Workspace Analysis of a Novel Parallel Robot Named 3-R2H2S with Three Freedoms

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1 Reserch Journl of Appled Scences, Engneerng nd Technology 6(0: , 013 ISS: ; e-iss: Mxwell Scentfc Orgnzton, 013 Submtted: Jnury 17, 013 Accepted: Februry, 013 Publshed: ovember 10, 013 Workspce Anlyss of ovel Prllel Robot med 3-RHS wth Three Freedoms Xn-Je Wng, Cho-Hu Zhng, C-Dong Wng nd Hu Zheng Mechncl nd Electrcl Engneerng Insttute, Zhengzhou Unversty of Lght Industry, Zhengzhou, Henn, 45000, Chn Abstrct: In order to meet the sortng nd pckng needs of the drug nd food ndustres, novel prllel robot mechnsm nmed 3-RHS s proposed n ths study, the knemtcs equton of the robot ws deduced nd the nverse knemtcs ws clculted. The workspce model of the robot s nlyzed by the boundry serch method through the MATLAB nd ADAMS knemtcs softwre. The nlyss results show tht the robot hs lrge effectve workspce wth smooth boundry nd cn be wdely ppled n the feld of ndustrl robots, the knemtcs of mcro robots nd 3D coordnte mesurements nd the workspce of the robot cn meet the needs of drug nd food utomton producton lne. Keywords: Prllel robot, poston nverse solutons, workspce ITRODUCTIO Prllel robot s new knd of robot; t hs seres of dvntges: hgher stffness, strong berng cpcty, smll error, hgh precson, smll rto of weght lod, good dynmc performnce, esy to control nd so on (Keml nd Korkmz, 009; col nd Vncenzo, 011. Prllel robot s wdely used n res such s flght smultor, prllel mchnes nd prllel mnpultors (Hung et l., 009; Yun et l., 008. The workspce of prllel robot s n mportnt ndex to evlute ts workng performnce, so t hs n mportnt prctcl sgnfcnce to nlyss nd reserch the workspce of the prllel robot (Chen et l., 010. In recent yers, mny scholrs t home or brod hve done lot of reserch work on prllel robot s workspce, lke Dun et l. (011 who hve reserched the knemtcs nd workspce of the 6-PUS/UPU prllel robot nd concluded the workspce of the mechnsm t dfferent flexble poses; Lee et l. (006 mde detled nlyss for the 3-UPS prllel mechnsm, lter they drw out the workspce nd concluded tht the workspce s symmetrcl n spce. At present, most of the workspce reserch s bsed on the robot s structure sze nd constrnt condtons to seek the workspce, whch s clled the postve problem, but the reserch of the reverse problem whch s bsed on the workspce of the robot to seek the structure sze nd constrnt condtons s less. Recently, lrge number of people re workng mong the food nd drug ndustres for the sortng tsks nd t hs lots of dsdvntges such s unsntry, unsfely nd hgh cost. In order to mprove the Rottonl jont Movng pltform Sttc pltform Ar sucton cup Actve rm Pssve rm Sphercl jont Fg. 1: 3-D model of 3-RHS prllel robot Hooke jont utomton degree of these enterprses nd gurntee the products qulty, novel prllel robot mechnsm nmed 3-RHS s proposed ccordng to the food nd drug sortng operton requrements. Ths study reserches the workspce of the prllel robot endeffect or bsed on the nverse soluton. STRUCTURE DESIG Accordng to the new prllel robot mechnsm n ths study, two sphercl jonts hve been replced by Hooke jonts bsed on the delt robot; the structure s shown n Fg. 1. The sttc pltform nd movng pltform re connected through three sme brnches nd the ngle of every two djcent brnches s 10, ech brnch s Correspondng Author: C-Dong Wng, Mechncl nd Electrcl Engneerng Insttute, Zhengzhou Unversty of Lght Industry, Zhengzhou, Henn, 45000, Chn 3847

2 Fg. : Structure dgrm of 3-RHS mechnsm consst of one Rottonl jont (R jont, two Hooke jonts (H jont nd two Sphercl jonts (S jont tht connectng n turn. The smulton result shows tht the new structure not only overcomes the trdtonl structure s problem tht the connectng br whch connect two sphercl jonts rotte round ts own shft (Zhu et l., 003, but lso moves smoothly nd hs bgger workspce nd good knemtcs performnce. An r sucton cup s fxed t the movng pltform s center, the sucton cup cn grbs drugs or foods by the negtve r pressure nd then the robot moves the drugs or foods nto the correspondng pckgng box n very fst speed. The sucton cup cn be exchnged ccordng to dfferent products to meet the sortng requrements. Freedom nlyss nd clculton: The structure dgrm of 3-RHS mechnsm s shown n Fg.. Accordng to the Kutzbch-Grubler formul of sptl mechnsm freedom, we cn clculte: g Res. J. Appl. Sc. Eng. Technol., 6(0: , 013 F = 6( n g 1 (1 n : The number of prts g : The number of knemtc prs gg ff = 33 : The sum freedoms of ll prs f In ths mechnsm, the nfluence of the locl freedom ws elmnted due to the replcement of two sphercl jonts wth two Hooke jonts n ech brnch, whch ws completely equvlent wth the trdtonl delt mechnsm n knemtcs. Accordng to the clculton formul, number of prts n = 11, number of knemtc prs g = 15, the sum freedoms of ll prs gg ff = 33, so the freedom of the mechnsm s 3. Inverse soluton of poston: The nverse soluton of robot poston s bsed on the reference pont s coordnte of movng pltform n the coordnte system, to clculte the three control motors rotton ngle on the sttc pltform; t s lso to clculte the three ctve rms pendulum ngle reltve to the sttc pltform. The nverse soluton of robot poston s the 3848 bss of trjectory plnnng for prllel robot; only obtn the correct soluton cn we mke the end mnpultor to rech the requred pose. Ths study uses geometry method to solve the mechnsm poston. As s shown n Fg., settng the sttc pltform s crcumscrbed crcle s rdus s R, the sttc pltform s crcumscrbed crcle s rdus s r, AB = l α, B C = l b, buldng sttc coordnte system O-XYZ n the center of the sttc pltform nd dynmc coordnte system O'-X'Y'Z' n center of the movng pltform. Accordng to the geometrcl reltonshp, the poston vector of the rottonl jont s center A n sttc coordnte system O-XYZ s: o ( cosα,sn α, T = R 0 ( = 1,, 3 ( α represents the ncluded ngle between OA nd the postve drecton of X xs: 4 3 α = π 6 ( = 1,, 3 Smlrly, we cn obtn the poston vector of the equvlent center C on the movng pltform n dynmc coordnte system s: o ( cosα, sn α, T c = r 0 ( = 1,, 3 (3 α represents the ncluded ngle between O'C' nd the postve drecton of X' xs: 4 3 α = π 6 ( = 1,, 3 Settng the rotte ngle form OA to A B s θ, from the geometrcl reltonshp, we cn obtn the poston vector of B n sttc coordnte system s: b o = ( R l ( R l l cosα snα snθ (4 Settng the coordnte of the center O' of movng pltform n the dynmc coordnte system O-XYZ s (x, y, z, the rotte ngle of the movng pltform reltve to sttc pltform n the drecton of Z xs s zero, so the vector OC n the dynmc coordnte system O-XYZ cn be expressed s: c o r cosα x = r sn α y z (5 For B C = l b, from the defnton of the vector module, we cn get the equton:

3 Res. J. Appl. Sc. Eng. Technol., 6(0: , 013 [( R l r cosα x] [( R l r snα y] ( l snθ z = l b (6 The bove formul s the nverse soluton equton of knemtcs. After reducton we cn obtn: M t t P = 0 ( = 1,, 3 (7 t M 1 = tn θ ( = 1,, 3 = ( R r l x y z lb ( R r( x cosα y snα l ( R r x cosα y snα nd the 8 groups of nverse soluton respectvely re: (θ 1, θ, θ 3 = (-7784π, π, π (θ 1, θ, θ 3 = (-7784π, π, π (θ 1, θ, θ 3 = (-7784π, π, π (θ 1, θ, θ 3 = (-7784π, π, π (θ 1, θ, θ 3 = (-31π, π, π (θ 1, θ, θ 3 = (-0.31π, π, π (θ 1, θ, θ 3 = (-0.31π, π, π (θ 1, θ, θ 3 = (-0.31π, π, π Some groups wll cuse nterference when the mechnsm n ctul moton n the bove 8 groups nverse soluton. Therefore, to clculte the prllel robot s nverse poston soluton s to fnd the optml soluton of the 8 groups, so tht the system cn relze the best nd fstest control nd hs the best knemtc performnce. WORKSPACE AALYSIS = 4zl P = ( R r l x y z lb ( R r( x cosα y snα l ( R r x cosα y snα Accordng to Eq. (7, we cn get: 4M P = ( = 1,, 3 M t ± The ngle θ cn be obtned by: ( t rctn (8 From the soluton we cn fnd tht there re 8 groups of jont postons of the mechnsm when the pose of movng pltform s gven. In order to vldte the correctness of the nverse poston soluton, we clculte nverse poston soluton through n exmple to observe the correspondng relton between nput nd output. Frst we set the mechnsm s bsc prmeters R = 105 mm, r = 50 mm, l α = 0 mm, l b = 495 mm, the center s coordnte of movng pltform s (x, y, z T = (35, 60, -31 T, then we cn clculte the three ctve rms pendulum ngle θ reltve to the sttc pltform. Accordng to the nverse soluton equton we cn get: ( π, 0. π 31 1 ( π, 0. π 1497 ( π, 0. π The workspce of prllel robot s the set of ponts where the end-effector cn rech, t s n mportnt ndex to evlute the robot s workng performnce, ts sze nd shpe determne the moton rnge of the endeffector nd t s lso the drect reflecton of the workng blty of prllel robot. Generlly spekng, the workspce s smll nd rregulr shpe hs restrcted the pplcton of prllel robot n certn degree; therefore, to nlyss the workspce s prtculrly mportnt. Accordng to ths structure, the workspce s sze nd shpe s mnly determned by the rms length, the crcumscrbed crcle rdus of sttc nd movng pltforms, the pendulum ngle rnge of ctve rm nd the turnng ngle rnge of sphercl jont nd Hooke jont n ech brnch. Consderng the nterference mong prts when the mechnsm s movng, the pendulum ngle of the three ctve rms nd the movement lmt of sphercl jont nd Hooke jont, we set the pendulum ngle rnge of the three ctve rms s: θ mn θ θ ( = 1,, 3 (9 mx The turnng ngle rnge of sphercl jont s: ( Rn L b θb = rccos θ ( = 1,, 3 (10 b mx L L : The br s length vector n b : The pose of sphercl jont n dynmc coordnte system θ bmx : The bggest turnng ngle of sphercl jont The turnng ngle rnge of sphercl jont s:

4 Res. J. Appl. Sc. Eng. Technol., 6(0: , 013 Prmeter ntlzton Determne the roughly rnge of workspce Determne the serch rnge The poston nverse soluton Judge the pendulum ngle Y Plot3(x,y,z Fg. 3: The flow chrt of serch process Fg. 4: Workspce of 3-RHS robot Fg. 6: Projecton of XZ plne Generlly, the workspce of prllel mechnsm s obtned through the knemtcs nverse soluton. One group of rms pendulum ngle cn be obtned from the correspondng pose mtrx of pont nd f the rms pendulum ngle meets the Eq. (9, we cn judge the poston pont belong the workspce, otherwse t doesn t. If we cn seek out ll the boundry ponts, then the prllel mechnsm workspce conssts of the ponts wthn or on the boundry, ths s the boundry serch method prncple of the workspce. Through the Eq. (10 nd (11, we cn fnd the roughly rnge of prllel mechnsm s workspce nd then specfy the correspondng serch rnge. Lter group of pendulum ngle of correspondng pont cn be obtned through the poston nverse soluton; f the ngles meet Eq. (9 nd then the pont s nsde of the work spce. The flow chrt of serch process s shown n Fg. 3. The structurl prmeters of the robot re: R = 105 mm, r = 50 mm, l α = 0 mm, l b = 495 mm, - 45 o θ 70 o, θ b 55 o, θ B 60 o. Bsed on robot knemtcs nverse soluton, the workspce model of the robot s nlyzed by the boundry serch method through the MATLAB nd ADAMS knemtcs softwre. The workspce of the movng pltform s center O' s obtned, s s shown n Fg. 4. The workspce s projectons n XZ plne nd YZ plne re shown n Fg. 5 nd 6, respectvely. The workspce s boundry s smooth nd the effectve workspce s lrge nd wthout holes n the spce. Fg. 5: Projecton of XY plne ( Rn L B θ B = rccos θ ( = 1,, 3 (11 B mx L L : The br s length vector n B : The pose of hooke jont n sttc coordnte system θ Bmx : The bggest turnng ngle of hooke jont 3850 COCLUSIO A novel prllel robot mechnsm nmed 3-RHS wth three freedoms ws proposed nd the mthemtcl model of the knemtcs nverse soluton ws lso estblshed. The workspce s symmetrcl bout XZ plne nd YZ plne, the movement spce s ncresng long wth the ncresng of constrnt turnng ngle when there no sngulr occurs. And the workspce of the robot cn meet the needs of drug utomton producton lne.

5 Res. J. Appl. Sc. Eng. Technol., 6(0: , 013 The workspce of prllel robot nmed 3-RHS wth three freedoms ws studed n ths study, whch hs provdes relble bss for the pplcton reserch, desgn nd ts full dvntge study of ths knd robots. ACKOWLEDGMET Ths study s supported by Scentfc nd technologcl project n Henn Provnce ( , Progrm for IRTSTH (01IRTSTH013 nd Scentfc nd technologcl project of Zhengzhou Cty (11PPTGG36-7. REFERECES Chen, H.Z., Z.Y. Zou nd X.Q. Ho, 010. Anlyss on output moton nd workspce of novel type 3- RCR prllel mechnsm wth three trnsltons. Mch. Tool Hyd., 38(5: 4-6, (In Chnese. Dun, Y.B., S.P. Lng, D.X. Zeng, et l., 011. Knemtcs nd workspce nlyss of 6-PUS/UPU prllel mnpultor. J. Mch. Des., 8(3: 36-40, (In Chnese. Hung, X.G., G.P. He, X.L. Tn, et l., 009. An ntroducton to prllel robot mechnsm. J.. Chn Unv. Tech., 1(3: Keml, S. nd O. Korkmz, 009. Trjectory trckng control of prllel robots n the presence of jont drve flexblty. J. Sound Vb., 319: Lee, S.H., W.K. Km, B.J. Y, et l., 006. Anlyss of two 3-DOF prllel mechnsms wth constrned Stewrt pltform structure. Proceedng of the IEEE RA, Orlndo, FL, pp: col, S. nd P.C. Vncenzo, 011. A novel 3D prllel mechnsm for the pssve moton smulton of the ptell-femur-tb complex. Meccnc, 46: Yun, Y., Q.S. Xu nd Y.M. L, 008. Survey on prllel mnpultors wth mcro/nno mnpulton technology nd pplctons. J. Mech. Eng., 44(1: 1-3. Zhu, Y.H., J. Zho nd H.G. C, 003. Confgurton desgn of knd of new typed double prllel mn mnpultor. J. Mch. Des., 0(8: