外文文獻翻譯--關于一種新型6自由度組合并聯(lián)機械臂的研究（英文）

1、Study on a Novel 6-DOF Combinational Parallel Manipulator Wei Zhao, Bing Li*, Hongjian Yu Ying Hu Shenzhen Graduate School, Harbin Institute of Technology Shenzhen, 518055, P. R. China State Key Laboratory of Robot

2、ics and System (HIT), Harbin 150001, P. R. China Cognitive Technologies Lab, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518067 China *Corresponding Author: Email: libing.sgs@hit.

3、edu.cn ying.hu@siat.ac.cn Abstract- A novel 6-DOF parallel manipulator composed of two limited-DOF manipulators is proposed in this paper, the degree of freedom (DOF) of this manipulator is analyzed and the position kin

4、ematic modeling is established. The Jacobian matrix is derived by vector loops equations. The workspace is determined considering the interference check by the numerical method. Furthermore, the performance of the mechan

5、ism is evaluated according to dexterity criteria. In order to satisfy the different configuration requirements, the two reconfigurable structures are presented based on the presented 6-DOF parallel mechanism. The work pr

6、ovides basis for the development of the novel robotic manipulator. Index Terms- Combinational manipulator, Kinematics, Workspace, Dexterity, Reconfigurable structure. I. INTRODUCTION Parallel mechanism has been used in

7、many fields such as aeroplane simulator, robot, machine tool since its better stiffness and accuracy, lighter weight, greater load bearing, higher velocity and acceleration and less powerful actuators [1]. The most c

8、lassical six-DOF parallel manipulators are Gough’s [2] tire testing machine and Stewart’s [3] motion simulator. But some parallel manipulators are less than six DOF, such as the Delta and 3-UPU manipulators. In recent

9、 years, reduced-DOF manipulators especially these with 3-DOF have been studied intensively. Fang [4], Miller [5], Kong [6] and Kok-Meng Lee [7] have reported several architectures with reduced-DOF, such as Tricept wh

10、ich has been applied in the aeroplane and automobile manufacturing extensively [8~9]. The flexible fixture based on combionational fixture has become a major element of modern development direction. In this paper, t

11、he author applies a 6-DOF parallel manipulator to the design of flexible fixture. It is composed of a spatial 3-RRS manipulator and a planar 3-RRR manipulator[10]. The characteristics of the mechanism are studied in

12、details: the degree of freedom, Jacobian, workspace and dexterity etc. At last, two reconfigurable structures based on this mechanism are also proposed which can be used for the different industrial fields. II. DESCR

13、IPTION OF THE NOVEL PARALLEL MANIPULATOR The manipulator investigated in this paper is shown in Fig.1. It is composed of two parallel manipulators. One is the planar 3-RRR manipulator and the other is the spatial 3-RRS

14、 manipulator. All the joints except the spherical joints associated with the moving platform are revolute joints, and the axes of them parallel to each other. If the spherical joint is replaced by three intersecting

15、unit screws, there would be five joint screws associated with each limb of the 3-RRS manipulator. So there exists a unique screw reciprocal to all the joint screws, which stands for a force applied to the point of the

16、 center of the spherical joint and parallels to the axes of the revolute joints. Then, there will be three constrained forces acting on the moving platform [11~12]. Generally, these 3 force screws are non-uniplanar a

17、nd linearly independent. So the possible movements are the translation along the normal of the fixed platform and spatial two-dimensional rotation about the lines which can intersect the three force screws at the same

18、 time. The planar 3-RRR manipulator has three DOFs including planar two-dimensional translation and one dimensional revolution. As the two combinational manipulators have different DOFs respectively, so the man

19、ipulator considered in this paper has a total of six DOFs. Fig.1 Model of the manipulator III. INVERSE KINEMATICS The kinematic diagram is given in Fig. 2. All the joints of the manipulator are shown in the figure. The

20、re are six active revolute joint variables represented by i θ and i η , where i= 1, 2, 3. The moving frame {m} is at the triangle Proceedings of the 2008 IEEE International Conference on Robotics and Biomimetics Bangkok

21、, Thailand, February 21 - 26, 2009978-1-4244-2679-9/08/$25.00 ©2008 IEEE 1469vector pointing to the positive Z-axis vector. Then we can get two equations as 1 1 1 1 1 1 12 2 2 2 2 2 23 3 3 3 3 3 31 1 1 1 1 12 2 2 2

22、 2 23 3 3 3 3 3( )( )( )( )( )( )θθθηηηωωωωωω? × × ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? × = × ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? × × ? ? ? ? ? ?′ ? ? ? × × ? ? ? ? ? ? ?

23、? ? ? ′ ? ? ? × = × ? ? ? ? ? ? ? ? ′ ? × × ? ? ? ? ?momok L l r l l ω k L l r l l v k L l r l lk a b r b bk a b r b bk a b r b b? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?oOoOωv(8)

24、Simplifying, = ? ? ? ? = ? ? ?1 1 12 2 2q θ x oq η x oJ ω J vJ ω J v(9) where θ ω and η ω are the angular velocities of the actuate joints, iq J and ix J are matrices derived in Eq. (8). vo1 and vo2 describe the output

25、 velocities of the two manipulators respectively, but the first one is presented in the frame {o} and the other is presented in the frame {O}. There are only three output of the 3-RRR planar manipulator, so vo2 can be

26、 written as ' [ ]T z x y w v v = 2 o v and 2x J becomes as '1 1 3 11 12'2 2 3 21 22'3 3 3 31 32'3 3( )( )( ) ××= ××? ? ? ? ? ? ? ? ? ?2xr b b bJ r b b br b b bwhere '3 ( ) &

27、#215; i i r b is the third column of ' × i i r b , ( 1,2) j = ij b is the jth column of i b . Then the second equation of (9) can be written as ' ' 1 ? ? = 2 2 2 q η o x J J ω v(10) As the Jacobian m

28、atrix represents the relationship between input velocity and output velocity, so we describe the input velocity in one equation as 00? ? ? ? ? ? = + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?1 1 1 1 2 1 2 2θ q x o o η q xω J J v

29、 v ω J J????(11) For the output velocity = + 1 2 o o v v v , equation (11) becomes as 0? ? ? ? ? ? ? = + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?1 1 1 1 1 1 2 1 2 2q x θ q x o η q xJ J ω J J v v ω J J? ??? ??(12) From equation (

30、10), we can get ' 1 ' ' 10 0 0 0 0 00 0 0 0 0 00 0 00 0 0 0 0 0? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2 2 2 2 2 2o x q q o x J v J J J vθη

31、 ηη ηωω ω (13) Describing the first matrix at the right of (13) as 3 J and substituting (13) into (12), then ( ) 0? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?31 1 1 1 1 11 2 2q x q xq xJ J J J J I v J Jθηθηωωωω? ??

32、? ??(14) Then we can get the Jacobian matrix of the manipulator is 1 ( ) 0? ? ? ? ? ? = ? ? ? ? ?? ? ? ? ? ? ? ?31 1 1 1 1 11 2 2q x q xq xJ J J J J J I J J? ??? ??(15) V. WORKSPACE It is well known that comparing wit

33、h serial ones, parallel manipulators have relatively small workspace. Thus, it is necessary to analyze the shape of the workspace to enhance the performance of parallel manipulator. The reachable workspace is defined

34、 as the space that can be reached by the reference point with at least one orientation. We select a point at w-axis with a distance above the centroid m of the moving platform as the reference point. There are three

35、steps to get the workspace for this manipulator. The first is to searching the boundary of the spatial 3-RRS manipulator with sphere coordinate searching method. The boundary of the planar 3-RRR manipulator is easily

36、 derived by normal boundary searching method, this is the second step. Then, moving the spatial workspace along the boundary of the planar curve getting in the second step, the resulting envelope is the workspace of t

37、he combined manipulator. Certainly, physical constraints should be considered during the design of a practical manipulator. The architectural parameters of the manipulator are selected as r=50mm, R=80mm, R’=260mm, L=

38、l=130mm, a=b=140mm. Suppose the orientation is zero, the workspace of the manipulator is generated by a MATLAB program as shown in Fig. 3 (a), (b) and (c). They represent the front view, top view and left view respec

39、tively in the figure. It is observed from Fig.3 that the reachable workspace is symmetrical about the motion directions of the three actuators. VI. DEXTERITY The dexterity of a manipulator can be regarded as the ab

40、ility of the manipulator that can arbitrarily change its positions and orientations, or to apply forces and torques in arbitrary directions. It has been a measure for manipulator’s kinematic performance index [14]. Th

41、e Jacobian matrix represents the mapping of both velocities and forces between the end-effector and the actuators of the manipulator, so its properties are used as a measure of dexterity generally. Different indices

42、of manipulator dexterity are presented as condition number, minimum singularity and manipulability. The condition number of the Jacobian matrix ranges in value from one (isotropy) to infinity (singularity) which