface. Requirements of low friction and no backslash

8、are critical in the design of force feedback devices (Hayward,1995). Moreover a uniform kinematic behavior of the mechanism over the workspace is required. A six-degree of freedom haptic device can be used to replicate the most of the physical interactions in Virtual Environments (VE). The aim of th

9、is research has been to design an Haptic Interface for the simulation in VE of all tasks involving dexterous manipulation and precise execution, e.g. Surgery, with the replication of all the components of the interaction wrench. The new manipulator design is composed of a mobile platform connected b

10、y four legs to a fixed platform. Two motors located on the base actuate each leg by a novel tendon drive system. Since eight tendons are used to control six degree-of-freedom, the configuration of the tendon driven system according to (Jacobsen et al. 1989) is redundant of type N+2. The tendon drive

11、 modifies the kinematic behavior of the system, so that it becomes statically equivalent to a mobile platform connected to the base by eight pistons, disposed in a triangulated pattern. By means of this static analogy, the mechanical architecture of the system recalls an octahedral like geometry wit

12、h two more linear actuators. But with respect to the octahedral parallel manipulator classical designs, the mechanical system is implemented by DC iron-less motors and steel cables, yielding an high fidelity force-feedback desktop device. KINEMATIC DESCRIPTION OF THE MECHANISM The kinematics of the

13、legs of the parallel manipulator is based on the closed 5-bar mechanism. An innovative tendon transmission has been devised to drive the closed 5-bar mechanism. It is composed of two tendons routed orderly over the pulleys mounted on each joint axis, as shown in figure 1. All the pulleys are idle, e

14、xcept the final driven pulleys of each tendon transmission that are bolted to the base link.Figure 1: Scheme of the closed-loop tendon drive The pulley radii are the same for all the joints, but with different winding directions. So differently from classical tendon transmissions used in serial mani

15、pulators, the final driven pulley is grounded and it is not connected to a moving driven link. This new tendon drive design allows, by properly choosing the tendon routing, to improve the kinematic performance of the closed 5-bar linkage, i.e. avoiding the singularities and improving the kinematic d

16、exterity. The closed-loop tendon drive We shall analyze now the properties of the tendon drive. Since the sum of the internal angles of a triangle is p, it is easy to show that for the angles of figure 1 the following differential relations hold: (1) Since the tendon branch tangent to two consecutiv

17、e pulleys is constant independently from the close 5 bar posture, the displacement dvi of the starting terminal of the tendon is determined only by the variations of the joint angles: (2) So by using the differential expressions (1) we obtain: (3) The above equation is very meaningful. Since (4) by

18、the duality principle between statics and kinematics, the action of the two tendon tensions T1 and T2 is equivalent to two linear actuators directed along QP and RP with thrusts: (5) But since tendon can generate only tension forces, the previous static analogy is incomplete and, depending by the im

19、plemented routing, the equivalent pistons can either only pushing upwards or pulling downwards. So the kineto-static behavior of a tendon driven closed 5-bar linkage can be reduced to one of the equivalent mechanisms showed in figure 2.Figure 2: Equivalent class of mechanisms This mechanical analogy

20、 is very worthwhile, since it permits to explain clearly the force capability of the tendon driven 5-bar linkage. The forces applied at the End Effector (EF) must be comprised in the angle formed by the two equivalent thrust vectors QP and RP, with the sign determined by the routing. Comparative ana

21、lysis We have studied the differential kinematics of the closed 5-bar linkage both with the direct drive of base joints and with the new tendon drive, in order to point out the difference in kinematics performance. Figure 3: Manipulability ellipses for the base joints drive Figure 4 : Manipulability

22、 ellipses for the closed-loop tendon drive Kinematics performance have been compared computing over all the workspace the manipulability ellipses of the two drive systems. The results of an exemplifying case study are reported in figures 3 and 4. The manipulability ellipses for the tendon driven 5-b

23、ars mechanism have a rounder shape than t-hose of the 5-bars mechanism actuated at the joints. So the proposed driving system improves the kinematics isotropy of the mechanism. The manipulability, i.e the ellipsis area, is also greater in the closed-loop tendon driven mechanism. Extension to six deg

24、rees-of-freedom kinematics The mechanical designs of both closed 5-bar linkages with a pushing type drive and with a pulling type drive have been developed. Then these two mechanisms have been assembled with a ball joint and with a rotational joint, as shown in figure 5, to give raise to two types o

25、f six-degree of freedom kinematic components, later on called for sake of simplicity pushing and pulling legs. Figure 5: CAD model of a 6-dof leg Then four legs have been assembled with a mobile platform and a fixed platform in a six degree-of-freedom parallel manipulator. Such a parallel manipulato

26、r is redundant in the actuation since eight command variables, namely eight tendon tensions or displacements, are independently used to control six degrees of freedom (Kurtz 1990). On the other side, the constraint on the positive sign of the tendon tension (Jacobsen 1989 ) limits the actuation capa

27、bility of the HI. The equation ruling the statics of the HI is the dual of the Jacobian equation: Figure 6: General kinematic architecture with F and t being the external force and torque on the moving platform and t being the eight-dimensional vector of tendon tensions. The HI can exert forces and

28、torques of arbitrary directions if and only if the kernel of contains a vector whose components are all positive. The points of the workspace where such a condition is verified belong to the controllable workspace. Our aim has been to enlarge the controllable workspace to the kinematically reachable

29、 workspace of the mechanism. So we have studied all the possible symmetric spatial arrangements of four legs, to find the most suitable architecture for an HI design maximizing the controllable workspace. Figure 7: Instantaneous kinematic equivalenceWe have chosen the architecture of fig. 6. The leg

30、s are located with an axial symmetry of 90 around an axis normal to the base plane; the base axes of the legs lay in the base plane; both the pushing and the pulling legs are two; the pulling and pushing legs are placed in alternate way around the symmetry axes. The mechanical analogy can be extende

31、d to the 6-dof parallel manipulator. Istantaneously the system is equivalent to the one depicted in figure 7. The equivalent pistons are disposed in a triangulated pattern. Parallel Architecture Geometric Analysis There is a geometric interpretation of the problem of controllability. Figure 8: Force

32、 closure in pure translations It can be shown that a given configuration belongs to the controllable workspace , if in that configuration the four legs can apply to the coupler a statically balanced system of forces. This problem is known in literature as the force-closure problem and it is related

33、with the study of stable grasps in robotics hands (Nguyen 1988). We can regard the four legs of the HI as four fingers that are grasping in four contact points without friction (corresponding to the ball joints) the coupler. In this way the legs can apply to the coupler four forces.From line geometr

34、y (Phillips 1984), it is known that four forces can be statically balanced if their lines of action belong to: a plane ; a bundle of lines; the system of lines constituted by two planar pencils of lines with a common generator; the Regulus of a hyperboloid (the general screws 3-system of null pitch

35、). In the controllable workspace the legs are always capable of applying to the coupler forces whose lines of action belong to one of the listed systems of lines and so statically balanced. In particular for the selected architecture, if we put aside the angular limitation and the sign limitatio-ns

36、of the forces which each legs can exert, it is always possible to find four forces exertable by the HI whose action lines belong to the simplified system of the type 3. Moreover it can be demonstrated that such architectures every pure translation of the mechanism from the initial position, belongs

37、to the controllable workspace. This property is true because there exists always a point to which the lines of actions of the leg thrusts converge, as shown in fig. 8. So it exists a system of lines of the type 2 aforementioned. KINEMATIC OPTIMIZATION AND MECHANICAL DESIGN The six kinematics paramet

38、ers which define the HI kinematics have been dimensioned aiming at maximizing the total volume W of the controllable workspace. The maximum controllable workspace volume has been computed for 7920 different kinematic configurations, ranging overall the search space of kinematic parameters. The analy

39、sis of the results has given the following indications. Figure 9: Translational workspace with zero orientation The smaller is the dimension of the base platform the larger is the controllable workspace. This dimension is lower bounded by the length of the base links of the 5-bars, since they cannot

40、 interfere. The base links dimensions depend on the dimensions of the mechanical components of the base joints of the 5-bars, including the transmission mechanisms. These values have then been chosen as the smallest possible. Larger controllable workspaces are obtained for larger values of the linea

41、r dimensions of the 5-bars links, which is related to the dimension of the legs workspaces. This value has then been chosen in order to meet the workspace requirements, but designing a compact mechanism with dimensions compatible with the requirements. The controllable workspace of the optimal solut

42、ion has been so estimated: in the zero orientation position the admitted translations are depicted in figure and range in -200;200 mm in the xy-plane and in -130;+130 mm in the vertical direction; the maximum and minimum admissible rotations around an axis in the horizontal plane have been estimated

43、 to 35 and when the mobile platform is in the zero-translation position. A maximum force of 20 N can be exerted in the plane with a motor torque of 500 mNm. The mechanical design of the solution addressed by the optimization process has then been designed in a CAD environment. The CAD model of the m

44、anipulator is shown in figure 1.Figure 10: CAD model of the Haptic Interfac Interference between parts has been assessed in the parametric solid CAD model.CONCLUSIONS The general kinematic description of a new six-degree-of-freedom tendon driven manipulator has been reported. Important properties of

45、 the system descend from the chosen kinematics architecture and can be deducted using elements of line geometry. An exhaustive search of all the possible kinematics solution has been numerically implemented. Finally the parameters of the kinematics architecture that yield the maximum controllable wo

46、rkspace have been determined. 桂林電子科技大學(xué)圖書(shū)館電子資源鏡像站點(diǎn)SpecialSciDBS(國(guó)道數(shù)據(jù))新型六自由度平行機(jī)構(gòu)設(shè)計(jì)和運(yùn)動(dòng)學(xué)參數(shù)的優(yōu)化摘要帶有力反饋能力的六自由度機(jī)構(gòu)已經(jīng)問(wèn)世。與計(jì)劃中的機(jī)械設(shè)計(jì)完全相同而且有額外的傳動(dòng)裝置。額外的傳動(dòng)裝置是指在不增加動(dòng)力的情況下，在機(jī)械控制上增加傳動(dòng)裝置?，F(xiàn)在，新型的電纜傳輸已經(jīng)用于六自由度裝置中的每一個(gè)自由度驅(qū)動(dòng)，允許所有的傳動(dòng)裝置置于地面。機(jī)械手靈敏性的運(yùn)動(dòng)學(xué)參數(shù)優(yōu)化和額外裝置已有所發(fā)展。這里所要展示的是機(jī)械設(shè)計(jì)的雛形。關(guān)鍵字接觸面， 關(guān)節(jié)運(yùn)動(dòng)， 六自由度平行機(jī)構(gòu)手引言 平行機(jī)械手因其顯著的性能（剛度好、位置精確

47、、良好的動(dòng)力性能）而被廣泛的研究。其眾所周知的平衡配比在工作空間大小及復(fù)雜的動(dòng)力學(xué)規(guī)則中是不足的。 少數(shù)平行機(jī)械手在文獻(xiàn)中都是基于八面體幾何系統(tǒng)而設(shè)計(jì)的。采用這一動(dòng)力學(xué)原理，連接處的幾何一致性導(dǎo)致了平臺(tái)與腿關(guān)節(jié)，基座與腿關(guān)節(jié)之間的不一致。腿部形成的“鋸齒形三角圖案”連接著基座與運(yùn)動(dòng)平臺(tái)。根據(jù)該動(dòng)力學(xué)原理，機(jī)械手通過(guò)增強(qiáng)剛度來(lái)支持外載荷，能基本改善動(dòng)力工作情況的特殊結(jié)構(gòu)。 論文中討論的新型機(jī)械手，是為實(shí)現(xiàn)六自由度運(yùn)動(dòng)而設(shè)計(jì)的，要求低摩擦，無(wú)齒隙及力反饋裝置的嚴(yán)密設(shè)計(jì)。此外還需要要求機(jī)械裝置在一定的工作空間內(nèi)運(yùn)動(dòng)。六自由度操作裝置在虛擬環(huán)境（VE）中的模擬能反復(fù)用于大多數(shù)的物理效應(yīng)。研究的目的是通

48、過(guò)虛擬環(huán)境（VE）的模擬來(lái)設(shè)計(jì)靈巧和精度的結(jié)構(gòu)，如：碰撞情況，各元件間的相互扭轉(zhuǎn)。 新機(jī)械手的設(shè)計(jì)由可動(dòng)平臺(tái)通過(guò)四條支腿與固定平臺(tái)相連而組成。兩臺(tái)電動(dòng)機(jī)被設(shè)置在基座上，通過(guò)新的關(guān)節(jié)驅(qū)動(dòng)系統(tǒng)來(lái)激勵(lì)腿部的運(yùn)動(dòng)。由于八個(gè)關(guān)節(jié)控制六自由度，關(guān)節(jié)驅(qū)動(dòng)系統(tǒng)的結(jié)構(gòu)參照應(yīng)為N+2型。 關(guān)節(jié)驅(qū)動(dòng)限制了系統(tǒng)的運(yùn)動(dòng)行為，所以是靜態(tài)的，等同于運(yùn)動(dòng)平臺(tái)通過(guò)八個(gè)活塞與基座相連的三角形圖案。 借助靜態(tài)分析，系統(tǒng)的機(jī)械結(jié)構(gòu)恢復(fù)八面體的幾何系統(tǒng)，并帶有兩個(gè)以上的線(xiàn)形傳動(dòng)裝置。顧慮到八面體平行機(jī)械手的典型設(shè)計(jì)，機(jī)械系統(tǒng)是由直流電動(dòng)機(jī)，鋼絲繩來(lái)執(zhí)行，產(chǎn)生一個(gè)高逼真的力反饋到上一級(jí)的裝置。機(jī)械裝置的動(dòng)力學(xué)描述 平行機(jī)械手的支腿的運(yùn)動(dòng)

49、是基于封閉五桿機(jī)構(gòu)的。 新型關(guān)節(jié)傳動(dòng)的設(shè)計(jì)是為了驅(qū)動(dòng)封閉五桿機(jī)構(gòu)的。 該機(jī)構(gòu)在每個(gè)關(guān)節(jié)軸線(xiàn)上各安裝有一個(gè)滑輪，如圖1所示。除了最后一個(gè)驅(qū)動(dòng)滑輪外，其它滑輪空轉(zhuǎn)并用螺栓固定在連桿上。圖1：封閉關(guān)節(jié)驅(qū)動(dòng)的示意圖 所有關(guān)節(jié)上的滑輪半徑都相同。但旋轉(zhuǎn)方向不同。與典型關(guān)節(jié)傳動(dòng)不同，用于連續(xù)的機(jī)械手，最后的驅(qū)動(dòng)滑輪是基礎(chǔ)，且不與運(yùn)動(dòng)的驅(qū)動(dòng)連桿相連結(jié)。新關(guān)節(jié)的驅(qū)動(dòng)設(shè)計(jì)允許在選擇合適的關(guān)節(jié)路線(xiàn)時(shí)，改善封閉五桿聯(lián)動(dòng)裝置的運(yùn)動(dòng)工況，如：避免異常情況和提高運(yùn)動(dòng)的靈活性。封閉關(guān)節(jié)的驅(qū)動(dòng) 現(xiàn)在我們應(yīng)分析一下關(guān)節(jié)驅(qū)動(dòng)的特性。 由于內(nèi)角的總和為P，容易看出圖1中各角度的不同關(guān)系包括： （1） 由于關(guān)節(jié)部分相鄰的兩個(gè)滑輪相對(duì)

50、封閉五桿機(jī)構(gòu)是獨(dú)立的，關(guān)節(jié)的起始極限位移dvi只是連接角度的變化量而確定的： （2）將（1）式代入，得： （3）以上方程意味著： （4）由于靜力學(xué)和運(yùn)動(dòng)學(xué)間的二元性原理，兩關(guān)節(jié)上的作用力T1和T2是相等的，沿QP 和 RP的軸向壓力為： （5） 但由于關(guān)節(jié)處產(chǎn)生了張力，先前的靜態(tài)分析是不完全的，且有賴(lài)于執(zhí)行路線(xiàn)，等效的活塞要么只能向上推，要么只能向下拉。 所以關(guān)節(jié)驅(qū)動(dòng)的封閉五桿聯(lián)動(dòng)裝置可以簡(jiǎn)化為圖2所示的等效裝置。 圖2： 等效裝置 機(jī)械分析是值得的，因?yàn)樗梢詫㈥P(guān)節(jié)驅(qū)動(dòng)的五桿聯(lián)動(dòng)裝置的力的能力解釋得非常清楚。力支持的終端操縱裝置（EF）必須包括沿推力矢量QP 和 RP方向生成的夾角，并作上記號(hào)。相對(duì)分析： 我們研究了封閉五桿聯(lián)動(dòng)裝置上基座關(guān)節(jié)處的直接驅(qū)動(dòng)和新關(guān)節(jié)驅(qū)動(dòng)在動(dòng)力學(xué)上的差異，為的是指出運(yùn)動(dòng)工作情況的不同。 以計(jì)算機(jī)模擬的兩個(gè)驅(qū)動(dòng)系統(tǒng)的橢圓工作圖來(lái)比較其運(yùn)動(dòng)工作情況。例證結(jié)果的研究圖3和圖4。 圖3：基座關(guān)節(jié)驅(qū)動(dòng)的橢圓工作圖 圖4：封閉關(guān)節(jié)驅(qū)動(dòng)