Kinematics and Application of a Hybrid Industrial Robot Delta-RST

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1 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 Sensors & ransducers by IFSA Publshng S L Knemat and Applcaton of a Hybrd Industral Robot Delta-RS Nng Lu unjun Wu College of Informaton Scence and echnology nan Unversty Chna Department of Software Guangdong Food and Drug Vocatonal College Chna el: -88 fax: -88 E-mal: junjun-wu@hotmalcom Receved: 9 Aprl /Accepted: 8 Aprl /Publshed: Aprl Abstract: Seral robots and parallel robots have ther own pros and cons Whle hybrd robots contng of both of them are poble and expected to retan ther merts and mnmze the dsadvantages he Delta-RS presented here s such a hybrd robot bult up by ntegratng a -DoFs tradtonal Delta parallel structure and a -DoFs RS robotc wrst In ths paper we focus on ts knemat analy and ts applcatons n ndustry Frstly the robotc system of the Delta-RS wll be descrbed brefly hen the complete and systemc knemat of ths knd of robot wll be presented n detal followed by smulatons and applcatons to demonstrate the correctne of the analy as well as the effectvene of the developed robotc system he closed-form knematc analy results are unversal for smlar hybrd robots constructng wth the Delta parallel mechansm and seral chans Copyrght IFSA Publshng S L Keywords: Hybrd robots Industral robots Knemat analy Control and applcaton Introducton In general most currently-exstng ndustral robots desgned are ether bult up of seral or parallel knematc chans [] Seral robots cont of a seres of actve jonts connectng the base to the end effector whle parallel robots are composed of a set of parallel chans (legs) wth actve and pave jonts Due to ther open-loop and cantlever-type knematc confguraton seral robots feature large workspaces and hgh dexterty but suffer from lack of stffne and from relatvely large postonng errors On the other hand as each ndependent leg formng a closed loop and connectng the base and the movng platform parallel robots are able to acheve hgh stffne and hgh force-to-weght rato However parallel robots are known for a restrcted workspace and low dexterty In a word seral robots and parallel robots have ther own advantages and dsadvantages A general manpulatng task n ndustry can be dvded nto a poston sub-task (poston mechansm) and an orentaton sub-task (orentaton mechansm) [] respectvely he poston mechansm controls the poston as the orentaton mechansm manpulates the orentaton of the end effecter It s natural to combne the seral and parallel chans together to obtan a hybrd ndustral robot so as to retan the merts of seral confguratons e large workspace and hgh dexterty and parallel structures e hgh stffne and hgh force-to-weght rato whle ther dsadvantages are mnmzed A smple way to do ths s to utlze a parallel mechansm to poston the end-effecter and connect seral jonts to adjust the orentaton and vce versa Owng to the above observaton hybrd robot manpulators have attracted more and more attenton 8 Artcle number P_PR_

Sensors & ransducers Vol 9 Iue Aprl pp 8-9 n the feld of robot although comparatvely lttle lterature on these robots s avalable currently Some researches have dealt wth the desgn of hybrd robots []

freedom hey have found varous commercal applcatons such as hgh-speed mllng weldng and component aemblng n an aeronautcal and automotve ndustry [7 8] In addton lots of researches have focused on the

respectvely; whle [] and [] amed to propose a unversal velocty-based model for the seral connecton type (eg parallel-parallel parallel-seral and seral-parallel) of hybrd robots whch certanly results

outstandng features ncludng lght-structure hgh-speed hgh-accuracy and smple-control Researches on the Delta parallel mechansm nclude almost all aspects [-8] However as a translatonal parallel

2 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 n the feld of robot although comparatvely lttle lterature on these robots s avalable currently Some researches have dealt wth the desgn of hybrd robots [] resultng n novel but well-known robots lke rcept [] rvarant [] and Exechon [] hese three robots could be treated as seral combnaton (connecton) of parallel and seral mechansms both wth few degrees of freedom hey have found varous commercal applcatons such as hgh-speed mllng weldng and component aemblng n an aeronautcal and automotve ndustry [7 8] In addton lots of researches have focused on the analy and modelng of several hybrd robots [9-] Lteratures [] and [] nvestgated the knemat and dynam of a type of hybrd robots constructed by serally connected non-redundant parallel modules respectvely; whle [] and [] amed to propose a unversal velocty-based model for the seral connecton type (eg parallel-parallel parallel-seral and seral-parallel) of hybrd robots whch certanly results n comparatvely low effcency and hgh complexty Snce nvented by Clavel n 98s [] the Delta parallel mechansm has been succefully and wdely used n many felds [] lke rapd pckng and packagng thanks to ts outstandng features ncludng lght-structure hgh-speed hgh-accuracy and smple-control Researches on the Delta parallel mechansm nclude almost all aspects [-8] However as a translatonal parallel manpulator ts applcaton s lmted because of lackng capablty to change the orentaton of the manpulated object As a potental soluton Delta wth orentaton s consdered as one of the tendences [9] resultng n commercal robots lke FANUC M-A/M-A serals [] and ABB IRB / FlexPcker [] However to the best of our knowledge there s not complete and systemc knematc analy reported for ths cla of robots n the lteratures In ths paper we present the closed-form knemat solutons for a parallel-seral hybrd robot the Delta-RS o some extents the Delta-RS may be regarded as a hybrd robot bult up through connectng a Delta parallel structure wth a seral robotc wrst However to completely analyze ts knemat and dynam the Delta-RS robot should be treated as a whole to obtan closed-form relatonshp between the base and the end-effector whch s crtcal and fundamental for further researches such as workspace analy dmensonal synthe and layout optmzaton and so on he presented analy and methods are able to be appled to smlar robots wth Delta parallel structure and seral chan fxed to the movng platform he rest of ths paper s organzed as follows Secton descrbes the Delta-RS robotc system Secton presents the complete knemat analy of Delta-RS-lke robots Experments and applcatons are provded n Secton followed by a concluson n Secton Robotc System o mprove ts dexterty to satsfy more ndustral applcatons demands the RS robotc wrst s ntegrated to the movng platform of the Delta parallel mechansm n our group as shown n Fg θ (a) he Delta-RS prototype x θ x y θ θ y z x z w x y θ x u (b) he knematc dagram of Delta-RS u v Fg he Delta-RS robot θ 87

3 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 he RS robotc wrst can be drven through three motors mounted on the fxed platform of the Delta mechansm and three correspondng axes wth unversal couplngs An alternatve s to confgure each drver wth ts correspondng axs on the movng platform respectvely Surely the former one may acheve hgh-speed and fastresponse snce the nerta of the movng part s le whle the latter opton s enttled to smple structure and control Usng the Kutzbach-Grubler formula [] t s convenent to obtan the degrees of freedom of the Delta-RS robot as ( ) F ng + f g n refers to the total number of movng lnks g to the number of jonts and f to the DoFs of the -th jont As regards to Delta-RS we have F ( ) Note that the Delta parallel structure has no rotatonal degree of freedom herefore Delta-RS s a hybrd robot wth sx degrees of freedom: three- DoFs Delta parallel mechansm to poston the end-effector whle three-dofs seral RS robotc wrst responsble for controllng the orentaton Owng to the dfferent roles played by the two sub-structures t s poble to derve the knemat and dynam of them separately and then combne them wth the general knowledge of robot to obtan that of the entre hybrd robot Knematc Analy In ths Secton we analyze the knemat of the Delta-RS robot usng the vector method and the confguraton matrx expreng approach Wthout lo of generalty denote ( xyzα βγ ) the confguraton of the end-effector and θ the rotatonal angle of each actve jont Forward Knemat Forward knemat s to compute the confguraton of the end-effector ( xyzα βγ ) from gven jont angles θ Settng up coordnate frames as shown n Fg (b) the poston of Pont A (I ) wth respect to the base frame {} can be expreed as [ l γ l γ ] u cos sn () γ π Smlarly Pont C relatve to Frame {} s u [ cos sn ] l γ l γ Descrbng Pont B wth respect to Frame {} we obtan ( ) ( ) v l + l cosθ cosγ l + l cosθ sn γ l snθ () Supposng the orgn of Frame {} relatve to Frame {} s e [ x y z ] C can be expreed also respect to Frame {} as w e + u Consderng the geometry of the Delta robot we have the followng constran whch can be further smplfed as v w l () x + y + z + a x + b y + c z + d () a l cosθ + l l cosγ ( ) ( θ ) b l cos + l l snγ c l snθ ( ) d l l + l l + ll cosθ ll cosθ Eq () leads to two lnear equatons as ( a a) x ( b b) y ( c c) z ( d d) ( a a ) x ( b b ) y ( c c ) z ( d d ) () As z n practce x and y can be represented by z resultng n x mz + n () y mz + n ( c c)( bb) ( cc)( b b) m ( aa)( b b) ( a a)( bb) ( d d)( bb) ( dd)( b b) n ( aa)( b b) ( a a)( bb) c c bb cc b b m aa b b a a bb d d bb dd b b n a a b b a a b b Substtutng Eq () nto Eq () we get az + b z + c (7) a m + m + b mn + mn+ a m+ a m c n + n + a n + a n + c z + d Solvng Eq (7) we have b b ac z a (8) 88

4 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 hen x and y can be computed wth Eq () Usng the homogeneous transformaton matrx the confguraton of the movng platform wth respect to the base frame s [ x y z ] (9) I I s the dentty matrx ( θ ) ( ) ( θ ) ( ) ( θ ) ( ) Rot z rans z l Rot y rans y l Rot z rans z l c s c s c s s c l s c l s c ccc c sc sl l scc s cc cl l + + sc c lcl () θ θ 9 c cosθ s snθ Hereafter smlar smplfed representatons wll be used As regards to the RS robotc wrst usng the Z-Y-Z Euler angle notaton (that s to say rotate around the Z -axs wth an angle of θ 9 frst then rotate θ around the Y -axs fnally rotate θ around the Z -axs referrng to Fg (b)) the homogeneous transformaton matrx can be computed as Eq () herefore the forward knemat of the Delta-RS s ccc c sc x+ sl l s cc + s + cc y cl l sc c z l cl Inverse Knemat () Inverse knemat s to solve the jont angles θ when gvng the target confguraton of the robot s end-effecter ( xyzα βγ ) As a Delta parallel mechansm has only the translatonal degrees of freedom the orentaton of the end-effecter s dependng on the RS robotc wrst Hence accordng to Eq () we smply have θ 9 + α θ β θ γ () From Eq () the center of the movng platform (also the orgn of Frame {}) can be computed as x x s l + c s l y y cl l + + z z+ l + cl () Recallng Eq () takng θ ( ) as the unknowns t can be transformed to a snθ + b cosθ + c () a z l b l x cosγ + y snγ l + l c x + y + z + l l + l l ( ) ( ) ( x γ + y γ )( l l ) cos sn Solvng Eq () yelds a + a + b c θ arctan c b acoban Matrx () o compute the acoban Matrx of the Delta-RS robot we can calculate that of the Delta parallel mechansm and of the RS robotc wrst respectvely and then combne them together wth recursve formula Gettng dervatve wth respect to θ ( ) of Eq () results n θ G v () θ θ θ G θ [ x y z ] v G G G G G G and G G G ( ) lz cosθ + l xcosγ + ysn γ l snθ G x lcosγ lcosθ cosγ G y lsnγ lcosθsn aγ G z + l snθ If G s not sngular we obtan v G θ (7) As regards to the RS robotc wrst ts velocty can be expreed as v θ (8) 89

5 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 v s the vector θ θ θ θ and s the matrx havng the form M M M M (9) S S S S M j Sj ( PRj) Sj ( j ) stands for the axal unt vector of the j-th jont P refers to the poston of the end-effector wth respect to Frame {} (also the base frame of the RS robotc wrst) R j to the poston vector of the j-th jont relatve to ts own coordnate Specfcally they are S S S c c sl R R cl l l sl l P R cl l l cl cl + l M sl l M M Hence we have cl + l M sl l S c c On the ba of the above analy buldng up the recurrence formula for the velocty of the RS robotc wrst from the perspectve of the entre Delta- RS robot we may obtan the followng equatons ω + R ω + θ + Z + () + v R + ˆ + As we know that c s c s R s c R s c ( v + ω P ) + c s R s c P l P l and as well as P accordng to Eq () we l obtan the angular velocty and lnear velocty of the j-th (j ) jont as ω v v [ ] ω θ v c + v s vz x y v R v vxs + vyc s θ ω θ c θ lc θ v R R v + ls θ sc θ + s θ ω θ + c θ c θ + θ lcc θl θlc θ v R v + lcs θ lsc θ + ls θ ls θ ccc scc + sc c R c sc s + cc Fnally we get () () () () v v θ θ () ω R G lcc l lc l lsc ls ls 9

Sensors & ransducers Vol 9 Iue Aprl pp 8-9 sc s c c herefore the velocty of each actve jont can be solved by computng the nverse of acoban matrx as v θ ω Experments and Applcatons Smulatons () We

Delta-RS robot smulatons and experments are conducted n ths secton In the smulaton we utlze the Delta-RS robot to machne the slope edge of a heart-shaped part Fg shows us some snapshots of the

6 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 sc s c c herefore the velocty of each actve jont can be solved by computng the nverse of acoban matrx as v θ ω Experments and Applcatons Smulatons () We have analyzed the knemat of the entre Delta-RS robot n the prevous secton In order to verfy the developed robotc prototype and to valdate the theoretcal analy of the closed-form knemat of the Delta-RS robot smulatons and experments are conducted n ths secton In the smulaton we utlze the Delta-RS robot to machne the slope edge of a heart-shaped part Fg shows us some snapshots of the machnng procedure From the fgure we can see that the Delta parallel mechansm poston the machnng tool accurately durng the manufacturng proce he orentaton of the machnng tool s also adjusted approprately by the RS robotc wrst to follow the slope edge of the part Experments he Delta parallel mechansm has been wldly used n the rapd pckng procedure n ndustry However one of ts drawbacks s that the orentaton of the manpulated object cannot be changed by ths robot lmted by ts translatonal- only degrees of freedom hs drawback can be easly overcome by the Delta-RS robot Fg shows us serals of snapshots of an experment n whch the Delta-RS robot s performng a rapd pck-and-place task In ths applcaton the robot needs to pck up some -shaped parts put randomly n ts workspace and stack them up one by one wth the rght orentaton on the tru Obvously ths task could not be fnshed by a tradtonal Delta Robot Fg Snapshots of manufacturng smulaton wth the Delta-RS robot o generate the machnng trajectory we have developed a CAD-model based off-lne programmng and plannng algorthm for the Delta-RS robot It frstly generates the trajectory of the machnng tool (also the end-effector) n the Cartesan workspace accordng to the gven CAD-model then utlzes the knemat presented n Secton III to perform moton plannng of the Delta-RS robot and fnally gets the trajectory of each actve jont Fg Snapshots of performng the rapd pck-and-place task wth the Delta-RS robot From Fg the Delta-RS robot frstly goes to the rght poston of the to-be-manpulated object and pre-adjusts the orentaton of the vacuum grpper by the gudance of machne vson hs orentaton pre-adjustng procedure ams at facltatng the 9

7 Sensors & ransducers Vol 9 Iue Aprl pp 8-9 placng and stackng proce as well as beng beneft to avod collsons wth the envronment After the robot reaches ts rght status the vacuum grpper pcks up the part hen the Delta-RS robot handles ths part to the target stack place smultaneously adjusts ts orentatons durng move and fnally puts down the manpulated part Owng to the Delta parallel mechansm the pck-and-place task can be conducted very fast herefore the Delta-RS robot has demonstrated ts potental to the applcatons n ndustry he proposed knematc analy s verfed n both smulatons and experments wth the Delta-RS robot Conclusons Hybrd robots merge the advantages from seral mechansms and parallel structures herefore they have great potentals n the feld of ndustry he treated robot Delta-RS n ths paper s constructed by the combnaton of a -DoFs translatonal Delta parallel mechansm and a -DoFs seral RS robotc wrst he Delta mechansm takes charge n postonng the end-effector whle the RS robotc wrst s responsble for orentatng the end-effector Hence t features not only hgh-speed and hghdexterty but also relatvely bg-workspace hs paper has brefly ntroduced the mechancal system and the control system of the Delta-RS robot developed n our group Closed-form knemat solutons of the Delta-RS robot have been deduced and presented n detal whch s the fundament of hgher-lever research Smulatons and experments n the realstc ndustral producton are carred out to verfy the effectvene of the analy and the robotc prototype he methodology and the analy results are unversal to smlar hybrd robots based on Delta Parallel structure and seral chans Recently we are conductng workspace and manpulablty analy wth the Delta-RS robot to study the task-orented layout optmzaton problem n the ndustral producton lne In the near future the dmensonal synthe wll also be consdered on the ba of specfc manpulaton task References [] B Sclano K Ouama Eds Sprnger handbook of robot Sprnger 8 [] C Goeln Determnaton of the workspace of -DOF parallel manpulators ournal of Mechancal Desgn 99 pp - [] Campos C Budde Heelbach A type synthe method for hybrd robot structures Mechansm and Machne heory 8 8 pp [] Sclano he rcept robot: Inverse knemat manpulablty analy and closed-loop drect knemat algorthm Robotca pp 7- [] Huang M L X M Zhao et al Conceptual desgn and dmensonal synthe for a -DOF module of the rvarant a novel -DOF reconfgurable hybrd robot IEEE ransactons on Robot pp 9- [] Z M B Y n Knematc modelng of Exechon parallel knematc machne Robot and Computer- Integrated Manufacturng 7 pp 8-9 [7] K E Neumann rcept applcatons n Proceedngs of the rd Chemntz Parallel Knemat Semnar Development Methods and Applcaton Experence of Parallel Knemat (PKS) pp 7- [8] Exechon [9] M K Lee K W Park B O Cho Knematc and dynamc models of hybrd robot manpulator for propeller grndng ournal of Robotc Systems 999 pp 7- [] K anev Knemat of a hybrd (parallel-seral) robot manpulator Mechansm and Machne heory 9 pp 8-9 [] Ibrahm W Khall Inverse and drect dynamc models of hybrd robots Mechansm and Machne heory pp 7- [] S Lee S Km Effcent nverse knemat for seral connectons of seral and parallel manpulators n Proceedngs of the IEEE/RS Internatonal Conference on Intellgent Robots and Systems 99 pp - [] G B Chung B Y D Lm et al An effcent dynamc modelng methodology for general type of hybrd robotc systems n Proceedngs of the IEEE Internatonal Conference on Robot and Automaton pp 79-8 [] R Clavel Devce for the movement and postonng of an element n space US Patent No 978 Dec 99 [] Bonev Delta parallel robot-the story of succe Newsletter [] P Vscher R Clavel Knematc calbraton of the parallel Delta robot Robotca 998 pp 7-8 [7] S Stacu D C Carp-Cocarda Dynamc analy of Clavel's delta parallel robot n Proceedngs of the IEEE Internatonal Conference on Robot and Automaton pp - [8] M A Larb L Romdhane S Zeghloul Analy and dmensonal synthe of the DELA robot for a prescrbed workspace Mechansm and Machne heory 7 7 pp [9] V Poppeova Urcek V Bulej he development of mechansm based on hybrd knematc structure Development pp 8-9 [] Fanuc M-A Delta Robot Introducton A_Delta_Robot_Introductonaspx [] ABB IRB FlexPcker /products/robot/ndustral-robots/rb- [] K Waldron G L Knzel G Knzel Knemat dynam and desgn of machnery Wley New York 999 Copyrght Internatonal Frequency Sensor Aocaton (IFSA) Publshng S L All rghts reserved ( 9

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