The motion simulation of three-dof parallel manipulator based on VBAI and MATLAB Zhuo Zhen, Chaoying Liu* and Xueling Song

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1 Internatonal Conference on Automaton, Mechancal Control and Computatonal Engneerng (AMCCE 25) he moton smulaton of three-dof parallel manpulator based on VBAI and MALAB Zhuo Zhen, Chaoyng Lu* and Xuelng Song Insttute of electrcal engneerng, Hebe Unversty of Scence and echnology, Shjazhuang, Hebe, 5, Chna Keywords: Machne vson, the three-dof parallel manpulator, VBAI, MALAB. Abstract. In order to truly reflect the object stuaton of catch and place of the three-dof parallel manpulator based on machne vson, and on the bass of the modelng of the trajectory and mechancal structure, ths paper manly focuses on the analyss on the manpulator system by usng the co-smulaton approach based on the MALAB and VBAI software, wth modelng and smulaton of target acquston, mechancal structure, and trajectory plannng for manpulator system bult. In addton to ths, the applcaton of machne vson technque has been proposed to sample and grasp the mage of an object. he smulaton results show that the manpulator system can meet to the requrements of the desgn accuracy and rapdty, whch proves the effectveness of the co-smulaton method.. Introducton Parallel manpulator has the advantages of hgh rgdty, hgh flexblty, strong carryng capacty, especally to acheve translatonal parallel mechansm has attracted ntense attenton [-2]. [3] he parallel manpulator based on Delta mechansm s the most representatve. he IRB 34 Flex [4-5] Pcker s a knd of vsual manpulators based on Detla parallel mechansm,w hch s developed by ABB company by Adpet technology. he robot can crawl dsorderly placed objects. he robot can make use of mage processng technques for automatc sortng and crawl. Based on vsual analyss of the robot has become a hot research. At present, domestc and foregn about parallel manpulator research manly focuses on the mechansm desgn theory, knematcs, dynamcs modelng and analyss, control strategy and so on. hs paper presents a smulaton method of moton of three degree of freedom parallel manpulator based on machne vson; the whole workng process of parallel manpulator based on machne vson was complete smulaton. 2. arget acquston and target postonng he robot use Vson Bulder AI software for target acquston and postonng. Vson Bulder AI NI Introduces referred VBAI s a software product for vsual nspecton. hs tool s an deal tool to lab for a quck vsual effect valdaton, and producton lne to acheve smple test deal test platform. arget object mage can be mported to the VBAI program by means of the camera. akng mechancal parts as expermental object, we wll mport the mage nto the VBAI program, then the followng treatment: ) Gradaton processng Frst of all to gray-scale mage processng, gray processng s to accelerate thereacton speed of software. Because we only need to get the object contour nformaton, so does the need for color mage. After gray mage after processng as shown n Fg. ; 2) Calbrate Image Because of the bass of mechancal hand graspng objects s the actual dstance, so we have to be the pxel value nto the actual dstance value. he actual dstance of the system unt s mm. Select two ponts on the mage, and then enter the actual dstance can be n software, dstance calbraton nterface as shown n Fg. 2; 25. he authors - Publshed by Atlants Press 57

3) Match Pattern he role of MMM s to establsh a template to capture objects, and then can be dentfed from the object test bench. emplate matchng the nterface as shown n Fg.

If you select the robot mechancal orgn poston for the upper left corner of the magng area, t can be drectly output target coordnates to the robot's moton controller.

Z-axs coordnate s determned based on the shape of the target object and preset trajectory and can be set drectly on the mechancal hand grasp program. Fg. Gradaton processng Fg. 2 Calbrate Image Fg.

2 3) Match Pattern he role of MMM s to establsh a template to capture objects, and then can be dentfed from the object test bench. emplate matchng the nterface as shown n Fg. 3; 4) Set Coordnate System Setup Locate the template matchng the geometry center as the center coordnates for the target poston, processng nterface as shown n Fg. 4. 5) Coordnate values of output Manpulator control system s set up coordnate system based on camera at the upper left of the area of orgn. If you select the robot mechancal orgn poston for the upper left corner of the magng area, t can be drectly output target coordnates to the robot's moton controller. he coordnate output nterface as shown n Fg s the X-axs coordnate and Y-axs coordnate s Z-axs coordnate s determned based on the shape of the target object and preset trajectory and can be set drectly on the mechancal hand grasp program. Fg. Gradaton processng Fg. 2 Calbrate Image Fg. 3 Match Pattern Fg. 4 Set Coordnate System Setup Fg. 5 Coordnate values of output 2. he poston nverse soluton of three degree of freedom parallel manpulator he movng platform s regarded as a pont O '. Reference coordnate system O -XYZ based on the statc platform Center O '. he poston vector of Movng platform reference pont O ' can be expressed as: r = [x, y, z]. Eq. ndcates the poston vector of pont O '. Fg.6he smplfed geometry structure dagram Fg.7 hree dmensonal model (MALAB) r= e + lu + l2 w, =, 2,3 () ( ) ( ) 2 π π e = e cos β sn β (2) β = (3)

3 ( cos cos sn cos sn ) u = β θ β θ θ (4) E E G + F θ = 2 arctan, =, 2,3 G F 2 ( ) [ ] 2 2s ( ) ( cos β sn β ) 2 2 ( ) ( ) E = l r e (6) F = r e X + Y, X = [ ], Y = [ ] (7) X G = r e r e + l l (8) 2 r e lu = l2 w, =, 2,3 (9) 2 ( r e lu) ( r e lu) = l () 2 E snθ + F cosθ + G =, =, 2,3 () he formula () expressed the poston vector. he mold of e sad the crcumscrbed crcle radus dfference between the statc platform and movng platform. Namely, O to vector n the Fg.6.It expressed the statc Angle of platform structure whch were the actve arm of branched chan respectvely and the slave arm length and unt vector. he formula (5) expressed the actve arm Angle. hs Angle can be used as the bass of a drve motor rotaton. he formula() turned to (9).It multpled by the respectve on both ends of transposed, and t got (), the formula (4) nto the formula (),and t got the formula().by expressed the formula (6), (7), (8), the reducton of the formula()whch can be the ntatve arm Angle expresson of the formula (5). 3. he modelng of three degree of freedom parallel manpulator In MALAB of SIMULINK module, the modelng of three degree of freedom parallel manpulator s set up [6].It s as shown n Fg. 7. ) Wth the ad of MALAB SmMechancs n the toolbox, the process of Modelng s fnshed. he toolkt provdes a number of correspondng to the actual system components. Usng these modules can be convenent to create dagrams to model complex mechancal system. hese modules can analyss mechancal system alone or n combnaton wth any of the controllers desgned by SIMULINK, and other comprehensve smulaton of dynamc system are lnked together. 2) As shown n the trangle of the Fg.7, parallel manpulator movng platform s smplfed as a bt of statc platform, and actve arm drven arm can be clearly represented. By SmMechancs toolkt actve to statc platform, we can also set the arm, the qualty of the slave arm, sze, ntal poston n order to a better smulaton. 4. rajectory plannng he three DOF parallel manpulator tasks s capture, transfer, placement, takng nto account the operaton of the process of a certan heght or wdth of the obstacle, So we put the moton path to the door shape. As shown n Fg. 8. herefore, a reasonable arc excessve model becomes the deal choce of the manpulator moton path. Accordng to the prncple of the shorter path frst, we set the moton trajectory of manpulator for Modfed trapezodal: (5) P3 P4 P5 P2 P P6 P7 P8 Fg. 8 rajectory plannng Fg. 9he smulaton module 573

4 ) he trajectory of three degrees of freedom parallel manpulator projecton n the Y-axs drecton s p3p6 ; X-axs drecton are pp 3and p6p8. he startng pont coordnates of movement track of the three DOF parallel manpulator s random, but the end pont of coordnate trajectory s fxed. Because the mechancal hand placed the object poston s fxed, so the end pont coordnates of coordnate manpulator moton trajectory s fxed. he basc trajectory of the three-dof parallel manpulator s pp2 p2p4 p4p5 p5p7 p7p8, as n Fg.8. 2) After the moton controller to get the coordnates of the target object from VBAI software, quckly moved to the coordnate poston. We set up three-dof parallel manpulator wth a pck and place tasks to complete are 3 seconds. pp 2 segment movement tme s.5s; p2p4 segment movement tme s.5s; p4p5 segment movement tme s s; p5p7 segment movement tme s.5s; p7p8 segment movement tme s.5s. Assumng the robot crawl objects need to upgrade the heght s 5 mm. he coordnate of the target object s (M, N), the coordnates of the placement pont s (, 2, -85). We can plan a robot movng platform at each nterval movement trajectory s: pp 2 :<t.5s he drecton of X axs: M; he drecton of Y axs: N; he drecton of Z axs: -85+5(t-( 2 π) sn(t)). 2 p2p4 :.5s<t s he drecton of X axs: he drecton of Y axs: he drecton of Z axs: 3 p4p5 :s<t 2s he drecton of X axs: he drecton of Y axs: he drecton of Z axs:-8. 4 p5p7 :2s<t 2.5s he drecton of X axs: he drecton of Y axs: he drecton of Z axs: 5 p7p8 :2.5s<t 3s M M + 5((t.5) sn(4 π ( t.5))) ; 2 N 4π N+5((t-.5)- sn(4 π (t-.5))) ; 4π -85+5(t- sn( t)). -M -M M+ 25+ (2-N-5) ((t-)- sn(2 π (t-))) ; 2 -N 2 -N N+25+(2-N-5)((t-)- sn(2 π (t-))) ; -M -M -M M+ (2-N- 5)+ 5((t-2)- sn(4 π (t-2))) ; 2 -N 2 -N 2 -N 4π (N+(2-N-25))+5((t-2)- sn(4 π (t-2))) ; 4π -8-5((t-2)- sn(2 π (t-2))). he drecton of X axs: ; he drecton of Y axs:2; 574

5 he drecton of Z axs: -8-5((t-2)- sn(2 π (t-2))). 5. the MALAB smulaton In the MALAB of SIMULINK module, the establshment of the model s as shown n Fg. 9. he model s set of three parts: the seral data recevng part, the robot moton control parts and mechancal manpulator model. VBAI and MALAB can be establshed through a seral port communcaton. It wll obtan the coordnates of the object under fetchng VBAI passed to the manpulator and gve the coordnates of the manpulator (M, N) n the assgnment. he heght of the Z drecton changng [- 85 mm, 85 mm].he desgn of the smulaton experments of three groups of dfferent grab poston whch s takng objects obtaned respectvely by VBAI coordnates (-, -2), (-2, -5), (-8, -23).he movng platform n the process of fetchng manpulator trajectory as shown n Fg. to 2.It can be seen from the Fg.. Accordng to certan manpulator trajectory by (M, N) coordnates movement comes to an end poston (,2). he movng platform trajectory(mm) X-drecton Y-drecton Z-drecton 2 3 he smulaton tme (s) he movng platform trajectory(mm) Y-drecton X-drecton Z-drecton 2 3 Fg. (M, N) s (-,-2) Fg. (M, N)s (-2, -5) he movng platform trajectory(mm) X-drecton Y-drecton Z-drecton 2 3 Fg. 2(M, N)s (-8, -23) X-axs(mm) Fg. 3rajectory (X-drecton) As the coordnates for fetchng thngs (-, -2,-85), the value of M and N are respectvely-, - 2.Mechancal hand platform s respectvely n the X, Y, Z drecton of the trajectory as shown n Fg. 3 and 5. he movng of the plat form Moton trajectory should be a straght lne. Because t s a straght lne n the XY plane target pont and end pont of the shortest path.as shown n Fg. 6, t s a straght lne whch s drven platform moton trajectory n space n the XY plane projecton. As shown n Fg. 7, the three-dmensonal space observed the actual trajectory of movng platform modfed trapezodal. Y-axs(mm) Fg. 4 rajectory (Y-drecton) Z-axs(mm) Fg. 5 rajectory (Z-drecton) 575

6 Y-axs(mm) X-axs(mm) Fg. 6 rajectory(xy-plane) Z-axs(mm) Y-axs(mm) X-axs(mm) Fg. 7 rajectory(hree-dmensonal space) 6. Summary For three degree of freedom parallel manpulator system, ths paper uses the VBAI software technology target. he MALAB software s used for trajectory plannng modelng and mechancal structure. It has carred on the VBAI and the combnaton of MALAB software smulaton proved that the parallel manpulator system meets the desgn requrements of accuracy and rapdty. he paper proves the jont smulaton method s effectve. Acknowledgements hs paper s supported by Insttute of electrcal engneerng, Hebe Unversty of Scence and echnology and Insttute of Appled Mathematcs, Hebe Academy of Scences. Correspondng author Chaoyng Lu, E-mal: lucy@hebust.edu.cn. References [] GOSSELIN C. Determnaton of the workspace of 6-DOF parallel manpulators [J]. Journal of Mechancal Desgn, 99, 2(3): [2] KEMALS, KORKMAZO, rajectory trackng control of parallel robots n the presence of jont drve flexblty [J]. Journal of Sound and Vbraton, 29, 39:77-9 [3] Clavel R. Delta, a fast robot wth parallel geometry[c]. Proceedngs of 8th Internatonal Symposum on Industral Robots, Sydney, Australa, 988: 9- [4] Clavel R, Dspostf pour le deplacement et le postonnement d un element dans l espace, Swtzerland patent, CH , 985 [5] Clavel R, Devce for the movement and postonng of an element n space, U.S. Patent, No. 4,976,582, 99 [6] Z.Zhen,C.Y.Lu,Y.K.Zhang andc.m.hao, he Combned Smulaton of Hgh-speed Parallel Manpulator based on MALAB, SoldWorks and ADAMS, Mechancal Engneerng and Materals Scence.ayuan,24,

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