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2 20 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm M. Falahan, H.M. Danal and S.M. Vared Babol Unversty of echnology Iran 1. Introducton Parallel manpulators have the advantages of hgh stffness and low nerta compared to seral ones (Merlet, 2006). Most pck-and-place operatons, ncludng pckng, packng and palletzng tasks; requre four-degree-of-freedom (DOF),.e. three translatons and one rotaton around a vertcal axs (Company et al, 2003). A new famly of 4-DOF parallel manpulator beng called H4 that could be useful for hgh-speed, pck-and-place applcatons s proposed by Perrot and Company (Perrot & Company, 1999). hs manpulator offers 3-DOF n translaton and 1-DOF n rotaton about a gven axs. he H4 manpulator s useful for hghspeed handlng n robotcs and mllng n machne tool ndustry snce t s a fully-parallel mechansm wth no passve chan whch can provde hgh performance n terms of speed and acceleraton (Wu et al, 2006). Its prototype, bult n the Robotcs Department of LIRMM, can reach 10g acceleratons and veloctes hgher than 5 m/s (Robotcs Department of LIRMM). Perrot et al. proved the effcency of H4 servng as a hgh-speed pck-and-place robot (Perrot et al, 2006). Corradn et al. evaluated the 4-DOFs parallel manpulator stffness by two methods and compared the results (Coradn & Fauroux, 2003). Renaud et al. presented the knematc calbraton of a H4 robot usng a vson-based measurng devce (Renaud et al, 2003). antawroon et al. desgned and analyzed a new famly of H4 parallel robots (antawroon & Sangveraphunsr, 2003). Pognet et al. estmated dynamc parameters of H4 wth nterval analyss (Pognet et al, 2003). Parallel manpulators suffer from smaller workspaces relatve to ther seral counterparts; therefore, many researchers addressed the optmzaton of ther workspaces (Boudreau & Gosseln, 1999; Larb et al, 2007). But optmzaton for such a purpose mght lead to a manpulator wth poor dexterty. o allevate ths drawback some others consdered both performance ndces and volume of workspace, smultaneously (L & Xu, 2006; Xu & L, 2006; Lara et al, 2010). hs chapter deals wth an optmal desgn of H4 parallel manpulator amed at mllng and Rapd-Prototypng applcatons wth three degrees of freedom n translaton and one n rotaton. he forward and nverse knematcs of the manpulator are solved. he forward knematcs analyss of H4 leads to a unvarate polynomal of degree eght. he workspace of the manpulator s parameterzed usng several desgn parameters. Some geometrc constrants are consdered n the problem, as well. Because of nonlnear dscontnuous behavour of the Correspondng Author

3 402 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton problem, Genetc Algorthm (GA) Method s used here to optmze the workspace. Fnally, usng GA, the manpulator s optmzed based on a mxed performance ndex that s a weghted sum of global condtonng ndex and ts workspace. It s shown that by ntroducng ths measure, the parallel manpulator s mproved at the cost of workspace reducton. 2. Descrpton and moblty analyss of a H4 parallel manpulator he basc concept of H4 s descrbed by a smple archtectural scheme as llustrated n Fg. 1, where jonts are represented by lnes (Perrot et al, 2001). he manpulator s based on four ndependent chans between the base and the End-Effector (EE); each chan s drven by an actuator whch s fxed on the base. Let P, R, U and S represent prsmatc, revolute, unversal, and sphercal jonts, respectvely. Each of the P-U-U and R-U-U chans must satsfy some geometrcal condtons to guarantee that the manpulator offers three translatons and one rotaton about a gven axs (see (Perrot & Company, 1999) for detals). he U-U and (S-S) 2 (or (U-S) 2 ) chans can be consdered as equvalent n terms of number and type of degrees of moton, so the P-U-U (or R-U-U) chans can be replaced by P-(U-S) 2 or P-(S-S) 2 chans (respectvely by R-(U-S) 2 or R-(S-S) 2 ). In ths chapter, P-(S-S) 2 chan s chosen for the mechansm archtecture of H4. Fg. 2 shows the archtecture of H4 (chan #1 s not plotted for sake of smplcty) (Pognet et al, 2010). Fg. 1. Archtectural scheme of H4 It s noteworthy that the four ndependent chans are not drectly connected to the EE. It s possble to add another revolute jont on ths end part and to couple t (wth gears, tmng belt, etc (Robotcs Department of LIRMM)) so that the range of moton obtaned on ths latter jont can be larger than the end part ones. It s even possble to equp ths passve revolute jont wth a sensor to mprove the robot accuracy. Moreover, the manpulator s a hgh-speed mechansm and can be easly controlled. So the H4 manpulator has the ablty of servng as an effcent pck-and-place robot. Consderng the H4 robotc structure as gven n Fg. 2, ts geometrcal parameters of are defned as follows: wo frames are defned, namely {A}: a reference frame fxed on the base; {B}: a coordnate frame fxed on the EE (C 1 -C 1 ). he actuators slde along gude-ways orented along a untary vector, k z ( kz s the unty vector parallel to the z axs n the reference frame {A}), and the orgn s pont P, so the poston of each pont A s gven by: APqz ; for =1, 4, n whch q s the actuator coordnates.

4 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 403 he parameters M, d and h are the length of the rods, the offset of the revolute-jont from the ball-jont, and the offset of each ball-jont from the center of the travelng plate, respectvely. B x y z and an angle θ, representng ts orentaton. he pose of the EE s defned by a poston vector a) Robot wth four lnes drves and (S S) 2 chans Fg. 2. H4 parallel manpulator b) Robot CAD model a b 0 Wthout losng generalty, n ths chapter we consder P for smplcty, Q z s the offset of {B} from {A} along the drecton of kz. One can effectvely analyze the moblty of a H4 parallel manpulator by resortng to screw theory, whch s a convenent tool to study nstantaneous moton systems that nclude both rotaton and translaton n three dmensonal spaces (Zhao et al, 2004). A screw s called a twst when t s used to descrbe the moton state of a rgd body and a wrench when t s used to represent the force and moment of a rgd body. If a wrench acts on a rgd body n such a way that t produces no work, whle the body s undergong an nfntesmal twst, the two screws are sad to be recprocal (L & Xu, 2007). In a parallel

5 404 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton manpulator, the recprocal screws assocated wth a seral lmb represent the wrench constrants mposed on the movng platform by the seral lmb. he motons of the movng platform are determned by the combned effect of all the wrench constrants mposed by each lmb. herefore, we can get the followng equaton: $ (1) r 0 $where r$s the recprocal screw and represents the recprocal producton of two screws (Da & Jones, 2007). Accordng to the physcal nterpretatons of recprocal screws, one can obtan the constrants spaces that should be spanned by all of the recprocal screws. As far as a H4 parallel manpulator s concerned, each S jont s equvalent to three ntersectng non-coplanar R jonts, and then the jont twsts assocated wth the th P-(S-S) 2 -R (or P-U-U-R) chan form a 6-system, whch can be dentfed n the fxed frame as follows: j 0 $, 1 s1 4 1s B $, B 1sB 2 1sA 5 A $, 1sA 2s B $, B 2sB 3 $ 2sA A $ 2sA s C 6 C sc where s denotes a unt vector along the jth jont axs of the th chan, for 1,...,4. herefore, the knematc screws of each knematc chan can be expressed as: $[ ] herefore, the recprocal screws of knematc chans can be derved as: $ $[ ] $ $r platform r r r r $$$$$ (2) $ (3) $ (4) Fnally one can compute null spaces of the foregong recprocal screws whch leads to the DOF of the manpulator; namely, DoF DoF DoF DoF hese mply that H4 robot has three translatonal and one rotatonal DOF. Fgure 3 shows the rotaton of C 1 C 2 lnk about z-axs as rotatonal DOF. 3. Knematc analyss 3.1 Inverse knematcs he nverse poston knematcs problem solves the actuated varables from a gven pose of EE. Let q q q q q be the array of the four actuator jont varables and (5)

6 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 405 Fg. 3. Desgn parameters of H4 x x y z be the array of the pose of the EE. he poston of ponts C 1 and C 2 are gven by [4]: ot RotRC B ( ) BC C B ( ) BC (6) where Rot ( ) denotes the rotaton matrx of the EE wth respect to reference frame and s defned as: A Rot( ) R R ( ) B cos( ) sn( ) 0 sn( ) cos( ) 0 (7) Moreover, the poston of each pont B s gven by: herefore, the followng can then be wrtten: z B1 C1 CB 1 1 B2 C1 CB 1 2 (8) B C CB B C CB 2 2 M A B (9) 2

7 406 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton hen, for the frst chan: A ( BRot( ) BC C B P ) q z (A B ) q 2q d.z d where d BRot( ) BC1 C B P. Fnally, the two solutons of Eq. 10 are gven by: q. (. ) M d1 z1 d1 z1 1 d1 (10) (11) Smlarly, q 1, q 2 and q 4 can be derved as: q 2 d2. z2 ( d2. z2) M 2 d2 d2 BRot( ) BC1 C1B2 P q 3 d3. z3 ( d3. z3) M 3 d3 d3 BRot( ) BC2 C2B3 P q d. z ( d. z ) M d d BRot( ) BC2 C B P (12) 3.2 Forward knematcs Forward knematc problem solves the pose of the EE from a gven actuators varables. It s well-known that forward knematc problem of parallel manpulators s challengng (Dasgupta & Mruthyunjaya, 2000) and nvolves the soluton of a system of nonlnear coupled algebrac equatons n the varables descrbng the platform posture. hs system of nonlnear equatons mght lead to solutons. Except n a lmted number of the problems, one has dffculty n fndng exact analytcal solutons for the problem. So these nonlnear smultaneous equatons should be solved usng other methods, namely, numercal or semexact analytcal methods. Some others beleve that the combnaton of numercal and semexact analytcal methods can also produce useful results (Hashem et al, 2007; Vared et al, 2009). Cho et al. solved forward knematc problem of H4 and showed that the problem lead to a 16th degree polynomal n a sngle varable (Cho et al, 2003). he EE s composed of three parts (two lateral bars and one central bar). Moreover, ponts B 1, B 2, B 3 and B 4 form a parallelogram. Let A A and A B represent the homogeneous coordnates of the ponts A n {A} and B n {A}, respectvely. hen, one can wrte (Wu et al, 2006): A xhe1 c P cx y he1 sde 2 P sy Q B z z 1 1 a b q 1 A A (13) where P he, Q de, E E 1, E E 1, E E 1, E E 1, ccos( ), ssn( ) (14) Substtutng these values n Eq.(9), upon smplfcatons, yelds:

8 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm (P cxa ) (P sy Q b ) (zq ) M 1,...,4 (15) Expandng and rearrangng Eq.(15) leads to: Ax By Cz D E 0 for 1,...,4 A 2(Pca ), B 2(PsQ b ) C 2q D a b q 2P(a c b s Q s ) 2Q b P Q M E x y z (16) Subtractng Eq.(16) for =3, 4 from the same equaton for =2, yelds to: where A23 xb23 yc23 zd23 0 (17) A24 xb24 yc24 zd24 0 (18) A 23 ( A 2 A 3 ), B 23 (B 2 B 3 ), C 23 (C 2 C 3 ), D 23 (D 2 D 3 ), A ( A A ), B (B B ), C (C C ), D (D D ), Eqs. (17) and (18) now can be solved for x and y, namely: 11z 12 x e ze z 22 y eze 3 4 (19) (20) where e,e,e,e, A B A B, B C B C, B D B D, A C A C, A D A D, Substtutng Eqs.(19) and (20) nto Eq.(16) for =2, yelds to the followng quadratc equaton. where z z 0 (21) e1e31, 12e1e22e3e4 A 2e1B 2e3C 2, e2 e4 A2e2 B2e4 D2 Eq.(21) can be solved for z. Substtutng ths value nto Eq.(16) for =1, upon smplfcatons leads: f((c ),(c ) (s ),(c ) (s ),(c ) (s ),(c ) (s ),(c ) (s ), (c ) (s ),(c ) (s ),(c ) (s ),(c ) (s ),(c ) (s ),(c ) (s ), (c ) (s ),(c ) (s ),(c ) (s ) ) 0 (22)

9 408 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton where f( x 1,x 2,...,x n) represents a lnear combnaton of x 1,x 2,...,x n. he coeffcents of Eq.(22) are the data depend on the desgn parameters of the H4 robot. In Eq.(22), we substtute now the equvalent expressons for c and s gven as: c, s, tan( / 2) Upon smplfcatons, Eq.(22) leads to a unvarate polynomal of degree eght, namely; (23) a b c d e f g h 0 (24) where a, b, c, d, e, f, g, h and depend on knematc parameters. he detaled expressons for them are not gven here because these expansons would be too large to serve any useful purpose. What s mportant to pont out here s that the above equaton admts eght solutons, whether real or complex, among whch we only nterested n the real ones. Substtutng the values of from Eq.(23) nto Eq.(19), Eq.(20) and Eq.(21), complete the solutons Numercal example of knematc analyss Here, we nclude a numercal example as shown n Fg.4. he desgn parameters of H4 are gven as: h d 6 (cm), Q 42 (cm),m M 3Q,M M 2Q (25) Substtutng these values n Eq.(13), yelds: A A A A z 1 2 z 3 4 z [ ], [ ], [ ], [ ], [6 48 0], [6 6 42], [48 6 0], [6 6 42]. x / 6 1 B1 2 B2 3 B3 4 B4 Gven, the poston and orentaton of the EE as knematcs are gven by:, nverse q [ ] (26) Next, the forward knematc problem, for the actuators coordnate as gven n Eq.(26), s solved. he polynomal equaton n Eq.(24) can be solved for, namely; (27) here are only two real solutons, for whch leads to x 5(cm) 5(cm) 30(cm) 0.524( rad) and , yelds:

10 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 409 x 3(cm) 7.95(cm) 14.58(cm) 2.47(rad). However, the latter confguraton cannot be realzed n practce because of the mutual nterference of the parallelograms as shown n Fg.4. 7 = = Fg. 4. he solutons for forward knematc problem 3.3 Jacoban matrx Jacoban matrx relates the actuated jont veloctes to the EE Cartesan veloctes, and s essental for the velocty and trajectory control of parallel robots. he velocty of the EE of H4 can be defned by resortng to a velocty for the translaton, v B x y z and a scalar for the rotaton about z; namely,. hus, the velocty of ponts C 1 and C 2 can be wrtten as follows (Wu et al, 2006): k v v ( ) BC v v k( ) BC (28) c B 1 c B Moreover, snce the lnks B 1 B 2 and B 3 B 4 only have translatonal moton, the followng relatons hold: On the other hand, velocty of ponts v v v v v v B B C B B C A s gven by: v A z (29) qk (30) he velocty relatonshp can then be wrtten thanks to the classcal property; namely, v. A B v. A B A B (31) Eq.(31) can be wrtten for =1,,4 and the results grouped n a matrx form as: J q J x (32) q x

11 410 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton Where x and q denote the vectors of the EE velocty and nput actuated jont rates, respectvely ; J q and J x are the Jacoban matrces, all are defned as: J q z2 2 2 z3 3 3 zq q q q q AB A B A B 0 z A B J x (33) x [x y z ] k(a1b 1) x (A1B 1) y (A1B 1) z (A1B1 BC 1). k (A2B 2) x (A2B 2) y (A2B 2) z (A2B2 BC 1). (A 3B 3) x (A3B 3) y (A3B 3) z (A3B3 BC 2). k (A 4B4) (AB) 4 4 y (AB) 4 4 z (AB 4 4 BC 2). kx If the mechansm s not n a sngular confguraton, the Jacoban and ts nverse are descrbed as: 1 x q J J J and 1 1 q x J J J (34) 4. Optmzaton of H4 4.1 Workspace evaluaton For a robot n the context of ndustral applcaton and gven parameters, t s very mportant to analyze the volume and the shape of ts workspace (Dombre & Khall, 2007). Calculaton of the workspace and ts boundares wth perfect precson s crucal, because they nfluence the dmensonal desgn, the manpulator s postonng n the work envronment, and ts dexterty to execute tasks (L & Xu, 2006). he workspace s lmted by several condtons. he prme lmtaton s the boundary obtaned through solvng the nverse knematc problem. Further, the workspace s lmted by the reachable extent of drves and jonts, then by the occurrence of sngulartes, and fnally by the lnks and platform collsons (Stan et al, 2008). Varous approaches may be used to calculate the workspace of a parallel robot. In the present work the boundary of workspace of H4 s determned geometrcally (Merlet, 2006). 4.2 Condton number In order to guarantee the regular workspace to be effectve, constrants on the dexterty ndex are ntroduced nto the desgn problem. A frequently used measure for dexterty of a manpulator s the nverse of the condton number of the knematcs Jacoban matrx (Hossen et al, 2011). Indeed, n order to determne the condton number of the Jacoban matrces, ther sngular values must be ordered from largest to smallest. However, n the presence of postonng and orentng tasks the sngular values assocated wth postonng, are dmensonless, whle those assocated wth orentaton have unts of length, thereby makng

12 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 411 mpossble such an orderng. hs dmensonal n-homogenety can be resolved by ntroducng a weghtng factor/length, whch s here equal to the length of the frst lnk (Hossen et al, 2011). hen, the condton number of homogeneous Jacoban s defned as the rato of ts largest sngular value to ts smallest one, (Gosseln & Angeles, 1991),.e. l s l ( J ) (35) Note that () J can attan any value from 1 to nfnty, n whch they correspond to sotropy and sngularty, respectvely. 4.3 Performance ndex he objectve functon for maxmzaton s defned here as a mxed performance ndex whch s a weghted sum of global dexterty ndex (GDI), d and space utlty rato ndex (SURI), ( Dasgupta & Mruthyunjaya, 2000),.e., s w (1w ) d d d s 1 1 V wd dv (1w d) V V where the weght parameter w d(0 wd 1) descrbes the proporton of GDI n the mxed ndex, and V represents the robot sze whch s evaluated by the product of area of the fxed platform and the maxmum reach of the EE n the z drecton. s V (36) 4.4 Desgn varables he archtectural parameters of a H4 nvolve the offset of {B} from {A} along the drecton k(q), length of the offset of the revolute-jont from the ball-jont (d) and the offset of of z z each ball-jont from the center of the travelng plate (h). In order to perform the optmzaton ndependent of the dmenson of each desgn canddate, the desgn varables are scaled by q,.e., the moton range of the actuators. hus, the desgn varables become d h Q,, z. However, we have the followng lmtatons for the desgn varables: q q q 1/ ( J ) >0.01, d h Q , , 0.35 z 0.55 q q q 4.5 Optmzaton result of H4 In order to perform an optmal desgn of H4 parallel robots, an objectve functon was developed frst, then GA s appled n order to optmze the objectve functon (Xu & L, 2006). For optmzaton settngs, regardng to the GA approach, normalzed geometrc selecton s adopted (Merlet, 2006), and the genetc operators are chosen to be non-unform mutaton wth the rato of 0.08 and arthmetc crossover wth the rato of 0.8. Moreover, the populaton sze s 30 and the generatons number s set to

13 412 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton Optmzaton based on maxmum workspace volume Frst we consder the volume of workspace as the objectve functon; namely, V*=max(V) Subject to 1. 1/ () J >0.01 d h Q , , 0.35 z 0.55 q q q he soluton of ths problem s gven n able 1. Moreover, the workspace for 0 and the condtonng ndex for 0 and z=0 are shown n Fg.5 and Fg.6, respectvely. Whle the workspace sze s acceptable, the manpulator suffers from a poor dexterty throughout ts workspace. Volume of workspace (rad)(cm 3 ) Average of condtonng ndex Robot s parameters d(cm) h(cm) Q z (cm) able 1. Optmzaton result for H4 As t s observed the GA reaches a convergence after 30 teratons as depcted n Fg Optmzaton based on GDI In ths secton we optmze the average of condtonng ndex n the workspace. herefore, the problem s stated as: GDI=max(average (1/ () J )) Subject to 1. 1/ () J > 0.01 d h Qz , , q q q As t s expected, the volume of the workspace s very small and only ncludes a small neghbourhood of a pont of the best condtonng ndex. hs optmal desgn s gven n able 2. Volume of workspace (rad)(cm 3 ) Average of condtonng ndex Robot s parameters d(cm) h(cm) Q z (cm) able 2. Optmzaton result for H4

14 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 413 Fg. 5. Workspace of H4 for 0 Fg. 6. Condtonng ndex for z=0 and 0

15 414 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton Fg. 7. Convergence of GA Optmzaton based on the mxed performance ndex For the problem at hand one needs a good ftness functon, because the optmzaton based on maxmal workspace volume, decreases the performance ndces and the optmzaton based on GDI decreases the workspace volume. herefore, one can optmze the manpulator based on performance ndex that descrbed n subsecton 5.3. he optmzaton results for w d =0.25, 0.5, 0.75 are gven n able 3. Moreover, for dfferent values of w d, the problem s solved and the GDI, SURI and the mxed performance ndex are calculated and plotted n Fg. 8. As the result, any value of w d greater than 0.74 leads to a lmted workspace and for any values smaller than that has no substantal effects on GDI and the workspace. herefore, t clearly shows that by ntroducng ths measure, the performance of the manpulator can be mproved at a mnor cost ts workspace volume. Fg. 8. GDI and SURI and Performance Index versus weght parameter

16 Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm 415 wd 0.25 wd 0.5 wd 0.75 Volume of workspace (rad)(cm 3 ) d(cm) h(cm) Q z (cm) GDI able 3. Optmzaton results for H4 5. Conclusons Frst, the forward and nverse knematcs of H4 parallel manpulator has been studed here, n whch the former problem has leaded to a unvarate polynomal of degree eght. hen, the optmal desgn of the manpulator has been addressed. Usng genetc algorthm the manpulator has been optmzed based on a mxed performance ndex that s a weghted sum of global condtonng ndex and ts workspace volume. It has been shown that by ntroducng ths measure, the parallel manpulator has been mproved at mnor cost of ts workspace volume. 6. References Boudreau, R.; Gosseln, C.M. (1999). he synthess of planar parallel manpulators wth a genetc algorthm,, Journal of Mechancal Desgn, 121(4), 1999, pp Cho, H.B.; Konno, A. & Uchyama, M. (2003). Closed-form solutons for the forward knematcs of a 4-DOFs parallel robot H4, Proceedngs of IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems, Las Vegas, USA, October, 2003, pp Company, O.; Marquet, F. & Perrot, F. (2003). A new hgh-speed 4DoF parallel robot synthess and modelng ssues. IEEE, ransactons on Robotcs and Automaton, Vol.19, No.3, 2003, pp Coradn, C.; Fauroux, J. (2003). Evaluaton of a 4-DOF parallel manpulator stffness, Mechansm and Machne Scence, Aug, Da, J.S.; Jones, J.R. (2007). A Lnear Algebrac Procedure n Obtanng Recprocal Screw Systems, J. Robotc Systems, 2007, 20(7), pp Dasgupta, B.; Mruthyunjaya,.S. (2000). he Stewart platform manpulator: A revew, Mechansm and Machne heory, 35, 2000, pp Dombre, E.; Khall, W. (2007). Modelng, Performance Analyss and Control of Robot Manpulators, ISE, Gosseln, C.; Angeles, J. (1991). A global performance ndex for the knematc optmzaton of robotc manpulators. ASME J Mech, December, 1991, 113(3), pp Hashem, S.H.; Danal, H.M. & Ganj, D.D. (2007). Numercal smulaton of the generalzed Huxley equaton by He s homotopy perturbaton method, Appled Mathematcs and Computaton, 2007, pp Hossen, M.A; Danal, H.M. & aghrad, H.D. (2011). Dexterous Workspace Optmzaton of a rcept Parallel Manpulator, Advanced Robotcs, Vol. 25, 2011, pp Lara-Molna, F.A.; Rosáro, J.M. & Dumur, D. (2010). Mult-Objectve Desgn of Parallel Manpulator Usng Global Indces, he Open Mechancal Engneerng Journal, 2010, 4, pp

17 416 Seral and Parallel Robot Manpulators Knematcs, Dynamcs, Control and Optmzaton Larb, M.A.; Romdhane, L. & Zeghloul, S. (2007). Analyss and dmensonal synthess of the DELA robot for a prescrbed workspace, Mechansm and Machne heory, 42, (2007), pp L, Yangmn.; Xu, Qngsong. (2006). A new approach to the archtecture optmzaton of a general 3-PUU translatonal parallel manpulator. J Int Robot System, 2006, 46, pp L, Yangmn.; Xu, Qngsong. (2007). Knematc analyss of a 3-PRS parallel manpulator, Robotcs and Computer-Integrated Manufacturng, 2007, 23, pp Merlet, J.P.; (2006). Parallel robots (second edton), sprnger. Perrot, F.; Company, O. (1999). H4: a new famly of 4-DoF parallel robots, Int Conf on Advanced Intellgent Mechatroncs, Proceedngs of the 1999 IEEE/ASME, pp Perrot, F.; Marquet, F. & Company, O. & Gl,. (2001). H4 parallel robot: modelng, desgn and prelmnary experments, Int Conf on Robotcs and Automaton, May, Pognet, Ph.; Ramdan, N. & Vvas, O.A. (2003). Robust estmaton of parallel robot dynamc parameters wth nterval analyss, Proceedngs of the 42nd IEEE, Conference on Decson and Control, Mau, Hawa USA, December, Renaud, P.; Andreff, N. & Marquet, F. & Martnet, P. (2003). Vson-based knematc calbraton of a H4 parallel mechansm, Int Conf on Robotcs and Automaton, Proceedogr of the 2003 IEEE, ape, awan, September Robotcs Department of LIRMM. (n.d.). H4 wth rotary drves: a member of H4 famly, dedcated to hgh speed applcatons, Stan, S.D.; Manc, M. & Măteş, M. & Bălan, R. (2008). Evolutonary approach to optmal desgn of 3 DOF ranslaton exoskeleton and medcal parallel robots, HSI 2008, IEEE Conference on Human System Interacton, Krakow, Poland, May 25-27, 2008, pp antawroon, N.; Sangveraphunsr, V. (2005). Desgn and analyss of a new H4 famly parallel manpulator, hammasat Int J. Scence ech, July-September, Vol. 10, No. 3, Vared, S.M.; Danal, H.M. & Ganj, D.D. (2009). Knematcs of an offset 3-UPU translatonal parallel manpulator by the homotopy contnuaton method, Nonlnear Analyss: Real World Applcatons 10, 2009, pp Wu, Jnbo.; Yn, Zhoupng. & Xong, Youlun. (2006). Sngularty analyss of a novel 4-DoF parallel manpulator H4, Int J Advanced Manuf ech, 29, pp Xu, Qngsong.; L, Yangmn. (2006). Knematc analyss and optmzaton of a New complant parallel mcromanpulator, Int J of Advanced Robotc Systems, 2006, Vol. 3, No. 4. Zhao, J.S.; Zhou, K. & Feng, Z.J. (2004). A theory of degrees of freedom for mechansms. Mechansm and Machne heory, 39, 2004, pp

18 Seral and Parallel Robot Manpulators - Knematcs, Dynamcs, Control and Optmzaton Edted by Dr. Serdar Kucuk ISBN Hard cover, 458 pages Publsher Inech Publshed onlne 30, March, 2012 Publshed n prnt edton March, 2012 he robotcs s an mportant part of modern engneerng and s related to a group of branches such as electrc & electroncs, computer, mathematcs and mechansm desgn. he nterest n robotcs has been steadly ncreasng durng the last decades. hs concern has drectly mpacted the development of the novel theoretcal research areas and products. hs new book provdes nformaton about fundamental topcs of seral and parallel manpulators such as knematcs & dynamcs modelng, optmzaton, control algorthms and desgn strateges. I would lke to thank all authors who have contrbuted the book chapters wth ther valuable novel deas and current developments. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: M. Falahan, H.M. Danal and S.M. Vared (2012). Optmzaton of H4 Parallel Manpulator Usng Genetc Algorthm, Seral and Parallel Robot Manpulators - Knematcs, Dynamcs, Control and Optmzaton, Dr. Serdar Kucuk (Ed.), ISBN: , Inech, Avalable from: Inech Europe Unversty Campus SeP R Slavka Krautzeka 83/A Rjeka, Croata Phone: +385 (51) Fax: +385 (51) Inech Chna Unt 405, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, , Chna Phone: Fax:

19 2012 he Author(s). Lcensee IntechOpen. hs s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton 3.0 Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted.