The Analysis and Simulation of Robot Kinematics and Dynamics Based on RoboAnalyzer

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1 nterntonl Journl of Emergng echnolog nd Advnced Engneerng Webste: (SSN 5-459, SO 9:8 Certfed Journl, Volume 5, ssue 4, Arl 5 he Anlss nd Smulton of Robot nemtcs nd nmcs Bsed on RoboAnlzer Q Fe, Png XueLng, Lu Je 3, Jng Y 4,,3,4 Jngnn Unverst, Jngsu Provnce e Lbortor of Advnced Food Mnufcturng Equment nd echnolog, Wu 4 Abstrct Robot nemtcs nd dnmcs s the bss of robotcs reserch, rovdng the mortnt bss for robot th lnnng nd moton control etc. he er focuses on the s degrees of freedom ndustrl robot whch s develoed ndeendentl, dots the -H method to do the forwrd nemtcs nlss nd nverse nemtcs nlss for robot, estblshes the nemtcs model, nd uses Lgrnge method for robots dnmcs nlss, nd then bulds the reltonl model mong mechncl rms nd ther force (or torque, t lst, the er uses the smulton softwre to llustrte the bove to rove the correctness nd rtonlt of the models. ewords robot, nemtcs, nmcs, smulton, -H method. NROUCON Wth the develoment of ndustrl utomton, the robot hs become the ndsensble nd che lbor n the roducton, nd the reserch of the robot s much hotter. Robot nemtcs nd dnmcs s the bss of robotcs reserch, nd robot nemtcs s to reserch the reltve reltonsh between the end ose of robot nd robot nemtcs rmeters, whch s the bss of robot control stud []. he robot dnmcs s mnl the stud of the correltve reltonsh between the movement of robot rm movement nd ts force (or torque []. Anlss of robot nemtcs nd dnmcs s the bse of robot technolog reserch nd the e to stud robot trector lnnng nd moton control [3]. he er nlses the s degrees of freedom ndustrl robot nemtcs whch s develoed ndeendentl, usng the -H method to estblsh the relton between forwrd nd nverse soluton n the robot nemtcs model so s to stud the robot nemtcs, nd dotng Lgrnge method to buld the relton between the movement of robot lns nd ts force (or torque. Fnll, the er shows the smulton test of robot nemtcs nd dnmcs usng RoboAnlzer smulton softwre.. ROBO NEMAC ANALYSS he er focused on the ndeendentl develoed S- OF ndustrl robot (the ln coordnte sstem s shown n the Fg., -H rmeters s shown n the tble, to nlze the nemtcs, nd bulds the relton between robot end ose nd robot rmeters through -H model whch s the estblshed nemtcs model usng the homogeneous coordnte trnsformton mtr tht envt nd Hrtenberg roosed [4]. he robot nemtcs ncludes forwrd nemtcs nd nverse nemtcs: forwrd nemtcs s to use ech nown ont ngle to solve the robot end ose; the nverse nemtcs s to use the nown end ose to solve ech ont ngle vlue. Fgure. he robot stereogrm nd -H coordnte grh

2 nterntonl Journl of Emergng echnolog nd Advnced Engneerng Webste: (SSN 5-459, SO 9:8 Certfed Journl, Volume 5, ssue 4, Arl 5 Ln ABLE HE -H PARAMEERS ABLE OF ROBO ( - ( - (mm d (mm (9 ( ( 5 4 4( (9 9 ( -9 β ( B. he nlss of robot nverse nemtcs he nverse nemtcs of the robot s to use the nown end ose of robot to solve ech ont ngle, nd the solvng methods of the nverse nemtcs re vrous. Among these methods, the most wdel used one s Closed Method, becuse t hs the quc clcultng seed nd hgh effcenc, nd t s es to rel-tme control [5]. Closed soluton contns two methods: geometrc method nd lgebrc method. Becuse of three ont shfts of the estblshed robot model ntersect t one ont, ths er wll dot the lgebrc method, whch refers to tht the nverse trnsformton mtr of ech ont re-multles both ends of equton set, nd sertes the ont vrbles, nd then solve ech ont vrble vlue ccordng to the equl elements of both end of mtr. Frst, the homogeneous coordnte trnsformton mtr of robot end ose cn be shown: A. he nlss of robot forwrd nemtcs he relton between dcent lns of robot cn be shown usng the homogeneous coordnte trnsformton mtr, frstl to estblsh the coordnte sstem of ech robot ont, nd then to get the homogeneous coordnte trnsformton mtr ccordng to the converson n the coordnte sstem, s shown n the formul (. Rot( X, c s c s s s rns( X, c c c s s c Rot( Z, rns( Z, d d s d c Among tht: s the ont code, c s cos, nd s s sn. θ, d, α, re the robot structure rmeters, whch shows the reltonsh mong the robot lns. θ s the ncluded ngle between robot onts - nd round the z s, nmel ln ngle. d s the trnsltonl dstnce of - nd long the z s, nmel the dstnce between two lns. s the rotton ngle of z - nd z round s, nmel the ont ngle. s the trnsltonl dstnce of z - nd z long the s, nmel the dstnce between two lns. Multl the trnsformton mtr mong ech robot ln to get the trnsformton mtr tht robot end coordnte s reltve to the bse coordnte of robot, s shown n the formul (. n o n o nz oz z z ( ( n o n o ( ( 3 ( 3 4 ( 4 5 ( 5 ( n z oz z z (3 he two ends of equton set re-multles resectvel ( 3 (,, 3 4 (,, 3, 4 5 (,, 3, 4, 5 to substtute nto the bove formul to solve ech ont vrble vlue θ θ θ 3 θ 4 θ 5 θ,s shown n the followng te. tn(, - tn(, sqrt( 3 3 tn(,-d - tn(, sqrt( d 4-4 tn(cc 3 sc 3 zs 3,s - c 5 tn(s5,c 5 tn(s,c For the s ont ngle, not ll of the ont ngle cn meet the requrement of ctul structure lmt, so t s necessr to select the otml one mong ll the nswers ccordng to the ctul condton, such s the shortest tme, the mnmum energ consumton, the smllest drvng force, the cblt to vod obstcles, etc.. HE ANALYSS OF ROBO YNAMC he stud of robot nemtcs s not nvolved n the generton of the movement of mechncl rm nd the reltonsh between the stresses of the mechncl rm, so t needs to stud the robot dnmcs. 7

3 nterntonl Journl of Emergng echnolog nd Advnced Engneerng Webste: (SSN 5-459, SO 9:8 Certfed Journl, Volume 5, ssue 4, Arl 5 he robot dnmcs mnl descrbes the reltonsh between the moton of mechncl rm nd ts force (or torque, whch ls e role n the desgn of the robot nd control. he dervton of dnmc equtons s not onl helful to choose the drvng devce durng robot desgn, but lso useful to the smulton of robot []. he estblshment of the robot dnmcs equton hs vret of methods: Newton - Euler tertve method, the Lgrnge-Euler method, ne method, Guss method, Robertson-Vutton method, vrtonl method, etc. [7]. he er dots the Lgrnge method to derve the robot dnmc equtons, nd fnds out the relton between the mechncl rm moton nd force of robot, n order to smlf the model, wthout consderng the frcton of mechncl rm. Accordng to the mchner dnmcs, solvng the totl netc energ of -OF ndustrl robot rm: t rce q q q q s the seudo nert of mechncl rm, s the homogeneous trnsformton mtrces of coordnte sstem { } reltve to the bse coordnte sstem. ue to solve the totl netcs energ of robot, the totl netcs energ of trnsmsson must be consdered: q s the equvlent mss moment of nert of trnsmsson. Accordng the equton (4 nd (5, the totl netc energ of robot s ths: t rce q q q q q he otentl energ of robot trnsmsson s fr less thn the otentl energ of the robot rms, therefore, trnsmsson devce cn be neglected. he totl otentl energ for the mechncl rm. P P m g r Plug L - P nto the equton ( nd (7, the Lgrnge functon of robot: (4 (5 ( (7 L P rce q q q q q Lgrnge method s to use the second Lgrnge equton to derve the dnmc equton of robot, s follows: d L L Τ ( dt q q n the formulton L=-P, s the netcs energ of q sstem, P s the otentl energ, s the generlzed coordnte of sstem, q s the corresondng seed, nd s the generlzed force. Plug the equton (8 nto (9, the dnmc equton of -OF robot s tht: q q Among tht: m(, m(,, P rce( q q P rce( q q q mg r q q (8 (9 ( V. HE REALZAON OF ROBOANALYZER SMULAON RoboAnlzer smulton softwre s develoed b S..Sh nd hs tem, nd t s 3 smulton softwre esecll for robot technolog stud, whch s mnl used for nemtcs nd dnmcs smulton of tndem robot or mechncl rm. Moreover, the softwre s smle nd convenent to oerte, nd cn generte the corresondng smulton grhcs so s to understnd the oerton form of robot ntutvel [8].Frst of ll, ccordng to the test obect, choose the te of robot n RoboAnlzer smulton softwre, nd on the bss of the rmeter vlues n tble, modf ntl -H vlue of the softwre, thus robot smulton model s estblshed. A. Forwrd nemtcs smulton Ech ont ngle of robot s, nd the corresondng ont ngle of one ose s q z / / /3, nd lug t nto the smulton softwre to solve the mtr of robot end ose. m g r 8

4 nterntonl Journl of Emergng echnolog nd Advnced Engneerng Webste: (SSN 5-459, SO 9:8 Certfed Journl, Volume 5, ssue 4, Arl 5 From the ntl ose to the end ose, the smulton tme s desgned s s nd the smulton ste number s, so the run trector of robot from ntl oston to the end oston on the,, nd z drecton s shown n the Fgure : C. he robot dnmc smulton Robot dnmc reserch s to solve the reltonsh between the robot's movement nd the robot force, nd robot dnmcs nlss not onl ls n mortnt role n the robot structure desgn, but lso ffects the selecton of ctutor, nd hs sgnfcnce on the robot seed nd the control of robot ccelerton. Frst, ccordng to the request of softwre, set the oston of center of grvt of ech ln, lns mterl denst, ccelerton of grvt, etc. And the force of ech ln n the rocess tht the robot stll run from the ntl ose to the end ose z of the robot. But the mn stress onts of robot re ont nd ont 3, onl ther stress condton re consderng n the robot movement rocess, the results re shown n Fgure 4: Fgure. he forwrd nemtcs smulton dgrm of robot B. he nverse nemtcs smulton he nverse nemtcs s the rocess of usng the nown robot end ose to solve the vlue of ech ont ngle. s the ntl end ose of robot, z s the end ose mtr of robot. nd z re resectvel:.85. z And then ut the -H rmeter of robot nd the end ose mtr of robot nto the smulton softwre, so tht get the nverse soluton, s shown n the Fgure 3: Fgure 3. he nverse nemtcs smulton dgrm of robot Fgure 4. he force (or torque of ont nd ont 3 of robot V. CONCLUSON he nemtcs nd dnmcs of the robot re the bss of robot reserch, so the er nlzes the nemtcs nd dnmcs of the robot, estblshes robot nemtcs model usng -H model, nd nlzes the ostve nd nverse soluton of the runnng model, nd use the Lgrnge equton for the netcs nlss to conclude the reltonsh between the robot movement nd the robot rm force. Fnll, the er dots the smulton softwre to llustrte the roblems n the robot nemtcs nd dnmcs models whch re dffcult to understnd, so tht the correctness of the model s verfed. REFERENCES [] LUO J-J, HU Guo-qng. Stud on the Smulton of Robot Moton Bsed on MALAB. Journl of Xmen Unverst (Nturl Scence.44.5 (5: [] WANG Jn-me, FU Cheng-long, HUANG Yun-ln, CHEN en. nmcs Smulton nd Bonc Control Pltform for Bed Robot wth Mtlb, Journl of Sstem Smulton,, 3(5:

5 nterntonl Journl of Emergng echnolog nd Advnced Engneerng Webste: (SSN 5-459, SO 9:8 Certfed Journl, Volume 5, ssue 4, Arl 5 [3] Sun Xoong, Xe Zhng, Jn ln, Zhng Jun. nmcs Anlss nd Smulton of -PSS Fleble Prllel Robot. rnscton of the Chnese Socet for Agrculturl Mchner,, 43(7: [4] S SAHA. ntroducton to Robotcs, CHNA MACHNE PRESS, 9: [5] Chen Lugng. nmcs smulton stud of weldng robot bsed on Adms. Jngnn unverst,. [] LU Y-ng, L Ru-feng, L ong-wn.nmc Smulton Stud on Alcton AAMS for the Uer Arm of Weldng Robot. Journl of Hrbn Unverst of Commerce Nturl Scences Edton, (3: 3-. [7] Lu Qfeng. he nmcs Anlss nd Structure esgn of QnJng weldng robot,school of mechncl engneerng zheng unverst, 7. [8] htt://