ON THE DESIGN OF LARGE SCALE REDUNDANT PARALLEL MANIPULATOR. Wu huapeng, Heikki handroos and Juha kilkki

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1 ON THE DESIGN OF LARGE SCALE REDUNDANT PARALLEL MANIPULATOR Wu huapeng, Hekk handroos and Juha klkk Machne Automaton Lab, Lappeenranta Unversty of Technology LPR-5385 Fnland Abstract: Ths paper presents a large scale redundant parallel manpulator. To desgn the manpulator some prelmnary consderatons are gven. The manpulator s bult based on two 3DOF parallel mechansms. Hydraulc cylnders are employed as actuators to acheve lnear moton and offer great force. The knematcs analyss s gven for the manpulator. The control schemes are dscussed n the paper and the smulaton results are presented. Keywords: Parallel manpulator, desgn method and knematcs analyss..introduction Recently most of rock drll machnes are desgned n seral lnker. The tool holder s always very heavy snce drll tools are very long. Durng drllng process the manpulator vbrates very much due to the low stffness of manpulator and great drllng force, and ths causes some problems such as the tools broken and bg naccuracy. To mprove stffness of those knds of manpulators, parallel mechansm can be consdered. Parallel manpulators have found wdely applcaton n ndustral robots n the last few years, because they have many substantal advantages compare wth conventonal seral lnker manpulators, such as hgher stffness, hgher accuracy, and mproved dynamc characterstc [][] [3]. The typcal parallel manpulator s so call Stewart platform (Stewart 965) has been studed n many lteratures [][5]. In ths paper we present a desgn procedure for a redundant parallel manpulator for the drllng task. The manpulator s consdered that at lest t has same workspace as the types used today, but more strongly wthout ncrease very much weght..preliminary CONSIDERATION The rock drll machnes are used n tunnel or n mne to make hole. Snce the work condtons always are very hard and envronments are very complex, the manpulators have to be made very stronger, sutable operatve and enough workspace capablty. In order to save the drll tool, the vbraton should be lmted as small as possble. That means the manpulators should have hgh stffness. To desgn the manpulator the follow prelmnary problems are consdered. Workspace: Bascally we hope the workspace capablty of the manpulator can be as bg as possble, n tunnel or n mne t s mpossble for more drllng machnes work together because the smaller room. The bg workspace capablty manpulator can ft dfferent sze tunnel, but unfortunately bg workspace capablty means large sze or more lnkages are need for the manpulator, ths wll reduce the stffness of manpulator and causes some problems such as vbraton, and so on. The sutable workspace s A=5m m, and ths workspace s requred for our parallel manpulator. Stffness: The stffness s very mportant for the manpulator. It s one mportant crtcal condton for us to desgn the manpulator. Normally the arms of manpulator are desgned by usng lght materal to reduce the weght of manpulator, however once the payloads are very heavy the complance of manpulator wll ncrease. Nowadays the deformaton errors of rock manpulators are always bgger than ± 0 mm at end effector, and vbratons are also very bg because the low stffness of manpulators. To ncrease the stffness of manpulators, t s more sutable to use parallel structure than to use stronger materal, whch wll make manpulator hgh cost and dffcult to be machned. The branches of parallel mechansm can be consdered to use hydraulc actuators, snce hydraulc cylnder can offer lnear moton and great force. Collson avodng: Normally, fve degrees freedoms are need for rock drll process. As the envronment s very complex n rock drllng, more 086_TB3.doc-

2 than fve degree freedoms for manpulator are suggested, so that the manpulator has the ablty of avodng collson. Usually, the collson happens between the end-effector and manpulator tself, duo to the longer length of end-effector. So mult-degree redundant manpulator s consdered. Control scheme: The control scheme can be alternatve n two algorthms: manul-operaton and auto-operaton. In manul-operaton one or more joystcks are need to control all the cylnders. In autooperaton all the poston and orentaton of the holes can be got from drllng process plannng program. And the drllng process wll execute automatcally under the computer control. consdered, frstly the cylnder should offer enough forces under maxmum pressure, and the maxmum pressure n drll system s about 60bar. Ths parameter can be used to calculate the dameters D and d of cylnder, the push force of cylnder s π D π ( D d ) F = P P () Where, P s pressure of blnd chamber, P s pressure of rod chamber, And draw back fore s π ( D d ) π D f = P P () 3.COMONENTS DESIGN For the above propose a redundant parallel manpulator s presented n Fg., Ths manpulator conssts of 7 drvers (sx hydraulc cylnders and one revolute hydraulc drver) based on two 3DOF parallel mechansms. In the frst stage the telescopc beam s connected to basement by a unverse jont whle t s fxed wth md plate. In the second stage the telescopc beam s fxed wth md plate and connected the end plate by a unverse jont. So the frst stage smlar to an arm and can be extended, the second stage looks lke a wrst and can be extended too. Unverse jonts are employed n the manpulator for all the hydraulc cylnder connectons. Fg. Parallel manpulator The specal character of the manpulator s that the end effector s very long. The long length of end effector wll lmt the workspace of manpulator, So an addton revolute actuator s used to enlarge the workspace and to make the moton of manpulator more nmble. 3. Hydraulc cylnder Hydraulc cylnders are employed n parallel mechansm snce they can offer great force and lnear moton. To desgn cylnder some condton should be Fg. Hydraulc cylnder Secondly, the workspace s manly determned by the length and extenson of cylnder and ther confgure sze n manpulator. The cylnder should offer enough length and extenson so that the manpulator can acheve requred workspace. All the cylnders have same szes n length and assemble n symmetrcal confguraton. As show n Fg.3 the bg sze of B, small sze L and e wll make manpulator stronger but smaller workspace. The parameter B s also constraned by the space on whch manpulator wll be mounted. Actually bgger B wll cause huge structure of manpulator, n ths case B s lmt less than one meter, then n order to reach the requred workspace, the sutable parameter L can be determned. Fg. 3 structure of manpulator Thrdly, the cylnder should satsfy the bulkng condton. As the downsde cylnders n manpulator always sustan the compressve force as shown n Fg.. 086_TB3.doc-

3 workspace s small. The structure of beam s llustrated n Fg.6. Fg. Bulkng of cylnder The crtcal bucklng load s gven by Euler equaton EI F = π (3) L Where, E s the modulus of elastcty, I s the moment nerta of rod. From Euler equaton we can see that the length L and dameter d determne the bulkng condton of the cylnder. So to determne all the parameter of cylnder, the condton of force, workspace, and bulkng crtcal should be consdered synthetcally. 3.. Jonts desgn All the connectng jonts n ths manpulator are unverse jonts. The jonts that connect the telescopc beam to the platform should be desgned to take great force and offer enough rotary angle, snce they strongly nfluence the stffness and workspace of manpulator. To desgn the unverse jonts fnte analyss method s used. The structure of unverse jont s llustrated n Fg. 5, those unverse jonts can offer rotary angles about two vertcal axes, and the 0 0 ranges of angles are ± 50 and ± 90. Fg.6 Telescopc beam The telescopc beams are standard components; the parameter t and g are determned by how much force they can take wth n the lmt deformaton. The sldng bearngs are used between the two components, and the length of the beam mast satsfes the maxmum extenson of manpulator. 3. Rotary actuator The rotary actuator s one knd of combned module, t manly consst of one cylnder and a translaton-to-rotaton converter. The man requrng of the actuators are offerng enough toque and rotary angle that must be great than 360 degree..kinematics ANALYSIS The knematcs analyss of the manpulator s based on matrx and geometry method, ncludng forward knematcs analyss and nverse knematcs analyss. The forward knematcs analyss s for the gven parameters of cylnders to fnd the poston of end-effector, whch can be used, n smulaton and workspace capablty analysng. The nverse knematcs analyss s for gven poston of endeffector to fnd the parameters for the entre cylnders, whch can be used n control of manpulator. The co-ordnate systems are bult for knematcs analyss as shown n Fg.3.. Forward knematcs analyss Fg.5 Unverse jont 3. 3 Telescope beam Unlke normal parallel manpulator ths parallel manpulator s one type of telescopc beam based, the man advantage ths knd structure s that the twst toque s taken by the telescopc beam not by the cylnders. In the Stewate structure the cylnder can take the twst toque but the structure s complex and The forward knematcs s fnd poston of endeffector for gven parameters of actuator. In our manpulator t s dffcult to fnd the soluton drectly snce the structure s very complex. Frstly we solve forward soluton based on the parameters of telescopc beam and parameters of jonts, and then fnd the relatons between those parameters and parameters of cylnders. The forward knematcs problem can defned as 086_TB3.doc- 3

4 x '' x y p z =T T y '' p z '' () p '' '' '' where x p, y p, z p are the coordnates of end '' '' '' '' effector wth respect to the frame x y z o, x, y, z are the coordnates of end-effector wth respect to the frame xyzo, T and T are the transform matrxes of two stages parallel mechansms. T,T are defned n the terms of the length of telescopc beams and the angles of jonts: cβ sβ sγ sβ cγ L sβ 0 cγ sγ L cβ sγ T= sβ cβ sγ cβ cγ L cβ cγ cβ sβ sγ sβ cγ 0 cγ sγ T = 0 0 sβ cβ sγ cβ cγ L And xp'' yp'' zp'' = Rsφ Rcφ Le (5) (6) (7) where, c = cos, s = sn,, γ ' β Are the angles about the y ' and the x '' axes. β, γ Are the angles about the y and the x axes. L, L Are the lengths of telescopc beam of two parallel mechansms. L e, R Are the lengths of rotary arm and beam of end-efector, those two parameters are always constant. '' φ s the angle of rotary actuator about z axs. Substtute equatons (7) (6) (5) nto equaton (), the poston of end-effector can be found by gvng the parameters β, γ, β, γ, L, L and φ. And the orentaton of end effector are β = β β ; γ = γ γ. (9) Up to now the forward problem seams to be solved, but we hope to fnd the relatons wth the parameters of cylnders. Accordng to the structures of parallel mechansm the relatonshps between the lengths of cylnder and β, γ, β, γ, L, L can gven by l l 3 And l = ( l l 3 =( m-m cγ +L s γ ) =(L sγ ) l +( m/ + (L cβ c γ - m/ +(-m/ 3 +m/ 3 cβ -ms β sγ -L s β c γ ) +(m/ 3 s β +m c β s γ +L c β cγ ) m+m c γ +Ls γ ) +m s c -L s c ) (0) +(-m/ 3 +m/ 3. cβ β γ β γ +(m/ 3 s β -m c β s γ +L c β c γ ) =( m3/ +(- m3/ 3 - m/ = (m-m3c γ ) = (-m+m3c γ ) 3 - m3/ 3 s β +L ) 3 cβ - L sβ c γ ) 3 sβ ) +(-m/ 3 +m3/ 3 cβ -m3s β s γ ) +(m3/ 3 sβ +m3c β sγ +L ) +(-m/ 3 +m3/ 3 c β +m3s β sγ +(m3/ 3 s - m3 c s +L ) ) β β γ 3 cβ ) () Where, m, m, m3 are the lengths of sdes of each three trangular plates. Fg.7 workspace From () to () we can determne the workspace of manpulator. Fg.7 shows the workspace of one manpulator.. nverse knematcs 086_TB3.doc-

5 Inverse knematcs problem s to fnd the all the parameters of actuator for the gvng poston and orentaton of the end-effector. In our manpulator, the nverse knematcs problem s to fnd all the parameters for all the hydraulc cylnders at gvng poston and orentaton of end-effector. It s defned as q= λ (p) () ) t s the vector of the poston and orentaton of the end effector wth respect to the base co-ordnate system xyzo. q=(l, l, l 3, l, l, l 3, φ ) t s Where, p=(x, y, z, β, γ the vector of the actuators, l j (I=,; j=,,3) are the length of cylnders and φ s the angle of the rotary actuator wth respect to z '' axs. In equaton () the vector p s a 5 vector, and vector q s a 7 vector. Ths means there are two redundant degrees n our manpulator, and make equaton () more dffcult to be solved. We can resolve equaton () nto followng two steps q = µ (r) (3) r = h (p) () Where, r = ( L, L, β, γ, β, γ,φ ) t. And equaton (3) s defned by equaton (0) and equaton (). So the nverse knematcs problem becomes to solve equaton (). In order to solve the equatons (3) and (), the optmal method s used, whch s to acheve the mnmum deflecton of manpulator at a certan poston of end-effector. The optmsaton problem s defned as the object functon, whch mnmse the deflecton of manpulator. Mn f( r ) (5) To solve the optmsaton problem, one evoluton search method s employed. Therefore, the nverse knematcs soluton can be found n real-tme control. 5.SYSTEM CONTROL The control method of manpulator s alternatve, manul-operaton and auto-operaton. Both of the methods are usng closed-loop control for all the actuators. The closed-loop control system ncludes hydraulc cylnder, poston sensors, servovalve, and computer (shown n Fg.8) Fg.8 closed-loop control 5. Control scheme The dfference between manu-operaton and autooperaton s that they use dfference nputs. In manuoperaton the joystck or keyboard s used to nput the parameters of poston and orentaton to the computer. However, n auto-operaton the datum of poston and orentaton are got from task plannng processor, whch s a program plans the trajectory of manpulator for drllng task and control the drllng process of the manpulator automatcally. The structure of whole control system s llustrated n Fg.9. And subject to the constrants of avodng collson condton Jonts lmt v ( r) 0 (6) mn β, γ β, γ max γ And lmt of cylnders β, (=,) (7) mn l l j max l ( =,; j=,,3) (8) 086_TB3.doc- 5

Fg.9 Control structure Actually ths structure s an open-loop control scheme for entre manpulator, snce t s mpossble to measure the poston and

That s why we employ the optmsaton method to acheve the mnmum deflecton n nverse knematcs model, so that n any poston the manpulator wll take as

Smulate results We bult smulate model of manpulator n ADAMS software, and control programs ncludng nverse knematcs model are desgned n C++ language.

model, and smulate n ADAMS. The Fg.0 are shown smulate results.

of end-effector s smooth from one pont to another pont. Fg.0 Smulaton results 6.

To desgn the manpulator some Prelmnary problems were consdered, such as stffness, workspace, operaton ablty, and collson avodng.

6 Fg.9 Control structure Actually ths structure s an open-loop control scheme for entre manpulator, snce t s mpossble to measure the poston and orentaton of end-effec n the drllng stuaton. Only the closed-loop controls are ntroduced to hydraulc cylnder actuator. That s why we employ the optmsaton method to acheve the mnmum deflecton n nverse knematcs model, so that n any poston the manpulator wll take as hgher stffness as possble. 5. Smulate results We bult smulate model of manpulator n ADAMS software, and control programs ncludng nverse knematcs model are desgned n C++ language. The process ncludes four steps: nput data (poston and orentaton), calculate control parameters by control program, translate the parameters to ADAMS model, and smulate n ADAMS. The Fg.0 are shown smulate results. The poston and orentaton for the ene-effector s (69,600,5500,0,0), to generate the moton of cylnder, cubc polynomal functon s used, so that the moton of end-effector s smooth from one pont to another pont. Fg.0 Smulaton results 6. CONCLUSIONS A large-scale 7-DOF parallel redundant manpulator has been developed. To desgn the manpulator some Prelmnary problems were consdered, such as stffness, workspace, operaton ablty, and collson avodng. Some desgn method for the key components of manpulator was presented. The knematcs model was dscussed. The control structure was bult. And the smulate result were gven by means of ADAMS model. REFERENCE [] D.Chakarov and P.Parushev,Synthess of parallel manpulators wth lnear drve modules. Mech. Meach. Theory Vol.9,No.7 pp.97-93,99. [] G.R.Dunlop,T.P.Jones Poston analyss of a two DOF parallel mechansm-the canterbury traker. Mech. Mach. Theory 3(999) [3] P.Kallo M.Lnd Q.Zhou H.Kovo A 3 DOF Pezohydraulc parallelhua mcromanpulator. 086_TB3.doc- 6

7 Proceedng of the 998 IEEE Internaton Conference Robotcs & Autmaton [] D.Stewart, Proc. of the Insttuton of Mechancal Engneers(London),Vol.80,Part,(965). [5] C.C.Nguyen, F.J.Pooran, Dy namc analyss of a 6 DOF CKCM robot end-effector for dual-arm telerobot system. Robotcs and autonomous systems. 5(989) _TB3.doc- 7

Inverse kinematic Modeling of 3RRR Parallel Robot

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