1、Engineering, 2012, 4, 850-856 /10.4236/eng.2012.412108 Published Online December 2012 (http:/www.SciRP.org/journal/eng) Kinematical Analysis and Simulation of High-Speed Plate Carrying Manipulator Based on Matlab Ke Wang, Jiping Zhou School of Mechanical Engineering, University of Ya

2、ngzhou, Yangzhou, China Email: w jpzhou Received October 13, 2012; revised November 14, 2012; accepted November 23, 2012 ABSTRACT In order to construct the more effective kinematics method for industry, by taking a high-speed plate handing robot as an example, the structure and paramete

3、rs of the robot linkages are analyzed, and the standard Denavit-Hartenberg me- thod is applied to establish the coordinates and the kinematic equation of the linkages. Depending on the graphics and matrix calculation ability of Matlab especially including the Robotics Toolbox, the handling robot has

4、 been modeled and its kinematics, inverse kinematics and the trajectory planning have been simulated. Therefore, the correctness of kinematic equation has been verified, meanwhile, the functions of displacement, velocity, acceleration and trajectory of all the joints are also obtained. In a further

5、step, this has verified the validity of all the structure parameters and pro- vided a reliable basis for the theoretical research on the design, dynamics analysis and trajectory planning of the ma- nipulator control system. Keywords: High-Speed Plate Carrying Manipulator; D-H Method; Robotics Toolbo

6、x; Trajectory Planning 1. Introduction As a typical representative and a main technical means of information technology and advanced manufacturing tech- nology, the complete set of automatic stamping process- ing line has become a high technology to which the deve- loped countries have paid much att

7、ention. And its devel- opment level has become one of the most important stan- dards to measure a nations technical development. It has been extensively applied in the industry of mechaniccal manufacturing, nuclear, aerospace, energy and transpor- tation, petroleum chemistry, building, electronic an

8、d etc. 1. But, one key aspect of the automatic stamping proc- essing line is to develop a mechanical manipulator with the characteristic of the high-speed and dynamic trans- mission. At present, the sheet metal forming production line is operated at the high productive rate of 15 - 25 SPM. Re- movin

9、g the time spent by the press stamping operations, there is only about 2 s left to the robot manipulator. In such a short period of time, the manipulator has to oper- ate at a high speed of 200 - 250 m/min, so that the opera- tions such as loading, moving and unloading can be ful- filled. And this h

10、as put forward higher requirements to the mechanical structure, material friction characteristics, and structural dynamic characteristics of the robot mani- pulator. Taking a high-speed plate carrying manipulator as the research object, this paper firstly analyzes the structure and connecting rod pa

11、rameters; then adopts the standard D-H method 2 to establish the kinematics equation; and then discusses the positive and inverse kinematics algo- rithm, and the trajectory planning problems; finally in the environment of Matlab, the kinematics model is built to take kinematics simulation by using o

12、f Robotics Toolbox 3. In simulation process, we can not only directly ob- serve the robot motion, but also get the required data in the graphic form. Therefore, the virtual performace of the product can be tested in the conceptual design stage, so as to improve the design performance, reduce design

13、cost and decrease product development time. 2. The Structure Design and Link Parameters of High-Speed Plate Carrying Manipulator 2.1. The Design Requirements of High-Speed Plate Carrying Manipulator 2.1.1. The Workplace of High-Speed Plate Carrying Manipulator The traditional stamping processing met

14、hod relies on a stand-alone manual which is inefficient, inaccurate and in- security. So it has already become increasingly unsuited to the requirements of modern mass production, espe- cially when the requirements of the sheet metal process- ing annual output exceeds thousands tons, this contradic-

15、 Copyright 2012 SciRes. ENG K. WANG, J. P. ZHOU 851 tion is more prominent. The current stamping equipment is toward the trend of automation, sets and online de- velopment. With the rapid development of Chinas mar- ket economy, especially in the coastal areas where the shortage of skilled workers is

16、 severe, and labor costs rises sharply, many machinery manufacturers have the urgent demand for manufacturing automation, and re- quire machine and equipment manufacturing industry to provide users with a complete set of on-line technical services to improve production efficiency and reduce labor co

17、sts. Therefore, the development of the technol- ogy of sheet metal production line is even more important. One of the core technologies of sheet metal stamping equipment line is the design of high-speed plate carrying manipulator. As shown in Figure 1, it is high-speed plate carrying manipulator in

18、the application of stamping pro- cessing complete sets of equipment on-line system. 2.1.2. The Operation Process of High-Speed Plate Carrying Manipulator According to the composition of the stamping process sets of on-line system and the role of the high-speed plate carrying manipulator, the working

19、 cycle of a manipulator contains nine action process, as shown in Figure 2: 1) From the point of origin, the left electromagnetic valve is energized after pressing the start button, then the manipulator moves to the left. It wont stop until it en- counters the left limit switch. 2) Simultaneously th

20、e manipulator begins to drop after the decreased electromagnetic valve opens, then, it wont stop until it encounters the lower limit switch. 3) At the same time the clamp electromagnetic valve is energized, then the manipulator is clamped. 4) After the rise electromagnetic valve is energized, the ma

21、nipulator begins to rise, then it wont stop until it encounters the rise limit switch. 5) Simultaneously the manipulator moves to the right after the right electromagnetic valve is energized, then, it wont stop until it encounters the right limit switch. 6) Simultaneously the manipulator begins to d

22、rop after the decreased electromagnetic valve is energized, then, it wont stop until it encounters the lower limit switch. 7) At the same time the clamp electromagnetic valve is opened, then, the manipulator is opened. 8) After the rise electromagnetic valve is energized, the manipulator begins to r

23、ise, then, it wont stop until it Double sets unstacker unit Feeding manipulator Press 1 Transfer manipulator 1 Press 2 Transfer manipulator 2 Press 3 Transfer manipulator 3 Figure 1. The composition of the stamping processing sets of on-line system. Figure 2. The operation process of the manipulator

24、. Copyright 2012 SciRes. ENG K. WANG, J. P. ZHOU 852 encounters the rise limit switch. 9) Simultaneously the manipulator moves to the origin after the left electromagnetic valve is energized, then, it wont stop until it encounters the left limit switch. So far, the manipulator after 9 step action co

25、mpletes a cycle of its movement, and then, it continues the cycle work. Based on the above analysis, we have developed a th- ree-dimensional model of the manipulator as shown in Fi- gure 3, which can be used to analyze the dynamic cha- racteristics of the manipulator. 2.2. The Design Parameters of H

26、igh-Speed Plate Carrying Manipulator 2.2.1. D-H Transformation In order to describe the translational and rotational rela- tionships between adjacent rods, Denavit and Hartenberg (1955) have proposed a matrix method to establish the possessed coordinate system for each rod in the linkage chain. This

27、 method is to establish a homogeneous trans- formation matrix for each of the join bar coordinate, which represents the relationship of the previous coordi- nate system of the bar, and the principle 4,5 is detailed as follows: OXYZ: A fixed reference coordinate system of the fix- ed coordinates, is

28、called the coordinate system. OiXiYiZi: Fixed connected with the member bar of num- ber I of the robot, the origin of coordinate is at the center point of the joint of the I + 1th. Identify and establish each coordinate system by fol- lowing three rules. 1): Zi1 axis along the motion shaft of the jo

29、in of the i th. Figure 3. The assembly model of manipulator, 1-body, 2- feeder, 3-beam, 4-slipway, 5-balance cylinder, 6-servo mo- tor, 7-X axis transmission system. 2): Xi axis vertical the axis of Zi and Zi1 and point to the direction of away from the Zi1 axis. 3): Yi axis according to the require

30、ments of the right hand coordinate system to establish. Meanwhile the notation of D-H of the rigid bar de- pends on the four parameters of the connecting rod. The angle of two connecting rod i : Xi1Xi around the corner of Zi1. The distance of two connecting rod : Xi1Xi along the distance of Zi1. i d

31、 The length of the connecting rod : Zi1Zi along the distance of Xi1. i a The torsion angle of the connecting rod: : Zi1Zi around the corner of Xi. i a For rotational joints, i is the joint variables, the rest are joint parameters (remain unchanged); for mobile jo- ints, is the joint variables, the r

32、est are joint parame- ters. i d 2.2.2. The Design Coordinate of Manipulator High-speed plate carrying manipulator is mainly compo- sed of vertical pillars (body), horizontal arm (beam), sli- ding table (Y axis transmission system) and base. Hori- zontal arm mounted on the machine body level can move

33、 around and can move up and down along the vertical pillars. By reference to the high-speed plate carrying ma- nipulator in Figure 3, we establish the coordinate system of manipulator in Figure 4 based on the above analysis. According to the D-H parameters method, four para- meters are defined for e

34、ach link: the connecting rod angle i , the distance of two connecting rod i, the length of the connecting rod i, the connecting rod torsion Angle i, the D-H parameters of manipulator as is shown in Table 1. d a a Z1 Y1 X1 X2 Y2 Figure 4. The D-H coordinate of high-speed plate carrying manipulator. C

35、opyright 2012 SciRes. ENG K. WANG, J. P. ZHOU 853 Table 1. The D-H parameters and joint variables of mani- pulator. Joint i di ai di 1 0 d1 0 90 2 0 d2 0 0 3. The Kinematics Simulation Algorithm of Manipulator 3.1.The Kinematics of Manipulator The so-called kinematics problem 4,5 is given to the ma-

36、 nipulator of each joint variable, and then obtains the po- sition and posture of the end of the actuator, and its es- sence is to establish the kinematics equations. For the so- lution of kinematics equation, this paper uses homoge- neous transformation matrix 1i i A i to describe the coor- dinate

37、system of i relative to the position and pose of the coordinate system of the i 1, this is the general formula for transformation matrix 1i A . 1 cossincossinsincos sincoscoscossinsin 0sincos 0001 iiiiii iiiiiii i ii a a A d i i i A (1) Now, putting the D-H parameters and joint variables of manipula

38、tor substitution of the Table 1 in (1), we get the homogeneous transformation matrix of the i co- ordinate system relative to the position and posture of the base coordinate system, expressed as: 0 i T 0011 12 i i TA A i (2) Especially, when , can be obtained, it determines the position and posture

39、of the end of the ma- nipulator relative to the base coordinate system, the ma- trix of T can be expressed as: 2i 0 2 TT 2001 212 1 1000 001 010 0001 d d TTA A (3) Note: 01 12 1 10001000 00100100 , 010001 00010001 d AA 2 d 1 1 3.2. The Inverse Kinematics Issue of Manipulator The inverse kinematics i

40、ssue of manipulator is defined as follows: with the known the position and posture of the end of the actuator, we need to solve the variables of each joint of the manipulator, here in our case the vari- ables are and . 12 The target point of the movement of the manipulator center is . By using the t

41、ransi- tional joint, the manipulators center point can coincide with the target point, and the target point can be ex- pressed as: , then we can estab- lish the following equation: dd T 0 00 0YZP 2 12 0ddP T 002 2 PTP (4) Combining (3) and (4) and solving the kinematics equation , we can get the fol

42、lowing equation. 20 2dY (5) 10 2dZ (6) 4. The Kinematics Simulation of Manipulator 4.1. Use Link and Robot Functions to Establish the Manipulators Object 1) Before the manipulators simulation, firstly input the manipulators parameters by calling the function Link: alpha, ,theta,sigma , standardLAD (

43、note: alpha, theta,AD represent the variables of i , i , i and di respectively; “sigma” represents the joint types: 0 for the rotational joint, and 1 for the transitional joint; “standard” is for the standard D-H parameters. The function robot is used to create a manipulator object by using the Link

44、 function in the format of Robot (Link). The commands for creating the high-speed plate carrying manipulators is expressed as follows: 1 2 12 2000.081 ,standard ; 0000.91 ,standard ; robot,Manipulator ; plot drivebot Lpi L rLL r r 2) We can immediately see the three-dimensional view of the manipulat

45、or which can be used in the form manu- ally for driving through the slider in the chart to drive the movement of the manipulator, which is just like the ac- tual control of the manipulator 3. As shown in Figure 5, it has brought great convenience for manipulators teach- ing and training. 4.2. The Te

46、st of Kinematic Model In the Figure 5, by moving each slide in the bar to move Copyright 2012 SciRes. ENG K. WANG, J. P. ZHOU Copyright 2012 SciRes. ENG 854 4.3. The Simulation of Trajectory Planning the manipulator, the first joint movement can change the height of the manipulator in the vertical d

47、irection. The second joint can change the length of the manipulator in horizontal direction, So that we can obtain different posi- tion and posture. By adjusting the slides and the joint va- riables, we can get the approximate model corresponding to the actual structure in Figure 3, as shown in Figu

48、re 6. According to the requirements of the task, trajectory planning will designate in advance the robots operating procedure and action process. The simulation method could describe in details the movement process of the industrial robot 6-10. Planning can be made in the space of both joint and ope

49、ration. We would introduce two main motions 4,5: 1) PTP, Point-To-Point motion; 2) CP, Continuous-Path. With regard to continuous-path, not only the initial and final points of the manipulator need to be set, but also some other points between the two points (called path points) which must move alon

50、g some specific path (path constraint) need to be indicated. In order to verify the correctness of the kinematics Equation (3), the geometric parameters and the joint va- riables of each rod of the manipulator are put into the ki- nematic equations to solve the setting position and pos- ture of the

51、coordinate system of the end link rod in rela- tion to the base coordinate system. And then the corres- ponding coordinate values are input to the manipulators trajectory planning, and the actual end position and pos- ture information are compared with the results from sol- ving the equation. Two gr

52、oups of joint variable values are randomly chosen : 1 2 1.00530.50265 0.502650.50265 q q The design of the high-speed plate carrying manipu- lator adopts a point-to-point trajectory planning. Set A as the starting point, moving to B where a task is finished, and then set B as a starting point, movin

53、g to C where a certain task is completed, and then set C as a starting point, moving to point C to complete the preset tasks, and continue to move, and so on. Here, the move from point A to point B and from point B to point C does not exist any point between them, and there is not any re- quirement

54、for the known path of the movement. There- fore, we can take this above planning as PTP planning. The error is very small through the comparative analy- sis of the actual value and set point, which explains that the kinematics equation and the model are reliable and consistent. The starting point is

55、 set to be 0 00 ,q ending point 1 0.628321.2566q , and between the two Figure 5. The three-dimensional diagram and slide block control chart of the high-speed plate carrying manipulator. Figure 6. A state of high-speed plate carrying manipulators three-dimensional diagram and slide block control cha

56、rt. K. WANG, J. P. ZHOU 855 points the initial and final speeds are both zero, with the time of movement time: , the relative program as follows: 2 st 01 01 00 ;0.628321.2566 0:0.1:2 jtraj, plot, qq t qqqt rq By conducting the above program, we can observe the whole process of the high-speed plate c

57、arrying manipu- lator moving from Figures 5 and 6. We can also draw, by way of the function of 01 ,jtraj,plot,:,qqdqddqqttqi each joints displacement curve, as shown in Figure 7(a) and (b). (note: q represents the displacement, i represents the joint Numbers). Also we can draw speed curve as shown in Figures 7(c)-(d), acceleration curve as shown in Figures 7(e)-(f), through the corresponding functions: plot,:,plot,:,tqditqddi 4.4. The Analysis Based on the Results of Simulation From Figures 7(a) and (b),