Robotics Lab Manual

Vaishnavi Institute of Technology & Science, Bhopal DEPARTMENT OF MECHANICAL MECHANICA L ENGINEERING

LABORATORY MANUAL

SUBJECT: ROBOTICS [SUBJECT CODE: MMMD-207] LAB-II

CLASS: M.TECH (MACHINE DESIGN) YEAR: 20!-20"

APPRO#ED BY:

H.O.D. [M$%&] P'. ANIL #ISH*+ARMA

PREPARED BY: P'. BY: P'. ANIL +. RAO

PRINCIPAL D'. A.C.#ARSHNEY

Vaishnavi Institute of Technology & Science, Bhopal DEPARTMENT ! ME"#ANI"A$ EN%INEERIN%

$ist of Epe'i(ents !A")$T*+ P'of ANI$ - RA *EAR+ ./01203 ./01203

S)B4E"T+ RBTI"S "$ASS+ M.TECH (MACHINE

1. Demonstration of Cartesian/ cylindrical/ spherical robot. 2. Demonstration of Articulated/ SCARA robot. 3. Virtual modeling for inematic and dynamic !erification any one robotic .

structure using suitable soft"are.

#. Design$ modeling and analysis of t"o different types of grippers. %. Study of sensor integration. &. '"o program for linear and non(linear path. ). Study of robotic system design. *. Setting robot for any one industrial application after industrial !isit.

DESIGN)

ROBOTICS , LABORATORY MANUAL

E5PERIMENT N 0 TIT$E+ DEMNSTRATIN ! "ARTESIAN6"*$INDRI"A$6SP#ERI"A$ RBT 78ective+ 'o study basic robot co(ordinate configurations. P'ela7+ 1. +a!e you seen cartesian/cylindrical/spherical configuration robot, 2. -i!e any practical eample of each of them. Int'o9uction+ ndustrial Robots Definition

A robot is a programmable arm simulator. 0A robot is a re(programmable$ multifunction manipulator designed to mo!e material$ parts$ tools$ or special de!ices through !ariable programmed motions for the performance of a !ariety of tass

"a'tesian "o2'9inate Ro7ot+

'he Cartesian co(ordinate robot is one that consists of a column and an arm. t is sometimes called an (y( robot$ indicating the aes of motion. 'he (ais is lateral motion$ the y(ais is longitudinal motion$ and the (ais is !ertical motion. 'hus$ the arm can mo!e up and do"n on the (ais the arm can slide along its base on the ( ais and then it can telescope to mo!e to and from the "or area on the y(ais. 'he Cartesian co(ordinate robot "as de!eloped mainly for arc "elding$ but it is also suited for many other assembly operations. Robots "ith Cartesian configurations consists of lins connected by linear 4oints 567. -antry robots are Cartesian robots 56667. A robot "ith 3 prismatic 4oints 8 the aes consistent "ith a Cartesian coordinate system. Commonly used for9    

:ic and place "or Assembly operations +andling machine tools Arc "elding

DEPARTMENT OF MECHANICAL ENGINEERING


;igure 19 Cartesian robot "ith its rectangular "orspace

Ad!antages9   

Ability to do straight line insertions into furnaces.
Disad!antages9  

 

Re>uires large operating !olume. <posed guiding surfaces re>uire co!ering en!ironments. Can only reach front of itself Aes hard to seal

in corrosi!e or dusty

"ylin9'ical "o2'9inate Ro7ot

'he cylindrical co(ordinate robot is a !ariation of the Cartesian robot. 'his robot consists of a base and a column$ but the column is able to rotate. t also carries an etending arm that can mo!e up and do"n on the column to pro!ide more freedom of mo!ement. 'he cylindrical co(ordinate robot is designed for handling machine tools and assembly.



Robots "ith cylindrical configuration ha!e one rotary 5 R7 4oint at the base and linear 567 4oints succeeded to connect the lins. A robot "ith 2 prismatic 4oints and a rotary 4oint 8 the aes consistent "ith a cylindrical coordinate system. Commonly used for9    

+andling at die(casting machines Assembly operations +andling machine tools Spot "elding

;igure 29 Cylindrical robot "ith its cylindrical "orspace

Ad!antages9     

Can reach all around itself Rotational ais easy to seal Relati!ely easy programming Rigid enough to handle hea!y loads through large "oring space -ood access into ca!ities and machine openings

Disad!antages9  

Can?t reach abo!e itself 6inear aes is hard to seal



 

@ont reach around obstacles <posed dri!es are difficult to co!er from dust and li>uids

Sphe'ical "o2'9inate Ro7ot

'he polar co(ordinate$ or spherical co(ordinate robot consists of a rotary base$ an ele!ation pi!ot$ and a telescoping etend(and(retract boom ais. 'hese robots operate according to spherical co(ordinates and offer greater fleibility. 'hey are used particularly in spot "elding. :olar robots ha!e a "or space of sphe'ical shape. -enerally$ the arm is connected to the base "ith a t"isting 5'7 4oint and rotatory 5R7 and linear 567 4oints follo". A robot "ith 1 prismatic 4oint and 2 rotary 4oints 8 the aes consistent "ith a polar coordinate system. Commonly used for9   

+andling at die casting or fettling machines +andling machine tools Arc/spot "elding

;igure 39 Spherical robot "ith its Spherical/:olar "orspace



Ad!antages9  

6arge "oring en!elope. '"o rotary dri!es are easily sealed against li>uids/dust.

Disad!antages9   

Comple coordinates more difficult to !isualie$ control$ and program. <posed linear dri!e. 6o" accuracy.

"onclusion+ 2 'he three basic robot configurations based on co(ordinate system is studied in details. 'his "ill help you in deciding the "orspace area of robot for a particular operation/tas and to choose correct type of co(ordinate configuration of robot for design. Postla7+ 1. Decide suitable robot co(ordinate configuration any seen or unseen application. 2. @hy do you prefer only that particular robot co(ordinate configuration,



E5PERIMENT N . TIT$E+ DEMNSTRATIN ! ARTI")$ATED6S"ARA RBT 78ective+ 'o study different robot configurations. P'ela7+ 1. +a!e you seen Articulated/SCARA configuration robot, 2. -i!e any practical eample of each of them. Int'o9uction+ ndustrial Robots Definition

A robot is a programmable arm simulator. 0A robot is a re(programmable$ multifunction manipulator designed to mo!e material$ parts$ tools$ or special de!ices through !ariable programmed motions for the performance of a !ariety of tass

A'ticulate9 Ro7ot+

'hose "ith the designation 'RR are also called articulated robots. An articulated robot more closely resembles the human arm. 'he 4ointed(arm is a combination of cylindrical and articulated configurations. 'he arm of the robot is connected to the base "ith a t"isting 4oint. 'he lins in the arm are connected by rotary 4oints. =any commercially a!ailable robots ha!e this configuration. A robot "ith at least 3 rotary 4oints. Commonly used for9     

Assembly operations @elding @eld sealing Spray painting +andling at die casting or fettling machines



;igure 19 Articulated robot

Ad!antages9   

All rotary 4oints allo"s for maimum fleibility Any point in total !olume can be reached. All 4oints can be sealed from the en!ironment.

Disad!antages9   

<tremely difficult to !isualie$ control$ and program. Restricted !olume co!erage. 6o" accuracy

S"ARA Ro7ot+

'he SCARA 5Selecti!e Compliance Assembly Robot Arm7 is a cylindrical type$ "hose reach is obtained by using a re!olute$ instead of a prismatic 4oint. SCARA robot is suitable for assembly operation and is therefore etensi!ely used in se!eral industries for this purpose. A robot "ith at least 2 parallel rotary 4oints.



Commonly used for9  

:ic and place "or Assembly operations

;igure 29 SCARA robot "ith its "orspace

Ad!antages9    

+igh speed. +eight ais is rigid 6arge "or area for floor space =oderately easy to program.



Disad!antages9    

6imited applications. 2 "ays to reach point Difficult to program off(line +ighly comple arm

"onclusion+ 2 'hese t"o configurations apart from three basic robot configurations based on co(ordinate system are for the ad!anced usages. 'his "ill help you in deciding the "orspace area of robot for a particular operation/tas and to choose correct type of co(ordinate configuration of robot for design. Postla7+ 1. Decide suitable robot co(ordinate configuration any seen or unseen application. 2. @hy do you prefer only that particular robot co(ordinate configuration,



E5PERIMENT N 1 TIT$E+ VERT)A$ MDE$IN% !R -INEMATI" AND D*NAMI" VERI!I"ATIN AN* NE RBTI" STR)"T)RE )SIN% S)ITAB$E S!T:ARE 78ective+ 'o !erify the in!erse inematic and in!erse dynamic modeling of one(lin arm or t"o(lin arm as robotic structure using =A'6AB. P'ela7+ 1. Do the in!erse inematic and dynamic !irtual modelings for one or t"o(lin arm robot/manipulator. 2. +o" much did you cope "ith =A'6AB, Int'o9uction+ 'o !erify the in!erse inematic and in!erse dynamic modeling of one the simple robotic structure =A'6AB program is "ritten. =A'6AB programming is one of the best "ays to !erify the problems.

;igure 19 inematics of three(lin planer arm :rog.17 Referring abo!e ;ig.1$ the input homogeneous matri$ ' is gi!en as 1/2$( E3/2$F$ E3G%/2 E3/2$1/2$F$ E3/2G1F$F$1$FF$F$F$1H "here IJ&FK$ and the non(ero constant D+ parameters from table a1Ja2J2 units$ and a3J1 unit. C2JF.*&& and



s2JF.%$ "hich yields L2J3FK. S1JF and c1J1. Value of 4oint angle L1 is obtained as L1JFK. ;inally$ L3J3FK. 'able9 D+ parameters of the three(lin arm $in; 7i
F F

M2 M3

a2 a3

F F

M is Noint Variable. n order to sol!e abo!e eample$ a =A'6AB program is "ritten$ as sho"n belo"$ "hich can be stored in a file that can be run to yield the abo!e results. O :rogram for in!erse inematics of 3(lin arm O Pon(ero constant D+ parameters. a1J2a2J2a3J1 Onput :hiJpi/3pJ2.%Gs>rt537pyJ1Gs>rt537/2 Ontermediate Calculations "Jp(a3Qcos5phi7 "yJpy(a3Qsin5phi7 delJ"Q"G"yQ"y OCalculations for theta2 c2J5del(a1Qa1(a2Qa27/52Qa1Qa27 s2Js>rt51(c2Qc27 th21Jatan25s2$c27 th22Jatan25(s2$c27 OCalculation for finding theta1 s11J55a1Ga2Qcos5th2177Q"y(a2Qs2Q"7/del c11J55a1Ga2Qcos5th2177Q"(a2Qs2Q"y7/del s12J55a1Ga2Qcos5th2277 Q"yGa2Qs2Q"7/del c12J55a1Ga2Qcos5th2277 Q"Ga2Qs2Q"y7/del th11Jatan25s11$c117 th12Jatan25s12$c127 OCalculation for theta3 th31Jphi(th11(th21 th32Jphi(th12(th22 OAngles in degree r2dJ1*F/pi DEPARTMENT OF MECHANICAL ENGINEERING


th11dJth11Qr2d$ th12dJth12Qr2d$ th21dJth21Qr2d$ th22dJth22Qr2d$ th31dJth31Qr2d$ th32dJth32Qr2d$ P'og.> ;or the t"o(lin manipulator as sho"n in figure 2$ consider a1Ja2J1$ and the 4oint angle !ariations for both 4oints$ L1 and L2$ are taen being the same as per e>uations ecept that their end conditions are different$ i.e. L15'7Jpi and L25'7Jpi/2. sing the =A'6AB program sho"n belo"$ the 4oint angle and tor>ue plots can be obtained.

;igure 29 A t"o(lin robot arm O n!erse dynamics for '"o(6in =anipulator O nput for tra4ectory and lin parameters 'J1F th1'Jpi th1FJF th2'Jpi/2 th2FJF m1J1 a1J1 m2J1 a1J1 a2J1  gJT.*1 con J 2Qpi/' delth1Jth1'(th1F delth2Jth2'(th2F iner21Jm2Qa1Qa2 for iJ19%1$ ti5i7J5i(17Q'/%F angJconQti5i7 ONoint tra4ectory th15i7Jth1FG5delth1/'7Q5ti5i7(sin5ang7/con7 th1d5i7Jdelth1Q51(cos5ang77/' th1dd5i7Jdelth1QconQsin5ang7/' th25i7J th2FG5delth2/'7Q5ti5i7(sin5ang7/con7



th2d5i7J delth2Q51(cos5ang77/' th2dd5i7Jdelth2QconQsin5ang7/' thddJth1dd5i7$ th2dd5i7H Onertia matri sth2Jsin5th25i77 cth2Jcos5th25i77 i22Jm2Qa2Qa2/3 i21Ji22Giner21Qcth2/2 i12Ji21 i11Ji22Gm1Qa1Qa1/3Gm2Qa1Qa1Giner21Qcth2 imJi11$i12$i21$i22H Oh(!ector h1J(5m2Qa1Qa2Qth1d5i7Giner21/2Qth2d5i77Qth2d5i7Qsth2 h2Jiner21/2Qsth2Qth1d5i7Qth1d5i7 h!Jh1$h2H Ogamma(!ector cth1Jcos5th15i77 cth12Jcos5th15i7Gth25i77 gam1Jm1QgQa1/2Qcth1Gm2QgQ5a1Qcth1Ga2/2Qcth127 gam2Jm1QgQa2/2Qcth12 g!Jgam1$gam2H ONoint tor>ue tauJimQthddGh!Gg! tor15i7Jtau5i7 tor25i7Jtau527 end plot5ti$th1$(U$ti$th2$97 figure plot5ti$tor1$($ti.tor2$97 "onclusion+ 2 ne of the critical modeling as in!erse inematics and dynamics of one or t"o(lin arm manipulator is can be !erified "ith ease using =A'6AB soft"are. t taes less time to !erify and gi!es better understanding too. Refe'ences+2 0ntroduction to Robotics by S.. Saha('ata =c-ra" +ill nc.

Postla7+ 1. Are you able to do it for more number of lins, 2. =odel some more structure and then !erify it using =A'6AB.



E5PERIMENT N ? TIT$E+ DESI%N, MDE$IN% AND ANA$*SIS ! T: DI!!ERENT T*PES ! %RIPPERS 78ective+ 'o design and !erify by modeling and analysis of t"o different robotic grippers. P'ela7+ 1. @hat are the different types of grippers, 2. Re!ie" of modeling and analysis of 3 D parts. Int'o9uction+ 'he design of the end(of(arm tooling for a robotic assembly system is !ery important for reducing errors and decreasing cycle times. 'his is the piece of the robotic parts handler or assembler that physically interacts "ith the en !ironment. @hile many factors may be blamed for the common failures of "orcells$ the culprit is !ery often the grippers. @ell designed grippers can increase throughput$ impro!e system reliability$ compensate for robot inaccuracy$ and perform !alue added functions to the assembly. Design+2 n order to design robot "e need to consider the gripping force of the robot end(effectors to grip the ob4ect "ithout slippage.

=odel 19 A simple pi!ot(type gripper is used to hold boes as sho"n follo"ing figure. 'he gripping force$ ;g re>uired is 2F gf. 'he gripper is to be actuated by a piston de!ice to apply an actuating force$ ;a. 'he corresponding le!er arms for the t"o forces are sho"n in the figure. 'aing moments of the forces on one arm and summing them to ero$ "e get$ ;g lg J ;a la r$ ;a J ;g lg lg J 2F  2F J *F gf. %



;igure9 :i!ot type gripper 'herefore$ the piston de!ice "ould ha!e to pro!ide an actuating force of *F gf to close the gripper "ith a force against the boes of 2F gf. =odel 29 A bloc of "eight ha!ing 1#FF P is to be gripped as sho"n in figure. ;ind the clamping force assuming a safety factor 2. Assume coefficient of friction J F.2. 'he centre of gripping does not coincide "ith the centre of gra!ity.

;igure9 gripper for clamping force Assuming acceleration a up"ard$ Resol!ing !ertical forces 1#FF G 2 ;2 J 2 ;1 8 5@a/g7 Resol!ing moments about :$ %F ;2 J 51#FF  2%F7/2



r$ ;2 J 51#FF  2%F7/5%F  27 J 3%FF P. 'herefore$ ;1 J %&FF P assuming a J 2gH Clamping force J 5;1 G ;27  safety factor / J 5T1FF  27 / F.2 P J T1FFF P 'his is greater than the !alue for gripping at the C.-. f the bloc is to be lifted by holding it at the C.-. of the bloc$ the gripping force "ill be less. Mo9eling+2 =odeling of different robot grippers is done using suitable modeling soft"are lie Solid
;igure 19 -ripper Approaching :art from Side Analysis+2 =odeled robotic gripper is analyed for the regions "here the maimum stresses are generated. 'he region of ma stresses is to be considered as a region of probability of failure. 'he crac propagation may from the same location "here there is maimum stresses and hence chances of failure. 'his failure region can be detected/analyed through the analysis soft"are lie APSWS or ABAXS "onclusion+ 2 '"o different types of grippers are designed and modeled using CAD soft"are. ;urther it is analye for maimum stresses using Analysis soft"are 5APSWS7. Postla7+ 1. Design grippers considering its types i.e.


E5PERIMENT N 3 TIT$E+ ST)D* ! SENSR INTE%RATIN 78ective+ 'o study the theory of sensory integration. P'ela7+ 1. @hat do you no" about Sensory ntegration 5S7, 2. @hat are the application areas of S, Int'o9uction+ @e "ould lie to tal about 0@hat is Sensory ntegration, Although this seems lie an ob!ious >uestion$ it is important to define "hat is and "hat is not sensory integration as many research studies purport to use S$ yet the modifications of treatment are so substantial as to mae one >uestion "hether the procedures truly are sensory integrati!e.

Characteristics of Sensory ntegration :rocedures9        



acti!e participation child directed indi!idualied treatment purposeful acti!ity need for adapti!e response3 input !aries based on childs response acti!ity rich in propriocepti!e$ !estibular and tactile input implied or stated goal of impro!ing processing and organiation of sensation 5not the teaching of specific sills7 administered by a trained therapist 5' or :'7

'hus$ studies "hich in!ol!e pure sensory stimulation such as that of controlled$ systematically applied !estibular stimulation 5e.g.$ the "or of antner7 should not be grouped "ith those of sensory integration. Similarly$ perceptual motor programs "hich tend to be preplanned$ therapist directed$ structured programs should be considered separately. 'he distinction is not al"ays clear(cut since some studies combine sensory integration and perceptual motor procedures. ;or eample$ +uff and +arris in their study "ith 3# mentally retarded adults utilied sensory integration acti!ities but in a specified se>uence. n their study$ each treatment session "as di!ided into four areas9 CPS normaliation 5ecitation or inhibition7$



sensory stimulation$ refle inhibition and gross motor acti!ity$ and !isual motor acti!ity. 'hus$ treatment "as substantially more structured than in sensory integration$ and "as therapist directed rather than therapist guided.
Are Sensory ntegration :rocedures
@hy and +o" Does Sensory ntegration @or , @e "ould net lie to discuss the issue of "hy and ho" sensory integration procedures are effecti!e. n sensory integration theory$ "e hypothesie that "e are



influencing brain organiation and brain change. 'he idea that the neural organiation is actually changing or de!eloping as a result of the sensory input/adapti!e response is contro!ersial. Brain change in humans is nonobser!able and thus$ it is !ery difficult to establish support for it. n demonstrating the effecti!eness of sensory integration$ "e are primarily limited to obser!able beha!iors. Brain change can be inferred only from indirect obser!able !ariables$ such as change in a childs performance it cannot be easily directly obser!ed ecept$ perhaps$ through autopsy. 'here is some possible support for the effect of sensory integration therapy on change in the ner!ous system. n a study by a"ar$ findings suggested that sensory integration therapy positi!ely influenced hemispheric specialiation as measured by a dichotic listening tas in a sample of children "ith learning disabilities. ttenbacher demonstrated change in postrotary nystagmus$ as measured by the Southern California :ostrotary Pystagmus 'est 5SC:P'7$ "ith multiple measurements of 3 children o!er a 2F("ee treatment period. +o"e!er$ as ttenbacher noted$ many factors contribute to postrotary nystagmus 5:RP7 as tested " ith the SC:P'$ thus it is not clear "hether or not the :RP change "as due to change in central ner!ous system physiology or to other factors.

;actors nfluencing the ualities of the patient or client$ for eample the childs age$ the diagnosis the degree of responsi!eness to certain inds of sensory input. ;or eample$ learning disabled children "ho sho" a shortened duration of postrotary nystagmus appear to impro!e to a greater degree from S treatment than those children "ho do not sho" this type of dysfunction. ;ollo"ing are some of the !ariables "hich may influence a childs response to therapy. 'hese can be categoried as treatment !ariables$ patient !ariables$ and therapist !ariables.

Variables @hich =ay nfluence Response to 'herapy9 

 

'reatment !ariables9 se>uence of inds of sensory input therapist induced !s. child induced stimulation :atient !ariables9 age$ se$ diagnosis$ se!erity 'herapist !ariables9 se$ personality$ epectations



Variables "hich influence the response to therapy can be eamined in a number of "ays917 through obser!ation of treatment$ 27 through theory$ and 37 through controlled testing. 6et us tae the eample using the !ariable of the childs age. 'hrough "oring "ith children of a !ariety of ages$ "e may clinically obser!e through treatment that children that mae the most rapid gains in therapy are children "ho ha!e not yet entered school$ thus primarily children under &. @e may dra" upon theories of brain plasticity "hich "ould indicate that the younger the child$ the more plastic the brain$ and since "e feel "e are influencing brain function$ "e may hypothesie that S "ould be most effecti!e "ith younger children. ;inally$ "e may carry out controlled testing specifically to eamine age effects$ or$ "e may re!ie" the literature$ in a meta(analysis$ and eamine the effect of age on outcome. "onclusion+ 2 +ere the Sensory ntegration 5S7 therapy is studied "hich is !ery important and effecti!e for the treatments. 'his concept is still a field of de!elopment and hence need to be "ell researched. Refe'ence+2 Sharon A. Cerma$ 0'he


E5PERIMENT N @ TIT$E+ T PR%RAM !R $INEAR AND NN2$INEAR PAT# 78ective+ 'o study the VA6 language programming for linear and non(linear path. P'ela7+ 1. @hat are different robot languages, 2. @hat are the different tra4ectory paths possible of robot manipulator, Int'o9uction+ VA$ $anguage+ VA6 is a popular tetual robot language de!eloped by nimation nc. for the :=A series of robots. VA6 has been upgraded to VA6  system "ith more interlocing facilities. Victor Sheinman de!eloped VA6 language. VA6 is !ery user( friendly. t pro!ides arm mo!ement in 4oint$ "orld and tool coordinates$ gripping and speed control. @A' and S-PA6 commands can be gi!en to implement a specific tas. 'he commands are subroutines "ritten in BASC and translated "ith the aid of an interpreter. Compiled BASC has more fleibility.

;ollo"ing are the t"o programs "hich are "ritten for specific tass and they are "ith linear and non(linear paths of manipulator. Depalletiing+ n a pallet ob4ects protruding #F mm from the face of the pallet are located in a number of ro"s and columns. 'he pallet has 3 ro"s that are 3F mm apart and # columns that are %F mm apart. 'he plane of the pallet is assumed to be parallel to the Y(W plane. 'he ro"s are parallel to Y(ais and the columns are parallel to W(ais. 'he ob4ects are to be piced up one after another from the pallet and placed in a location of sliding channel 5chute7. ;igure 1 indicates the pallet.

:R-RA= D<:A66<' 1 R<=AR :R-RA= ' :C BN


1F

S<' :C J CRP

 

The el9 t'a8ecto'y+ A "eldment is to be made as sho"n in figure 2. 'he "eld tra4ectory is a continuous path arc "elding along the paths Y2(Y3 "ith triangular "ea!ing$ Y3(Y# "ith straight "eld$ Y#(Y%(Y& "ith circular interpolation$ Y&(Y) "ith straight "eld$ Y)(Y*(YT "ith circular arc$ YT(Y1F "ith straight "eld and Y1F(Y11 "ith fi!e point "ea!ing. 'he "eld torch begins its mo!ement from home position Y1 and departs to location Y12. Craterfilling is done at the end of trapeoidal "ea!ing. @rite a VA6 program for suitable arc "elding.



;igure 19 Depalletiing



:R:-RA= @<6D CRV< 1 @S<' 1 J 1F$ #F$ %F 2 @S<' 2 J *$ 3%$ &F 3 @S<' 3 J 12$ #F$ %% # @VS<' 1 J %$ % % @VS<' 2 J 1F$ )$ 2$ F$ 1$ 2$ F & =V< Y1 ) =V< Y2 * @S'AR' 1$1 T =V< Y3 1F @




13 1# 1% 1& 1) 1* 1T 2F 21 22
CRC6< Y#$ Y%$ Y& =V
;igure 29 'he "eld tra4ectory "onclusion+ 2 ne of the Robot :rogramming 6anguages 5R:67 i.e. VA6 language is used for linear and non(linear paths and "hich is collecti!ely$ found easier "ay of programming. Refe'ence+2 0RB'CS '

Robotics Lab Manual

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