機(jī)械手-集裝箱波紋板焊接機(jī)器人機(jī)構(gòu)運(yùn)動(dòng)學(xué)分析及車體結(jié)構(gòu)設(shè)計(jì)
機(jī)械手-集裝箱波紋板焊接機(jī)器人機(jī)構(gòu)運(yùn)動(dòng)學(xué)分析及車體結(jié)構(gòu)設(shè)計(jì),機(jī)械手,集裝箱,波紋,焊接,機(jī)器人,機(jī)構(gòu),運(yùn)動(dòng)學(xué),分析,車體,結(jié)構(gòu)設(shè)計(jì)
The inverse kinematics analysis of 3-D.O.F welding robot designed for ripple polygonal line seam of container
Yu-Qiang Zhang-Hua Mao Zhi-wei Ye Jian-xiong
（Robot&Welding Automation Key Laboratory Jiang Xi Nanchang University, Nanchang, 330029）
Abstract:To resolve the welding problem existing in ripple polygonal line seam of container,we develop a 3-D.O.F welding robot. An inverse kinematics analysis of the designed welding-robot based on D-H displacement transformation matrix was put forward in this paper. In order to make the welding gun fastend on the end effector keep a certain posture, the three joints of robot should act coordinately, thus this makes an assurerance for the consistency of welding quality. This paper presents the possibility that the robot can track the trajectory under a certain unchanged welding velocity by controlling the discipline of the three joints, and it is verified by means of simulation in MATLAB.
Key words:3-D.O.F; inverse kinematics; act coordinately ; welding posture
0． Introduction.
Figure.1 Ripple polygonal line seam of container
When welding,the welding torch makes the relative motion along the weld seam line by a certain posture .The choice of the welding posture is the key to guarantee a good welding quality,and the welding torch position posture has an important influence to forming of the weld seam.At present,in the welding process of ripple polygonal line seam of container,the welding torch cannot adjust the angle between itself and the welding speed with the profile change.As is shown in the figure.1,the shaping of weld seam at linear section is not consistent with that at hypotenuse section.To resolve the welding problem existing in ripple polygonal line seam of container,this paper make an inverse kinematics analysis of the designed 3-D.O.F welding robot through developing the kinematics equation of the robot which lets the posture of the welding torch make a suitable adjustment with the profile change ,while making sure of the welding torch movement along the curve of weld seam with an constant speed ,thus improve the shaping of the weld seam and then make sure the welding equality.
1.The principle of the mechanism movement of 3-D.O.F welding robot
To resolve the welding problem existing in ripple polygonal line seam of container at present.We developed a kind of 3-D.O.F robot.
This robot have three movement joints: about translate between right and left the welding robot main body 1; about translate up and down the cross slide 2;the terminal effector 3 which making the rotary motion.We achieve that the welding speed does not change with the change of the posture of the terminal effector through the coordinated movement of the three joints.
2.The inverse kinematics analysis of 3-D.O.F welding robot.
2.1 The simplification of kinematics models
Figure. 2 The moving diagram of 3-D.O.F welding robot .
As shown in figure.2,the welding torch(which is presented by a dark point at the end of movement joint 3) is attached at the terminal effector 3 of the welding robot.In the process of welding,the position posture of the welding torch should make a suitable adjustment with the shape change of the weld seam.The adjustment presents as the coordinated movement.
2.2 The establishment of kinematics model
In order to portray the movements of each joint ,a decca rectangular coordinate system is established for the moving mechanism of the robot ,as shown in figure.1.The initial space position relations of the coordinate systems established on each rigid body .Those coordinate systems are presented in figure.3.{0} is the base coordinate system,{1},{2},{3} are the moving coordinate sysytems established on the robot main body ,on the cross slide and the terminal effector.we will analyze the moving law of the movement joint by using the movements of {1},{2},{3}.
We could portray the coordinate value of a point of {B} in {A} by using equal time coordinate transformation matrix .Establishing three equal time coordinate transformation matrix 、、.
，，
Where l0,L1,L2 represent the initial distances between each coordinate system separately;S1,S2 are the displacement of {1},{2} in certain time t-t0,and , , V1,V2 are the speed of the zero point of {1},{2} separately ;θis the rotated angle of the third movement joint ;
，
By transformation equation ,we have:
Then we could establish the transformation relation between the description of one point in {0} and that in {3}:
=,that is =………..(a)
Where: (x0,y0,z0),(x3,y3,z3) are the coordinate value of point p in {0} and {3} separately.
2.3 The inverse kinematics solutions
During the process of welding ,we should make sure of the vertical angle between the welding torch and the weld seam .Its movement has two restraints: a constant speed ; a determined weld seam curve.We take a cycle of the ripple for carrying on the reverse kinematics solution ,and analyze the driving laws which the three movement joints’ coordinated actions should follow so that satisfy the two restraints .In a cycle the welding torch needs to pass through four turning points .This article take the first turning point as an example to explain the process of the reverse solution .This process is divided into three stages ,namely linear section ,circular arc change-over section and hypoteneuse section .
As the moving path of the welding torch ,in free time t ,the coordinates of the point at the end of the welding torch are (x3,y3,z3,1)=(0,r,0,1) and {x0,y0,z0,1} respect to {3} and {0} separately .
By expression (a), we have
=……………………..(b)
According to the weld seam in reality ,we assume the third movement joint’s angle acceleration as .
2.3.1 The movement of the point in linear section
We assume the start time of the movement as t0,the coordinates of the point at time t respect to {0} are x0=l0+vwt; ,
Substituting equation (b) into it , and making differentiation with respect to time on S1,S2,we have the moving law of movement joints 1 and 2:
2.3.2 The movement of the point in circular arc change-over section
Figure.4 The graphical representation of the arc transition at the turning point.
Suppose the robot move to this stage at time t1, the point’s position relative to {0} is: ,the angle speed of {3} w=0.
When the robot is moving ,by spatial geometry relations,we have :
,
,the speed law of movement joints 1 and 2 are :
The speed of the end of the welding torch along the direction which is parallel to the direction of the weld seam is constant,that is the welding speed is constant.
By the spatial geometry: ,therefore ,
.
Thus
2.3.3 The movement of the point in wave hypoteneuse section
Suppose the robot moving to this stage at time t1’,the coordinates of the point respect to {0} is
=,after the reverse solution yields .
According to the same method, we could get the coordinated movements law of the three movement joints ,and satisfy the constraint conditions in a ripple cycle .And then we could make sure of the perpendicular relation between the welding torch and the weld seam at different section.
3. The simulation of the reverse kinematic analysis of the 3-D.O.F welding robot
The calculation is based on the determined moving law of the third joint and make sure that it satisfy the two constraint conditions ,and reverse deduce the moving law of the two other joints {1},{2} .
To verify the process of reverse solution ,we carry on the simulation by the matlab software .we establish some spatial geometry size : ,the rotating radius of the rotating joint r=0.1m , the angle between the linear section and hypoteneuse section at the turning point is .
In a welding cycle ,the change rule of the rotating arm’s angle acceleration is shown as figure.5
Figure.5 The angle acceleration change rule of joint 3
Thus we could obtain the change rule of the third joint’s rotating angle ,as shown in figure.6
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