Research Article Kinematics Analysis and Modeling of 6 Degree of Freedom Robotic Arm from DFROBOT on Labview

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1 Research Joural of Applied Scieces, Egieerig ad Techology 13(7): , 2016 DOI: /rjaset ISSN: ; e-issn: Maxwell Scietific Publicatio Corp. Submitted: May 5, 2016 Accepted: Jue 7, 2016 Published: October 05, 2016 Research Article Kiematics Aalysis ad Modelig of 6 Degree of Freedom Robotic Arm from DFROBOT o Labview 1 Haa A.R. Akkar ad 2 Ahlam Najim A-Amir 1 Departmet of Electrical Egieerig, Uiversity of Techology, 2 Departmet of Electrical Egieerig, Al-Mustasiriya Uiversity, Baghdad, Iraq Abstract: The aim of this study is to aalyze the robot arm kiematics which is very importat for the movemet of all robotic joits. Also they are very importat to obtai the idicatio for cotrollig or movig of the robot arm i the workspace. I this study the kiematics of ROB0036 DFROBOT Arm will be accomplished by usig LabVIEW. Fidig the parameters of Deavit-Harteberg represetatio, the kiematic equatios of motio ca be derived which solve the problems of automatic cotrol of the 6 revolute joits DFROBOT maipulator. The kiematics solutio of the LabVIEW program was foud to be earest to the robot arms actual measuremets. Keywords: DFROBOT 6DOF robot arm, forward kiematics, iverse kiematics, LabVIEW, robot maipulator INTRODUCTION The kiematics problem is related to fidig the trasformatio from the Cartesia space to thejoit space ad vice versa. The solutios of the kiematics problem of ay robot maipulatorhave two types; the forward kiematic ad iverse kiematics. Whe all joits are kow the forward kiematic will determie the Cartesia space, or where the maipulator arm will be. I the iverse kiematic the calculatios of all joits is doe if the desired positio ad orietatio of the ed- effectors is determied, that meas by the iverse kiematic the robotic arm joit space agles will be calculated as referred to Craig (2005). A six degree of freedom DFROBOT has five rotatioal joits with a gripper ad operate with their servo motors coected as a itersectig or parallel joit axis, it is a low cost educatioal robot maipulator, flexible ad similar to idustrial robot arms. I this study the parameters of the stadard Deavit Hardeberg listed i Table 1 for the 6DOF Robot Arm show i Fig. 1 has bee used for modelig ad simplifyig its associated kiematics. The kiematic aalysis of idustrial robots was discussed i may literatures (Craig, 2005; Spog et al., 2005). Koyucu ad Guzel (2007) suggested a method for solvig the kiematics of the Lyx 6d of Robot ad propose a software package amed MSG that used to test the behavior of robot motio. Qassem et al. (2010) proposed a software package to solve the kiematics of the AL5B Robot arm. More aalysis have bee achieved for modelig a 6dof robotic maipulators usig the MATLAB software for their simulatio by Iqbal et al. (2012), Kumar et al. (2013) ad Sigh et al. (2015). Forward kiematic is much easier tha iverse kiematic ad so called direct kiematic, Mohammed ad Suar (2015) bega their kiematic aalysis by usig the product of Expoetial Formula (PE) to simplify the aalysis. I this study a simple ad direct solutio to the mathematical model ad kiematical aalysis of the DFROBOT equatios which relate all joits together as refer to the base is achieved. Applyig the robot arm kiematics o LabVIEW, the maipulator motio ca be itroduced with respect to its mathematical aalysis. I this study the target will be o the Kiematics ad how to obtai the joit agles from the iverse kiematics modelig that ca be used for the cotrol of a variety of idustrial processes. The work takes the beefit of usig the umeric values for the positio ad orietatio of the ed- effector which is the results of the forward kiematics ad fid all the joit agles of the robot arm from the iverse kiematic solutios applied i the ew developed closed form package of the 6 DOF robot which is the case study of this study. DFROBOT MODELING The DFROBOT is a 6DOF robotic arm delivers fast, accurate ad repeatable movemet ad called articulated because it has a series maipulator havig Correspodig Author: Haa A.R. Akkar, Departmet of Electrical Egieerig, Uiversity of Techology, Baghdad, Iraq This work is licesed uder a Creative Commos Attributio 4.0 Iteratioal Licese (URL: 569

2 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 Table 1: The DH parameters of the DFROBOT Joit Lik a i-1 mi α i-1 degree d i mm FORWARD KINEMATICS θi degree θ 1 θ 2 θ 3 θ 4 θ 5 gripper Fig. 1: 6DOF robot maipulator Fig. 2: Kiematic modelig block diagram The joit variables of the robot are give to determie the positio ad orietatio of the ed- effector. Each joit for each frame has a sigle degree of freedom ad ca be represeted by a sigle umber, which is the agle of rotatio i the case of a revolute joit i.e., (θ, θ,.., θ, θ. Startig from the base which is deoted as lik 0 to the liks the cumulative effect of the joit variables ca be calculated. z is a uit vector alog the axis i space betwee liks i-1 ad i. Next, each lik is attached with coordiate frames from 1 to, the frame i is rigidly attached to lik i. Figure 3 illustrates the DFROBOT frames ad liks coectios. Assigmets of joits ad all parameters used to defie the robot frames ca be defied by usig the DH parameters table explaied by Tahsee (2013). Table 1 shows the related six joits parameters of the robotic arm ROB0036 maipulator i order to fid the positio ad orietatio of the rigid body which is useful for obtaiig the compositio of coordiate trasformatios betwee the cosecutive frames: where, a : The legth distace from z to z measured alog z α : The twist agle betwee z ad z measured about x d : The offset distace from x to x measured alog z θ : The agle betwee x ad x measured about z Forward kiematics aalysis is the process of calculatig the positio ad orietatio of the edeffector with give joits agles so by substitutig these parameters i the homogeous trasformatio matrix from joit i to joit i+1 (Craig, 2005): Fig. 3: The robot coordiate frame θi SθiCαi SθiSαi Ai = Sθi CθiCαi CθiSαii 0 Sαi Cαi aicθi aisθi di 1 all joits as revolute. The mai features of this kid: base rotatio, sigle plae shoulder, elbow, wrist motio, fuctioal gripper ad optioal wrist rotate. The kiematic modelig requires the solutios of the forward ad iverse kiematics of the maipulator ad the lik parameters are eeded for the two solutios as show i the block diagram of Fig The trasformatio matrices A ad A for the DFROBOT joits ca be obtaied as show: C S 0 0 A S A = C d (1)

3 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 where, the matrix A for example shows the trasformatio betwee frames 0 ad 1, C = cosθ ad S = siθ : C 0 S 0 A S A = 0 C 0 (2) C S 0 a C A S A = C 0 a S (3) C S 0 a C A S A = C 0 a S (4) C 0 S 0 A S A = 0 C 0 (5) d C S 0 0 A S A = C 0 0 (6) Performig the compositio from the - th frame to the base frame we multiply the six matrices from 1 to 6: p a C C C a C S S + S d + a C C p a S C C a S S S C d + a S C p a S C + a C S + a S + d (8) where, C = cos (θ + θ, S si(θ + θ, C cos(θ + θ + θ ad S = si(θ + θ + θ Makig use of some trigoometric equatios helps for easy solutios: C C C S S S C S + S C C C (C C S S S (C S + C S S S (C C S S + C (S C +C S. INVERSE KINEMATICS The solutio of Iverse kiematics is more complex tha forward kiematics ad there is may solutios approach such as geometric ad algebraic aalysisused for fidig the iverse kiematics cosiderig the system structure of the robotic arm. I case of iverse kiematics the joit agles ca be determied for ay desired positio ad orietatio i Cartesia space. For simplicity of solutios to fid the joit agles of 6d of articulated robot arm of the DFROBOT the trasformatio matrix i Eq. (7) ca be multiplied by A for = 1,,6 o both sides of the equatio sequetially, the solvig the produced equatios obtaied by equatig terms of the both sides of matrices: A = A. A.. A = A = R P 0 1 where, R is a 3 3 matrix for rotatio ad P is the positio, so the total matrix of trasformatio: A = A A A A A A o a p = o o a a p p (7) where, p, p, p represet the positio ad {(,, ), (o, o, o ), (a, a, a }, represet the orietatio of the ed- effector, they ca be calculated i terms of joit agles: C C C S S C S C + C S = C S o C S C S C o S S C + C C o S S a C S a S S a C 571 C S 0 0 S A = C 0 0 (9) d C S 0 0 A = (10) S C 0 0 C S 0 a S A = C 0 0 (11) C S 0 a S A = C 0 0 (12) C S d A = (13) S C 0 0 C S 0 0 S A = C 0 0 (14)

4 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 INVERSE KINEMATIC SOLUTIONS To solve the matrix i Eq. (7) it is easy to use the algebraic solutio techique for: A = A A A A A A (15) To solve for θi whe A is give as umeric values, multiply each side bya : o a p A o a p = A o a p A A A A A A (16) The matrix maipulatios has resulted the followig matrix solutios:.. C a + S a C p + S p.. C S a C C + a C C + S d.. S ax + C a S p + C p.. S S a S C a S C C d (17).. a p d.. C a S + a S Both matrix elemets i Eq. (17) are equated to each other ad the resultat θ values are extracted. By takig (1, 4) (2, 4): C p +S p = a C C + a C C + S d (18) S p + C p = a S C + a S C C d (19) Squarig ad addig the two Eq. (18) ad (19): C = Cos θ = θ = Cos = Ata2 ( 1, (20) Eq. (3, 4): S a S p + d θ Ata2 p d a S + a S, 1 (21) θ θ θ (22) Multiplyig each side of Eq. (15) witha A : o a p A A o o a a p A p A A A (23)... C C p + C S p + S p C C S C S a C + a C... S C p S S p + C p C S S S C a S + a S S C S o C o. S p C p d S C 0 d (24) 572

5 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 Equatig elemets (3, 4) of the right had side matrix ad the left had side matrix of Eq. (24): S p C p d d S p C p d + d θ = ata2p, p ata2 p + p (d + d, (d + d (25) From Eq. (8) we ca obtai: a S S a C S Dividig the two equatios: = θ = ata2 (a,a ) (26) Ad the we fid: θ θ θ (27) The also equatig elemets (3, 1) ad (3, 2) of the two sides of the matrices i Eq. (24): S S C OrS C S C S o C o Or C C o S o θ Ata2C S, C o S o (28) Or alteratively: θ Ata2 1 C o S o, C o S o (29) Now multiply each side of Eq. (15) by: o a p A A A o a p = A o a p A A (30) C C C S S a C C o a p C C S C S a C S C S S C a S C o a p C = RHS S S S C a S = LHS (31) S C 0 a S d o a p S C 0 d Equatig elemets (3, 4) from the two sides of Eq. (31): S p C p a S d d S p C p a S + d + d θ ata2 p x, p y ata2 p x 2 + p y 2 a 3 S 2 + d 1 + d 5 2, (a 3 S 2 + d 1 + d 5 (32) θ 3 θ 23 θ 2 (33) From the Eq. i (8) we ca also obtai: C 345 a z θ 345 ata2 1 a 2 z, a z (34) θ 5 θ 345 θ 3 θ 4 (35) 573

6 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 Fig. 6: Iverse kiematic simulatio Fig. 4: The robot agles The developed software will calculate the required agles for target orietatio ad target positioig, the agle values are calculated by usig the equatios as follows: θ 2 ata2 p x, p y ata2 p 2 x + p 2 y (d 1 + d 5 2, (d 1 + d 5 θ 12 = ata2 (a y,a x ) θ 1 θ 12 θ θ 23 ata2 p x, p y ata2 p 2 x + p 2 2 y a 3 S 2 + d 1 + d 5, (a3 S 2 + d 1 + d 5 θ 3 θ 23 θ 2 θ 3 = Cos 1 = Ata2 ( 1 2,, where, θ 2 = Cos θ 3 = p x 2 p 2 2 y d θ 34 Ata2 a 3S 3 p z + d 1 4 θ 4 θ 34 θ θ 345 ata2 1 a z 2, a z, 11 a 3S 3 p z + d 1 θ Fig. 5: Forward kiematics simulatio with the matrices A 6 ad A ot show i diagram 574 θ 5 θ 345 θ 3 θ 4 θ 6 Ata2 C 2 y S 2 x, C 2 o y S 2 o x

7 Res. J. Appl. Sci. Eg. Techol., 13(7): , 2016 RESULTS AND DISCUSSION Kiematic aalysis with mathematical solutios of the 6dof DFROBOT was doe i this study. With the Deavit-Harteberg method ad for a give joit agles to be applied as the desired agles for a example (45.92, 75.3, 45.92, 20.20, 90, 31.23) i degrees show i Fig. 4, forward ad iverse kiematic solutios are geerated by the developed software with LabVIEW. Figure 5 shows the implemetatios of these agles to fid the total homogeous trasformatio matrix which cotais positio ad orietatio parameters related to the motio kiematic of the robot arm. The other simulator isthe iverse kiematic part with aew aalysis techique for the user that use the result parameters of equatios (8) beig solved to obtai the ew joit agles θ, θ, θ, θ, θ ad θ for a give task of the Robot Arm. For ay desired joit frame with the positio ad orietatio show i total matrix the iverse kiematic oliear system solver will be ru as show i Fig. 6. CONCLUSION A aalytical solutio with a ewly developed system solver for the Kiematics of a 6dof Robot Arm from DFROBOT is derived ad developed i this study. This model gives correct joit agles so that the robot arm with its ed- effector ca easily moved to ay reachable positios ad orietatios for performig a pick ad place task. Less differece is foud betwee measured ad calculated valued which give a exactdesired poits i the kiematics simulatio process. Also this method ca be used to solve kiematics for other robotics arm. REFERENCES Craig, J.J., Itroductio to Robotics: Mechaics ad Cotrol. 3rd Ed., Pearso, Pretice Hall, Upper Saddle River, NJ, USA. Iqbal, J., M.R.U. Islam ad H. Kha, Modelig ad aalysis of a 6 DOF robotic arm maipulator. Ca. J. Electr. Electro. Eg., 3(6): Koyucu, B. ad M.S. Guzel, Software developmet for the kiematic aalysis of a Lyx 6 robot arm. It. J. Comput. Electr. Automat. Cotrol Iform. Eg., 1(6): Kumar, K.K., A. Sriath, G. Jugalavesh, R. Premsai ad M. Suresh, Kiematic aalysis adsimulatio of 6Dof KukaKr5 robot for weldig applicatio. It. J. Eg. Res. Appl., 3(2): Mohammed, A.A. ad M. Suar, Kiematics modelig of a 4-DOF robotic arm. Proceedig of the IEEE Iteratioal Coferece o Cotrol Automatio ad Robotics. Sigapore, pp: Qassem, M.A., I. Abuhadrous ad H. Elaydi, Modelig ad simulatio of 5 DOF educatioal robot arm. Proceedig of the 2d Iteratioal Coferece o Advaced Computer Cotrol (ICACC, 2010). Sheyag, pp: Sigh, E.H., N. Dhillo ad E.I. Asari, Forward ad iverse kiematics solutio for six DOF with the help of robotics tool box i matlab. It. J. Appl. Iov. Eg. Maage., 4(3): Spog, M.W., S. Hutchiso ad M. Vidyasagar, Robot Modelig ad Cotrol. 1st Ed., Joh Wiley ad Sos Ic., New York. Tahsee, F.A., Forward kiematics modelig of 5DOF statioary articulated robots. Eg. Tech. J., 31(3):