新型高速并聯(lián)機(jī)械手的動(dòng)態(tài)靜力學(xué)探析

1、新型高速并聯(lián)機(jī)械手的動(dòng)態(tài)靜力學(xué)探析    Kineto-Static Analysis of a Novel High-Speed Parallel Manipulator with Rigid-Flexible Coupled Links Abstract: A novel-invented high-speed parallel kinematic machine (PKM) named Delta-S parallel manipulator is proposed in this paper, which consists of a fixed

2、base connected to a moving platform through three limbs with identical topology. Each limb is composed of one driving arm and one follower arm, herein, the latter includes two strings and one middle rod, all locating on a same plane. Compared to similar manipulators with uniform parameters, the nove

3、l and unique topology as well as the addition of two strings of Delta-S manipulator may removes the clearance of the spherical joints, reduces the inertial load of components further and can improves the positioning accuracy and dynamic performance, and so on, which draw considerable attention. In o

4、rder to formulate the kineto-static model of Delta-S manipulator, the kineto-static analyses and models of the driving arm, the generalized follower and the moving platform can be carried out firstly by means of the D Alembert principle. For the sake of obtaining the force analytic results of string

5、s, the deformation compatibility condition of strings and the middle rod are determined in this paper with the method of Hooks law. Furthermore, in virtue of the assumption of small deformation and the linear superposition principle, the minimal pre-tightening force of the strings is calculated, its

6、 main results includes the loads of the strings and the middle rod must greater than “zero” and the pre-tightening force over the workspace must greater than the minimal pre-tightening force at any time within the workspace, which lay the foundation for the dynamic analysis and the prototype manufac

7、ture of Delta-S manipulator. Key words: parallel kinematic machines (PKMs); Delta-S manipulator; kineto-static analysis; deformation compatibility condition; pre-tightening force    1 Introduction The parallel kinematic machines (PKMs) have attracted much attention because of man

8、y merits and then have experienced 6-degree-of-freedom (6-DoF) PKMs and the limited-DoF PKMs including 5-DoF, 4-DoF, 3-DoF and 2-DoF PKMs . However, the invention and application of Delta robot modify the peoples conventional comprehension on general PKMs and may be a breakthrough of the high-speed

9、limited-DoF PKMs. The application of the light-weight and slender limbs in Delta robot gain the high velocity and acceleration of the end-effector, which can be applied in the production line of Pick-and Place and advances the production efficiency availably, and then the more important is that the

10、supply of creative ideas for some similar mechanisms such as HEXA robot, UWA Delta robot, Deltabot, Diamond and so on. However, many rods in the limbs of Delta robot or Delta-like mechanisms may lead to the occurrence of large inertia and intense impact in the high-speed motions, which may influence

11、 the precision and stability of the mechanism systems. In order to settle these related problems, a novel high-speed PKM with rigid-flexible coupled links named Delta-S (S stands for String) manipulator is proposed in this paper. Compared to Delta robot, the follower arm of Delta-S consists two stri

12、ngs instead of the two rods in the Delta robot and adds a middle rod between the two strings. The application of the strings can decrease the inertia and the impact effectively, besides, the precision and the stability of Delta-S parallel manipulator may be improved accordingly. Compared to the stud

13、ies of Delta robot, the string research in Delta-S is a more difficult and challenging problem, the analysis of the string is replaced by that of the cable in lots of references based on their similar characters. Back to 17 centuries, G. Galileo, J. Bernoulli, S. D. Poisson take their own contributi

14、ons to string researches regarding the foundational theory, followed by the formulation of the numerical solution for the planar cable by OBrien, which accelerates the cable developments greatly. Besides, stiffness problem of the cable is preceded by H. M. Irvine, J. C. Russell, T. J. Lardner and so

15、 on. Based on the researches of the cable and the string, a novel-invented high-speed PKM with rigid-flexible coupled links called after Delta-S manipulator is presented in this paper, composed of a fixed base, a moving platform and three identical limbs. The topology of each limb includes one drivi

16、ng arm and one follower arm, however, two strings and one middle rod constitute the follower arm and locate in one same plane. The kineto-static analyses of the driving arm, the follower arm and the moving platform may be executed respectively in the first place and then the kineto-static model of D

17、elta-S parallel manipulator is formulated based on the D Alembert principle. Furthermore, the minimal pre-tightening force of the two strings in the follower arm is calculated after determining its deformation compatibility condition. Finally, one example is demonstrated in this paper and proves the

18、 validity of the method mentioned-above.    2 Description and definition As demonstrated, the Delta-S parallel manipulator is composed of a fixed base, a moving platform and three limbs with identical topology and layout. Each limb includes one driving arm BiCi and one follower a

19、rm CiAi, herein, the former joins the fixed base with a revolute joint (R joint), and the follower containing two strings and one middle rod connects the driving arm and the moving platform all with spherical joints (S joint). Without loss of generality, the planes of the fixed base and moving platf

20、orm are assumed as two equilateral triangles B1B2B3 and A1A2A3 whose circumradius are nominated as rb and ra. A global coordinate frame designated as the O-xyz frame is fixed at the center of the fixed base with the z-axis pointing vertically upwards and the y-axis pointing to the point B3, while a

21、moving coordinate frame O'-x'y'z' is assigned to the center of the moving platform, whose three axes are parallel to these of the frame O-xyz. Therefore, the closed-form equation may be obtained as follows: 12(1,2,3iiiilli=+=rbauw (1)where r, bi and ai denote the position vectors of

22、point O', Bi and Ai in frame O-xyz, respectively. l1 and l2 represent the lengths of the driving arm and the middle rod, ui and wi are the unit vectors of the ith driving arm and the ith middle rod. It is noteworthy that the similarity of the topology between Delta-S manipulator and Delta robot

23、yields the homogeny of the inverse problems, and then the related parameter values of Delta-S manipulator can be obtained easily after according to the inverse problem analysis of Delta robot, such as the unit vector of the axis of R joint vi, the angle i between wi and (vi×ui), the rotating an

24、gle i, the acceleration and angular acceleration (iand i as their notation) of the driving arm, the centric acceleration vector aui of the driving arm, the angular velocity and angular acceleration vector of the follower arm expressed by wi and wi, the centric velocity vector and the centric acceler

25、ation of the follower arm denoted by vwi and awi.    3 Kineto-static analysis of Delta-S Due to the little mass of the string, its gravity and inertial force can be ignored, and then the direction of the remaining force applied at the string may be only considered along its axis.

26、 Based on these hypotheses, the follower arm is similar to the parallelogram and be regarded as generalized follower arm, each generalized follower arm exerts constraint force on both the moving platform and the driving arm through the S joints of the middle rod, and the forces can be nominated as F

27、s1 i and Fs2 i, respectively. In addition, the different axial forces applied on the string lead to the occurrence of the constraint couples exerted on the moving platform and the driving arm, and the couples may be expressed by Mi and Mi, whose directions are orthogonal to the follower arm planes.

28、Furthermore, the kineto-static analyses of the driving arm, the follower arm and the moving platform can be preceded as follows. 3.1 Driving arm the kineto-static model of the driving arm, F1 i is defined as the constraint force of the driving arm exerted by the fixed base, according to the force re

29、lationship, the kineto-static equation of the driving arm may be formulated as follows. 3.2 Follower arm After ignoring the mass of the string, the forces exerted on the generalized follower arm only includes the gravity and inertia force of the middle rod, the constraint forces Fs1 i and Fs2 i. A body-fixed coordinate frame designated as the Si-x''y''z'' frame is fixed at the centroid Si of the middle rod with the z''-axis along wi and the y'