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2 2 Knematcs of AdeptThree Robot Arm Adelhard Ben Rehara Unversty of Papua Indonesa 1. Introducton Robots are very powerful elements of today s ndustry. They are capable of performng many dfferent tasks and operatons precsely and do not requre common safety and comfort elements humans need. However, t takes much effort and many resources to make a robot functon properly. Most companes that made ndustral robots can be found n the market such as Adept Robotcs, Staubl Robotcs and Fanuc Robotcs. As a result, there are many thousands of robots n ndustry. An AdeptThree robot arm s a selectvely complant assembly robot arm (SCARA) manufactured by the Adept Company. In general, tradtonal SCARA's are 4-axs robot arms wthn ther work envelope. They have the jonted two-lnk arm layout smlar to our human arms and commonly used n pck-and-place, assembly, and packagng applcatons. As a SCARA robot, an AdeptThree robot has 4 jonts whch denote that t has 4 degree of freedom (DOF). The robot has been desgned wth completed components ncludng operatng system and programmng language namely V+ (Rehara and Smt, 2010). In robotc, there are two mportant studes whch are knematcs and dynamcs studes. Robot knematcs s the study of robot moton wthout regards to the forces that result t. On the other hand, the relatonshp between moton, and the assocated forces and torques s studed n robot dynamcs. In ths chapter, knematcs problem for an AdeptThree robot wll be explaned n detal. 2. AdeptThree robot system An AdeptThree robot s a 4-axs SCARA robot whch s desgned for assemblng and parthandlng tasks. The body of the robot s too bg compared to the most SCARAs but t has strength and rgdty to carry a load about 25 kg (55 lb) as ts maxmum payload. For the workng envelope, t has a 1067 mm maxmum radal that can make more than two meters n dameter and also t has 305 mm Z-axs stroke. Fg. 1 shows the physcal system of an AdepthThree robot arm. All of the fgures n ths secton are provded by Adept company (1991). As manufactured by Adept Company, AdeptThree robot s desgned to be compatble wth the other Adept products ether the Adept MC or the Adept CC controller nterface. All of the control and operaton of the AdeptThree robot are programmed through the selected controller. In ths case, the robot s usng the Adept MC controller.

3 22 Robot Arms (a) Fg. 1. (a) Physcs of an AdeptThree Robot Arm and (b) Jonts and lnks names 2.1 Jonts moton An AdeptThree robot has 4 jonts whch are lnked to the robot. Jont 3 s a translatonal jont whch can move along Z-axs whle jont 1, 2, and 4 are rotatonal jonts. Workng envelope of the robot s shown n fg.2 (b). Frst jont s the base jont and t s also called the shoulder as ts functon looks lke a human shoulder. In ths jont, the rotatonal movement of the nner lnk and the column wll be provded. The jont has a maxmum movement of about that can be separated n to the left and to the rght as n fg.2 (a). (b) (a) Fg. 2. (a) 1 st jont moton and (b) workng envelope Second jont s called the elbow as ts functon looks lke a human elbow. In ths jont, both the outer lnk and nner lnk are lnked. Furthermore ths jont s smlar to 1 st jont, the maxmum movement of the jont s also about (b)

4 Knematcs of AdeptThree Robot Arm 23 (a) Fg. 3. (a) 2 nd jont, (b) 3 rd and 4 th jont movements Fgure 3(a) shows the movement of the 2 nd jont. In order to avod any ambguty to program the robot, the robot can be programmed to move lke a human left or rght arm by usng the syntax LEFTY or RIGHTY. Thrd jont s placed at the end of the outer lnk. It has a maxmum stroke of about 12 nches or 30.5 cm. Fg. 3(b) shows the 3 rd jont and also 4 th jont. Fourth jont s also called the "the wrst. The jont can be moved over a range of Its functon s smlar to a human wrst and t can be rotated as a human hand to tghten a bolt or unscrew a screw. Although the AdeptThree robot has the wdest workng envelope, t stll has a lmtaton. The lmtaton s about the travellng of each jont and t was bult to avod the damage of the robot. The maxmum jont travel s confned by soft-stop and hard-stop. Soft-stop and hard stop occur when the jont s expected to pass the lmt angle. Whle both stops happen, robot power wll be turned off. Soft-stop can be a programmed cancellaton and t requres the robot arm to be moved manually nto ts workng envelope. After the arm nto the workng envelope, the robot arm can be used drectly wthout any other settng. On the other hand, the acton of the hardstop s to cancel all of the robot operatons and t requres to move the robot manually by usng the manual control pendant (MCP) to ts workng area. 2.2 Operatng system The AdeptThree robot has ts own operatng system called V+ that also can recognze some syntaxes n programmng the robot. As an operatng system, the V+ can handle all of the system operatons. The programmng language n the robot operatng system s a hgh level programmng language. It s smlar to C or Pascal programmng and t can transfer syntaxes to machne language. The V+ real-tme and mult-taskng operatng system manages all system level operatons, such as nput/output (I/O), program executon, task management, memory management and dsk fle operatons. As a programmng language, V+ has a rch hstory and has evolved nto the most powerful, safe and predctable, robot programmng language avalable today. V+ s the only language to provde an ntegrated soluton to all of the programmng needs n a robotc work cell, ncludng safety, robot moton, vson operatons, force sensng and I/O. (b)

5 24 Robot Arms In general, the syntaxes usng by V+ can be categorzed nto 4 parts: Montor command, t can be used drectly by typng t one by one. Program command, t wll be run f t s used n a program lnes. Real-tme command, t only can be run n a program. Strng command, t s used to handle all operatons wth strng varable. It can be used n montor and program command. 2.3 Robot setup Before usng the robot, t s needed to be booted by usng ts operaton system V+. The bootng screen of the Adept + s placed n fg. 4. Dot (.) command n the last lne means that the robot s ready to be commanded by applyng the V+ syntaxes. Fg. 4. Adept V+ bootng screen As shown n fg.4, the robot conssts of some modules whch are software (V+ verson 10.4), controller module and a robot arm. Unlke most computers, the controller does not have BIOS (basc nput output system) memory; therefore the robot tme needs to be changed wth the actual tme every tme after tuned on. 3. Knematcs Knematcs n robotcs s a statement form about geometrcal descrpton of a robot structure. From the geometrcal equaton we can get relatonshp among jonts spatal geometry concept on a robot wth ordnary co-ordnate concept whch s used to determne the poston of an object. In other word, knematcs s the relatonshps between the postons, veloctes, and acceleratons of the lnks of a robot arm. The am of knematcs s to defne poston relatve of a frame to ts orgnal coordnates. Usng knematcs model, a programmer can determne the confguraton of nput reference that should be fed to every actuator so that the robot can do concde movements of all jont to reach the desred poston. On the other hand, wth nformaton of poston that s shown by every jont whle robot s dong a movement, the programmer by means of knematcs analyss can determne where s arm tp poston or whch parts of the robot should be moved n spatal coordnate. Knematcs problem conssts of forward and nverse knematcs and each type of the knematcs has ts own functon as llustrated n fg.5. From fg. 5, forward knematcs s used for transferrng jont varable to get end-effector poston. On the other hand, nverse knematcs wll be appled to fnd jont varable from end-effector poston.

6 Knematcs of AdeptThree Robot Arm 25 Fg. 5. Forward and nverse knematcs dagram 3.1 Forward knematcs Forward knematcs problem s deal wth fndng the poston and orentaton of a robot end-effector as a functon of ts jont angles. Forward knematcs problem s relatvely smple and t s easy to be mplemented. There are two methods for buldng forward knematcs provded n ths secton Graphcal method A smple forward knematcs can be derved from ts space usng graphcal soluton. Wth a three lnk planar robot n fg.6, the graphcal method for solvng forward knematcs wll be descrbed n ths secton. Fg. 6. Geometrc of three lnk planar robot Usng the vector algebra soluton to analyse the graph, the coordnate of the robot endeffector can be solved as follows. x l cos( ) l cos( ) l cos( ) y l sn( ) l sn( ) l sn( ) (1) Maple s mathematcal software whch s wdely used n computaton, modellng and smulaton. In each secton of the knematcs and Jacobean, the scrpt of the software s

7 26 Robot Arms provded. The Maple scrpt for buldng forward knematcs usng the graphcal method s lsted as follows. > restart: > n:=3:y:=0:c:=0: > for from 1 to n do > for j from to n do > c:=c+theta[j]; > end do; > y:=y+l[n-+1]*cos(c):c:=0: > end do; D-H conventon The steps to get the poston n usng D-H conventon are fndng the Denavd-Hartenberg (D-H) parameters, buldng A matrces, and calculatng T matrx wth the coordnate poston whch s desred. D-H Parameters D-H notaton s a method of assgnng coordnate frames to the dfferent jonts of a robotc manpulator. The method nvolves determnng four parameters to buld a complete homogeneous transformaton matrx. These parameters are the twst angle α, lnk length a, lnk offset d, and jont angle θ (Jaydev, 2005). Based on the manpulator geometry, two of the parameters whch are and a have constant values, whle the d and θ parameters can be varable dependng on whether the jont s prsmatc or revolute. Jaydev (2005) has provded 10 steps to denote the systematc dervaton of the D-H parameters as : 1. Label each axs n the manpulator wth a number startng from 1 as the base to n as the end-effector. Every jont must have an axs assgned to t. 2. Set up a coordnate frame for each jont. Startng wth the base jont, set up a rght handed coordnate frame for each jont. For a rotatonal jont, the axs of rotaton for axs s always along Z 1. If the jont s a prsmatc jont, Z 1 should pont n the drecton of translaton. 3. The X axs should always pont away from the Z 1 axs. 4. Y should be drected such that a rght-handed orthonormal coordnate frame s created. 5. For the next jont, f t s not the end-effector frame, steps 2 4 should be repeated. 6. For the end-effector, the Z n axs should pont n the drecton of the end-effector approach. 7. Jont angle θ s the rotaton about Z 1 to make X 1 parallel to X. 8. Twst angle s the rotaton about X axs to make Z 1 parallel to Z. 9. Lnk length a s the perpendcular dstance between axs and axs Lnk offset d s the offset along the Z 1 axs. A Matrx The A matrx s a homogenous 4x4 transformaton matrx whch descrbe the poston of a pont on an object and the orentaton of the object n a three dmensonal space. The homogeneous transformaton matrx from one frame to the next frame can be derved by the determnng D-H parameters. The homogenous rotaton matrx along an axs s gven by

8 Knematcs of AdeptThree Robot Arm 27 cos cos sn sn sn 0 sn cos cos sn sn 0 Rot 0 sn cos (2) and the homogeneous translaton matrx transformng coordnates from a frame to the next frame s gven by Trans a d (3) Where the four quanttes θ, a, d, are the names jont angle, lnk length, lnk offset, and twst angle respectvely. These names derve from specfc aspects of the geometrc relatonshp between two coordnate frames. The four parameters are assocated wth lnk and jont. In Denavt-Hartenberg conventon, each homogeneous transformaton matrx A s represented as a product of four basc transformatons as follows. or n completed form as A Rot( z, ) Trans ( z, d ) Trans ( x, a ) Rot( x, ) (4) A cos( ) sn( ) sn( ) cos( ) d a cos( ) sn( ) sn( ) cos( ) (5) By smplfyng equaton 5, the matrx A whch s known as D-H conventon matrx s gven n equaton 6. A cos cos sn sn sn a cos sn cos cos sn sn a sn 0 sn cos d (6) In the matrx A, about three of the four quanttes are constant for a gven lnk. Whle the other parameter whch s θ for a revolute jont and d for a prsmatc jont s varable for a

9 28 Robot Arms jont. The A matrx contans a 3x3 rotaton matrx, a 3x1 translaton vector, a 1x3 perspectve vector and a scalng factor. The A matrx can be smplfed as follows. T Matrx R P 0 1 1x3 3x3 3x1 A The T matrx s a knematcs chan of transformaton. The matrx can be used to obtan coordnates of an end-effector n terms of the base lnk. The matrx can be bult from 2 or more A matrces dependng on the number of manpulator jont(s). The T matrx can be formulated as T T A A,..., A (8) n 1 2 n Insde the T matrx, the drect knematcs can be found n the translaton matrx P whle the X, Y and Z postons are P 1, P 2 and P 3 respectvely. Soluton for the robot An AdeptThree robot arm wth four jonts s fgured n fg. 7. The AdeptThree robot jont motons are revoluton, revoluton, prsmatc and revoluton (RRPR) respectvely from jont 1 to 4. So the robot has four degrees of freedom. From fg. 7, jonts 1, 2, and 4 are revolute jonts; then the values of θ are varable. Snce there s no rotaton about prsmatc jont n jont 3, the θ values for jont 3 s zero whle d s varable. (7) Fg. 7. Lnks and jonts parameters of an AdeptThree robot arm

10 Knematcs of AdeptThree Robot Arm 29 Each axs of the AdeptThree robot was numbered from 1 to 4 based on the algorthm explaned before. After establshed coordnate frames, the next step s to determne the D- H parameters by frst determnng. The s the rotaton about X to make Z 1 parallel wth Z. Startng from axs 1, 1 s 0 because Z 0 and Z 1 are parallel. For axs 2, the 2 s or 180 because Z 2 s opposte of Z 0 whch s pontng down along the translaton of the prsmatc jont. 3 and 4 values are zero because Z 3 s parallel wth Z 2 and Z 4 s also parallel wth Z 3. The next step s to determne a and d. For axs 1, there s an offset d 1 between axes 1 and 2 n the Z 0 drecton. There s also a dstance a 1 between both axes. For axs 2, there s a dstance a 2 between axes 2 and 3 away from the Z 1 axs. No offset s found n ths axs so d 2 s zero. In axs 3, due to prsmatc jont, the offset d 3 s varable. Between axes 3 and 4, there s an offset d 4 whch s equal to ths dstance, whle a 3 and a 4 are zero. The completed D-H parameters are lsted n table 1. Axs Number Jont Angle Lnk Offset d Lnk Length a Twst Angle 1 1 d 1 l l d d Table 1. D-H Parameters of an AdeptThree Robot The transformaton matrx A can now be computed. Usng the expresson n equaton 6 the A matrces of each jont can be buld as A 0 1 c s 0 lc s c 0 l s d (9) c s 0 l c s c l s A (10) 2 A d (11)

11 30 Robot Arms A 3 4 c s s c d T matrx s created by multplyng each A matrx defned usng equaton 9 to 12 and the result s as follows. s4s s4c T cc cs sc 4 12 ss 4 12 cs 4 12 cc l2c1 2 l1c 1 l 2s1 2 l1s 1 d 4 d3 d1 1 Where c and s are the cosnes and snus of, c 1+2 and s 1+2 are cos( ) and sn( ), l s the length of lnk and d s the offset of lnk. By usng the T matrx, t s possble to calculate the values of (P x, P y, P z ) wth respect to the fxed coordnate system. Then the P x, P y, P z whch are obtaned wth drect knematcs are equatons whch are lsted below: (12) (13) P l c lc x y z P l s l s P d d d (14) Where constant parameters l 1 =559 mm, l 2 =508 mm, and d 1 =876.3 mm. The drect knematcs can be used to fnd the end-effector coordnate of the robot movement by substtutng the constant parameter values to the above equaton. Maple scrpt for the D-H conventon of forward knematcs s lsted as follows. > restart: > DH:=Matrx(<<theta[1],theta[2],0,theta[4]> <d[1],0,d[3],d[4]> <l[1],l[2], 0, 0> <0,p,0,0>>): > for from 1 to 4 do > A[]:=Matrx(<<cos(DH[,1]),sn(DH[,1]),0,0> <-cos(dh[,4])*sn(dh[,1]), cos(dh[,4])*cos(dh[,1]),sn(dh[,4]),0> <sn(dh[,4])*sn(dh[,1]),- sn(dh[,4])*sn(dh[,1]),cos(dh[,4]),0> <DH[,3]*cos(DH[,1]),DH[,3]*s n(dh[,1]),dh[,2],1>>); > end do: > T:=smplfy(A1.A2.A3.A4); Inverse knematcs Inverse knematcs deals wth the problem of fndng the approprated jont angles to get a certan desred poston and orentaton of the end-effector. Fndng the nverse knematcs soluton for a general manpulator can be a very trcky task. In general, nverse knematcs solutons are non lnear. To fnd those equatons can be complcated and sometmes there s no soluton for the problem. Geometrc and algebrac methods are provded n ths secton for solvng nverse knematcs of a robot arm.

12 Knematcs of AdeptThree Robot Arm Geometrc method One of the smple ways to solve the nverse knematcs problem s by usng geometrc soluton. Wth ths method, cosnes law can be used. A two planar manpulator wll be used to revew ths knematcs problem as n followng fgure. Fg. 8. Geometrc of two lnk planar robot Wth cosnes law, we get x y l l 2l l cos(180 ) (15) Snce cos(180-2 ) = -cos( 2 ) then the equaton 15 wll become x y l l 2l l cos( ) (16) By solvng the equaton 16 for gettng the cos( 2 ), Therefore the 2 wll be determned by takng nverse cosnes as x y l l 1 2 cos (17) 2 2ll 1 2 Agan lookng the fg. 8, we get x y l l 1 2 arccos 2 2ll 1 2 (18) sn sn l 2 ; arctan y 2 2 x y x (19) Where sn() = sn(180-2 ) = sn( 2 ). By replacng sn() wth sn( 2 ), the equaton 19 wll become

13 32 Robot Arms sn( ) 2 2 arcsn l 2 2 x y (20) Snce 1 = +, the 1 can be solved as sn( ) arcsn l arctan y x y x Maple scrpt for the geometrc method of nverse knematcs s lsted as follows. (21) > restart: > beta:=solve(sn(beta)/l2=sn(theta2)/sqrt(x^2+y^2), beta): > alpha:=arctan(y,x): > theta1:=beta+alpha;... > theta2:=solve(y^2+x^2=l1^2+l2^2+(2*l1*l2*cos(theta)),theta); Algebrac method The other smple ways to solve the nverse knematcs problem s by usng algebrac soluton. Ths method s used to make an nvert of forward knematcs. Rewrtng the endeffector coordnate from forward knematcs: x lc l c y ls ls (22) Usng the square of the coordnate, we get x y l c l ( c ) 2 l l c ( c ) ls l( s ) 2 lls( s ) (23) Snce cos(a) 2 +sn(a) 2 = 1 and also cos(a+b) 2 +sn(a+b) 2 = 1, the equaton 23 can be smplfy as Note that x y l l 2 l l c ( c ) s ( s ) (24) cos( ab) cos( a)cos( b) sn( a)sn( b) sn( ab) cos( a)sn( b) sn( a)cos( b) (25) By smplfyng the formulaton nsde the parenthess n equaton 24 wth the rule n equaton 25, the only left parameter s cos( 2 ); so the equaton 24 wll become x y l l 2l l c (26) Now the 2 can be formulated as the functon of nverse cosnes

14 Knematcs of AdeptThree Robot Arm x y l l 1 2 arccos 2 2ll 1 2 Usng the rule of snus and cosnes n equaton 25, the end-effector coordnate can be rewrtten as (27) x lc l c c l s s y ls lsc lcs (28) There are two unknown parameters nsde the equaton whch are cos( 1 ) and sn( 1 ). The cos( 1 ) can be defned from the rewrtten x as c 1 x l s s l l c (29) The sn( 1 ) s stll a mssng parameter and t s need to be solved. Substtutng c 1 to y n equaton 28, we get x l s s l l c y ls ls lsc (30) The equaton 28 wll become, xl s l s s l s l l s c y l l c l l c llsc lsc l l c (31) Smplfyng the equaton 31 we get xl s s l l 2l l c y l l c (32) The parenthess n equaton 32 can be replaced usng cosnes law wth x 2 + y 2. Therefore the snus of 1 can derved from the above equaton as xl s s x y y l l c (33) Now the 1 wll be got as the functon of nverse snus as y l l c xl s arcsn x y (34) Untl now we had defned both 1 and 2 of a two planar robot that s smlar to the AdeptThree robot. The jont angles can be used by applyng lnk length of the robot to the equaton of those angles.

15 34 Robot Arms Maple scrpt for the algebrac method of nverse knematcs s lsted below. > restart: > theta2:=solve(x^2+y^2=l1^2+l2^2+(2*l1*l2*cos(theta2)),theta2);... > restart: > cos(theta1):=solve(x=l1*cos(theta1)+l2*cos(theta1)*cos(theta2)- l2*sn(theta1)*sn(theta2),cos(theta1)): > theta1:=smplfy(solve(y=l1*sn(theta1)+l2*sn(theta1)*cos(theta2)+ l2*cos(theta1)*sn(theta2),theta1)); Jacobean The Jacobean defnes the transformaton between the robot hand velocty and the jont velocty. Knowng the jont velocty, the jont angles and the parameters of the arm, the Jacobean can be computed and the hand velocty calculated n terms of the hand Cartesan coordnates. The Jacobean s an mportant component n many robot control algorthms. Normally, a control system receves sensory nformaton about the robot s envronment, most naturally mplemented usng Cartesan coordnates, yet robots operate n the jont or world coordnates. Transforms are needed between Cartesan coordnates and jont coordnates and vce versa. The transformaton between the velocty of the arm, n terms of ts jont speeds, and the velocty of the arm n Cartesan coordnates, n a partcular frame of reference, s very mportant. Solvng the nverse knematcs can provde a transform, but ths would be a dffcult task to perform n real-tme and n most cases no unque solutons exst for the nverse knematcs. An alternatve s to use the Jacobean (Zomaya et al., 1999). Many ways to desgn a Jacobean matrx of a robot arm were provded. Zomaya et al. (1999) had presented three knds of algorthms to perform a Jacobean matrx. Frst algorthm s the smple way. Wthout usng matrx calculaton, the Jacobean can be bult from T matrx. Second algorthm was found to perform very well usng a sequental processng method. Thrd algorthm s also provded to sequental machne, but t would be nterestng to study how well t maps onto the mesh wth multple buses. The other algorthm was provded by Manjunath (2007) and Frank (2006). It uses tool confguraton vector to perform the Jacobean. The last algorthm wll be used and explaned n ths paper (Rehara, 2011). Gven jont varable coordnate of the end effectors: q [ q q... q ] T n (35) 1 2 Where q = for a rotary jont and q = d for a prsmatc jont. Nonlnear transformaton from jont varable q(t) to y(t) s defned as y=h(q), then the veloctes of jont axes s gven by h y q Jq (36) q Where J s the Jacobean of manpulator. Inverse of the Jacobean J -1 relates the change n the end-effector to the change n axs dsplacements, 1 q J y (37)

16 Knematcs of AdeptThree Robot Arm 35 The Jacobean s not always nvertble, n certan postons t wll happen. These postons are called geometrc sngulartes of the mechansm. A rotaton matrx n a T matrx s formed by three 3x1 vector. In smple, the T matrx can be rewrtng as n o a p T Where a s the approach vector of the end-effector, o s the orentaton vector whch s the drecton specfyng the orentaton of the hand, from fngertp to fngertp whle n s the normal vector whch s chosen to complete the defnton of a rght-handed coordnate system (Frank, 2006). The T matrx can be used to desgn the Jacobean by frst defnng the tool confguraton vector w as follows. (38) p ( q) ae n ( q / ) Rewrtng p and a vector from equaton 13, we get the tool confguraton vector as (39) lc lc ls ls d d d ( q) e Then the Jacobean matrx s the dfferental of the tool confguraton vector as (40) w Jq ( ) (41) q By takng a dfferentaton of the eq. 40, the Jacobean for the AdeptThree robot s defnes as ls ls ls lc lc lc Jq ( ) e The frst 3x3 matrx n the Jacobean s also called drect Jacobean. Because the Jacobean n eq. 42 s not a square matrx, t s not nvertble. In ths condton, the drect Jacobean can be useful snce t s a square and nvertble matrx. 4 (42)

17 36 Robot Arms Maple scrpt for formng the Jacobean s lsted below. > restart: wth(lnearalgebra): > q:=vector(4,[ph1,ph2,d3,ph4]): > J:=matrx(6,4): > w[1]:=l1*cos(ph1)+l2*cos(ph1+ph2): > w[2]:=l1*sn(ph1)+l2*sn(ph1+ph2): > w[3]:=-d4-d3+d1; > w[4]:=0; > w[5]:=0; > w[6]:=exp(q[4]/p); > for from 1 to 4 do > for j from 1 to 6 do > J[j,]:=dff(w[j],q[]); > end do; > end do; > prnt(j); Knematcs smulaton A Vrtual Instrumentaton (VI) was bult to the secton of knematcs smulaton for supportng the manual calculaton of a four DOF SCARA robot. The VI s a product of Fg. 9. SCARA robot smulaton

18 Knematcs of AdeptThree Robot Arm 37 graphcal programmng n LabVew whch s produced by Natonal Instrumentaton. The desgned VI can smulate vsual movement of the SCARA robot. The advantage of utlzng LabVew s that the graphcal programmng language s easy and smple to be used. A user only needs to set each property to program the VI. As shown n fg.9, the VI can be used to move the robot by applyng the method of forward and nverse knematcs. To support the vsual jont trackng, the VI s provded wth smultaneous movng and sequence movng buttons. In smultaneous movng mode, each jont move together n same tme. On the other hand sequence movng mode provdes the moton of each jont one by one. Started from 1 st jont to 4 th jont, each jont wll move after the other fnshed ts task. The poston of the end-effector s gven n X, Y and Z boxes, whle the jont varables are shown n q 1, q 2 and q 3 boxes. 6. Concluson Ths paper formulates and solves the knematcs problem for an AdeptThree robot arm. The forward knematcs of an AdeptThree robot was explaned utlzng D-H conventon whle nverse knematcs of the robot was desgn usng the prncpal cosnes. Jacobean for the robot was desgn by usng tool confguraton vectors and drect Jacobean. Some scrpt to desgn forward and nverse knematcs and also Jacobean matrx were provded usng Maple. A graphcal soluton for smulatng and calculatng the robot knematcs was mplemented n a vrtual nstrumentaton (VI) of LabVew. Usng the VI, forward knematcs for a four dof SCARA robot can be smulated. Inverse knematcs for the robot can also be calculated wth ths VI. 7. References [1] Jaydev P. Desa (2005). D-H Conventon, Robot and Automaton Handbook, CRC Press, USA, ISBN [2]Zomaya A.Y., Smtha H., Olarub S., Computng robot Jacobans on meshes wth multple buses, Mcroprocessors and Mcrosystems, no. 23, (1999), pp [3] Frank L.Lews, Darren M.Dawson, Chaouk T.Abdallah (2006), Robot Manpulators Control, Marcel Dekker, Inc., New York. [4] Bulent Ozkan, Kemal Ozgoren, Invald Jont Arrangements and Actuator Related Sngular Confguraton of a System of two Cooperatng SCARA Manpulator, Journal of Mechatroncs, Vol.11, (2001), pp [5] Taylan Das M., L. Canan Dulger, Mathematcal Modelng, Smulaton and Expermental Verfcaton of a SCARA Robot, Journal of Smulaton Modellng Practce and Theory, Vol.13, (2005), pp [6] Mete Kalyoncu, Mustafa Tnkr (2006), Mathematcal Modelng for Smulaton and Control of Nonlnear Vbraton of a Sngle Flexble Lnk, Procedngs of Intellgent Manufacturng Systems Symposum, Sakarya Unversty Turkey, May 29-31, [7] Mustafa Nl, Ugur Yuzgec, Murat Sonmez, Bekr Cakr (2006),, Fuzzy Neural Network Based Intellgent Controller for 3-DOF Robot Manpulator Procedngs of Intellgent Manufacturng Systems Symposum, Sakarya Unversty Turkey, May 29-31, [8] Rast Koker, Ceml Oz, Tark Cakar, Huseyn Ekz, A Study of Neural Network Based Inverse Knematcs Soluton for a Three-Jont Robot, Journal of Robotcs and Autonomous System, Vol.49, (2004), pp

19 38 Robot Arms [9] Adept, (1991), AdeptThree Robot: User s Gude, Adept Technology, USA. [10] Manjunath T.C., Ardl C., Development of a Jacobean Model for 4-Axes ndgenously developed SCARA System, Internatonal Journal of Computer and Informaton Scence and Engneerng, Vol. 1 No 3, (2007), pp [11] John Faber Archla Daz, Max Suell Dutra, Clauda Johana Daz (2007), Desgn and Constructon of a Manpulator Type Scara, Implementng a Control System, Proceedngs of COBEM, 19th Internatonal Congress of Mechancal Engneerng, November 5-9, 2007, Brasíla. [12] Rehara Adelhard Ben, Smt Wm (2010), Controller Desgn of a Modeled AdeptThree Robot Arm, Proceedngs of the 2010 Internatonal Conference on Modellng, Identfcaton and Control, Japan, July 17-19, 2010, pp [13] Rehara Adelhard Ben, System Identfcaton Soluton for Developng an AdeptThree Robot Arm Model, Journal of Selected Areas n Robotcs and Control, February Edton, (2011), pp. 1-5 avalable at

20 Robot Arms Edted by Prof. Satoru Goto ISBN Hard cover, 262 pages Publsher InTech Publshed onlne 09, June, 2011 Publshed n prnt edton June, 2011 Robot arms have been developng snce 1960's, and those are wdely used n ndustral factores such as weldng, pantng, assembly, transportaton, etc. Nowadays, the robot arms are ndspensable for automaton of factores. Moreover, applcatons of the robot arms are not lmted to the ndustral factory but expanded to lvng space or outer space. The robot arm s an ntegrated technology, and ts technologcal elements are actuators, sensors, mechansm, control and system, etc. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: Adelhard Ben Rehara (2011). Knematcs of AdeptThree Robot Arm, Robot Arms, Prof. Satoru Goto (Ed.), ISBN: , InTech, Avalable from: InTech Europe Unversty Campus STeP R Slavka Krautzeka 83/A Rjeka, Croata Phone: +385 (51) Fax: +385 (51) InTech Chna Unt 405, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, , Chna Phone: Fax: