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PHNG TRNH NG HC NGC ROBOT PUMABi ton ng hc ngc l rt kh, i vi tay my 6 khp c ba khp cuing quy ti mt im, ta c th tch bi ton ng hc ngc thnh hai bi tonn gin hn l ng hc ngc v tr v ng hc ngc hng + Tm v tr giao im cc trc c tay (tm c tay) + Tm hng ca c tay.Ta biu din thnh hai h phng trnh nh sau: Trong OvR l hng v v tr ca dng c, c biu din i vi h ta c nh bn ngoi (world coordinate system).Ta phi gii bi ton trn i vi ccn6 1, , q q .C cu 6 khp quay c 3 khp cui giao nhau c phng php gii nh sau:V tr ca tm c tay,PC xc nh qua v tr cng c (The given tool position) v phng ca Tool pointing(6Z).Do v tr ca tm c tay ph thuc vo 3 bin khp u tin.The relative wrist oriention 63R 6Ccbinkhp 4 5 6, , xcnhtmatrnnhhngctay(Thearm orientation) 30R v ma trn nh hng cng c (The given tool orientation) 06R.+ Ma trn trng thi (The given tool pose) 06T+ Solve porions ca ng hc ngc tm ra 03R1 2 3( , , ) v 36 4 5 6( , , ) R .+ nh v tr catm c taycOc ta cho trc nh sau:060. . 01CO O d R1 1 1 1 ]trong OvR l hng v v tr ca dng c, c biudin i vi h ta c nh bn ngoi (world coordinate system).cP as 6d(ct cui cng ca 06T) 6d(tool offset length)*6Z(3 ct ca ma trn 06T)+Thit lp cP=ct cui cngca03R1 2 3( , , ) tmraccbinkhp 1 2 3, , Tnh 13 0 06 3 6R R Rsau khi thay gi tr ca cc bin khp vo1 2 3, , vo 03R1 2 3( , , ) +So snh 36R v 36 4 5 6( , , ) R rt ra 4 5 6, , Ta ca im C trong h ta 6R:6rC = 006dt 1 1 1 1 1 1 ]Ta ca C trong h ta 0R:rC =ET.6rE =666.00 ..6110 0 0 1x py pz pn s a pa d xx x x xn s a pa d yy y y yda d zn s a pz z z z 1 1 1 + 1 1 1 1 1 +1 1 1 11 +1 1 1 1 1 11 ] ] ](*)Ma trn chuyn t h ta 03:7 0R3= A1.A2.A3 =23 3 23 2 2 1 23 23 2 2 1 23 23 2 2. ( . . ) .1 23 1 11. ( . . ) .1 1 23 11. .023 1 2301 0 0CS C C C a C aC S dSS S S S a C aC C dCS a S a S d C 1+ 1 1+ 1 1 + 1 1 ]Ta ca C trong 0R:rC =0R3.4rC =4 3 23 2 1 2 1 24 3 23 2 1 2 1 24 23 3 23 2 2 1. . . . . .1 23 1. . . . . .1 23 1. . .CS d a C C aC C S dS S d aS C a S C C dd C a S a S dt 1+ + 1 1+ + + 1 1 + 1 ](**)i chiu (*) v (**) ta c h 3 phng trnh 3 n :1 23 4 3 23 2 2 1 2 61 23 4 3 23 2 2 1 2 64 23 3 23 2 2 6 1( . . . ) . .( . . . ) . .. . . .p xp yp zC S d a C a C S d x a dSS d a C a C C d y a dd C a S a S z a d d+ + + + + Nhn (2) vi cos 1 tr i (1) nhn vi sin 1 :2 6 1 6 121 6 62 26 6( ) os ( )sincos tan 2( , )( ) ( )p y p xp x p yp y p xd y a d c x a ddAr A x a d y a dy a d x a d _ t + ,Nhn (2) vi sin1 cng vi (1) nhn vi cos1 v kt hp vi (3) ta c h 23 4 3 23 2 2 6 6 123 4 3 23 2 2 6 1. . . ( . ) sin ( . ) os. . . .p y p x xp z yS d a C a C y a d x a d c PC d a S a S z a d d P + + + Bnh phng 2 v cng li ta c:2 2 2 2 24 3 2 4 2 3 2 3 32 2 2 2 24 2 3 2 3 3 3 2 42 sin 2 os2 sin 2 os ( )x yx yd a a d a a a c P Pd a a a c P P a a d + + + + + + + + +2 2 2 2 23 2 43 4 2 2 32 22 4 3( )cos tan 2( , )2x yP P a a dArc A d a a aa d a _+ + + t + + ,Khai trin h phng trnh lin ktta c:83 3 2 3 4 2 3 4 3 3 23 4 3 3 2 2 3 4 3 3 2( . . ) ( . .sin ) sin( . . ) os ( . . os ) sinxya C a S d C C d a PC d a Sc a S d a c P + + + + + 2 23 3 2 3 4 3 4 3 33 3 2 3 4 3 4 3 34 3 3 3 2 4 3 3 3( . . ) ( . . )( . . ) ( . . )( . ) ( . )c x ys x ya C a S d C d a Sa C a S d P C d a S Pd C a S P a d S a CP 1 + + + ] 1 + + + ] 1 + + ]2tan 2( , )s cA 2 4 3 3 3 2 4 3 3 3 2 4 3 3 3 4 3 3 3tan 2 ( ) ( ) , ( ) ( )x y xA d C a S P a d S a CP a d S a CP d C a S 1 + + + + + ]Ta c 36R=4 5 6A A A=4 44 440 00 00 1 10 0 0 1C SS Cd1 1 1 1 1 ]5 55 50 00 00 1 0 00 0 0 1C SS C 1 1 1 1 1 ]6 66 660 00 00 0 10 0 0 1C SS Cd1 1 1 1 1 ]=Mt khc:1 2 3A A A4 5 6A A A =ET0 33 6.ER R T 3 0( 1)6 3.ER R T 1 23 1 23 23 1 23 1 23 23 1 23 1 23 23 141 1 1 1 1 1 241 23 1 23 23 1 23 1 23 23 1 23 1 23 23 340 0 0 1x y z x y z x y zx y x y x yx y z x y z x y zC C n S C n S n C C s S C s S s C C a S C a S a fS n C n S s C s S a C a fC S n S S n C n C S s S S s C s C S a S S a C a f+ + + 1 1 + + + 1 1 + + + 1 ] Ch cn quan tm ti phn nh hng tc l ma trn [3,3].So snh cc phn t ca 2 ma trn [3,3] :[ ]363, 3 R cos 5 23 1 1 23( )x y zS C a S a C a + 5 23 1 1 23cos ( )x y zArc S C a S a C a1 t + ]Nu sin50 9[ ][ ]36 4 5 1 11 14536 4 5 23 1 1 2323 1 1 23451 1 23 1 1 2345 52, 3 sin *sin * ** *sinsin1, 3 os *sin ( * * )( * * )ossin* * ( * * )tan 2( , )sin sinx yx yx y zx y zx y x y zR S a C aS a C aR c C C a S a S aC C a S a S acS a C a C C a S a S aA + + + + + + [ ][ ]36 6 5 1 23 1 23 231 23 1 23 236536 6 5 1 23 1 23 231 23 1 23 236523 1 1 23 23 1 1653, 2 sin *sinsinsin3,1 os *sinossin( ) ( )tan 2( ,sinx y zx y zx y zx y zx y z x yR C S s S S s C sC S s S S s C sR c C S n S S n C nC S n S S n C ncS C s S s C s S C n S n CA + ++ + + ++ + + + + + 235)sinznVy bi ton ng hc ngc cho ta kt qu nh sau: 21 6 62 26 6cos tan 2( , )( ) ( )p x p yp y p xdAr A x a d y a dy a d x a d _ t + ,2 4 3 3 3 2 4 3 3 3 2 4 3 3 3 4 3 3 3tan 2 ( ) ( ) , ( ) ( )x y xA d C a S P a d S a CP a d S a CP d C a S 1 + + + + + ]2 2 2 2 23 2 43 4 2 2 32 22 4 3( )cos tan 2( , )2x yP P a a dArc A d a a aa d a _+ + + t + + ,1 1 23 1 1 2345 5* * ( * * )tan 2( , )sin sinx y x y zS a C a C C a S a S aA + + 5 23 1 1 23cos ( )x y zArc S C a S a C a 1 t + ]23 1 1 23 23 1 1 2365 5( ) ( )tan 2( , )sin sinx y z x y zS C s S s C s S C n S n C nA + + + + 10V.THIT K M HNH ROBOT PUMA DNG SOLIDWORK.1. Nhim v ca robot. Gp mt vt nng khi lng di 1Kg di chuyn trong min lm vic2. Phn tch v la chn kt cu. 2.1 La chn bi, ln cho c cu.-Do tnh cht lm vic chu ti tng i nh (ti trng c khi lng di 1kg) ca Robot nn ta s chn ln cho cc khu nh sau:+ Khu 1: Dng bi mt dy c k hiu 305.+ Khu 2: Dng bi mt dy c k hiu 1000902.+ Khu 3: Dng bi mt dy c k hiu 1000901.+ Khu 4: Dng bi mt dy c k hiu 1000901.+ Khu 5: Dng bi mt dy c k hiu 1000099.2.2 La chn ng c cho Robot.Do yu cu iu khin chnh xc v tr im tc ng cui ca robot, ta chn ng c cho cc khp quay l loi ng c Servo. 11y l loi ng c cho php ta iu khin chnh xc c tc v v tr ca rotor. ng c tch hp mt mch encoder, phn hi trng thi v tr ca trc ra, da vo ta gim thiu c sai s do ti trng bn ngoi thay iDa vo yu cu lm vic ca robot, ta chn c ng c cho cc khp nh sau:Khp S hiu DC Khp S hiu1 T720-012 4 T406-0122 T511-012 5 T404-0123 T506-012 6 T402-011Kch thc v thng s k thut cc ng c nh sau:1213143. Thit k m hnh dng phn mm SolidWorksBn v chi tit phn thit k (2D v 3D) ca cc khu ca robot c km theo phn ph lc. Say y l mt s hnh nh m hnh 3D ca robot.15VI. M PHNG NG HC ROBOT PUMA DNG VISUAL C++ V OPENGLGiao din phn mm m phng c xy dng nh sau: 16Phnmm cxy dngbng visualC++. Phn ha clp trnh bng cc th vin OpenGL.Giao din chng trnh gm hai phn chnh. Khung bn phi cha cc nt lnh iu khin, v chn cc nhim v ca Robot cn thc hin. Khung bn phi dng th hin m hnh ca robot c dng m phng. M hnh robotc v bng phn mm SolidWork v xut ra file cad 3D di dng STL sau dng Visual C++ c cc file ny vo chng trnh. Sau dng cc hm OpenGL v cc m hnh ny. Phn ng hc thun v ngc trong chng trnh c tnh trong cc hm thnh vin SolveInverseKinematic v SolveForwardKinematic ca lp CSerialRobot.Cc hm ny nh sau: void CSerialRobot::SolveInverseKinematic(const CFrame& end ,float* jointVar){CVector nn =end.GetXDir ().GetDirection ();17CVector ss=end.GetYDir ().GetDirection ();CVector aa=end.GetZDir ().GetDirection ();//CVector aa =CrossProduct (nn,ss);CPoint3D pp =end.GetOrigin ();float nx=nn.GetX ();float ny=nn.GetY ();float nz=nn.GetZ ();float sx =ss.GetX ();float sy =ss.GetY ();float sz =ss.GetZ ();float ax =aa.GetX ();float ay =aa.GetY ();float az =aa.GetZ ();float px =pp.GetX ();float py=pp.GetY ();float pz=pp.GetZ ();//joint vars are contained herefloat tt1,tt2,tt3,tt4,tt5,tt6;//link and joint configuefloat a2=ROBOT_A2;float a3=ROBOT_A3;float d1 =ROBOT_D1;float d2=ROBOT_D2;float d4=ROBOT_D4;float d6=ROBOT_D6;// calculate theta 118float m =px -ax*d6;float n =py -ay*d6;tt1= acosf(d2/sqrt(m*m+n*n)) -atan2(m,n);float s1=sinf(tt1);float c1=cosf(tt1);float K1 = n*s1 + m * c1;float K2 = pz -az*d6 -d1;//calulate theta 3float p=K1*K1+K2*K2 -(a3*a3+a2*a2 +d4*d4);float q=2*a2*sqrt(d4*d4+a3*a3);tt3= acosf(p/q) + atan2(d4,a3);//check the criteriafloat c3=cosf(tt3);float s3=sinf(tt3);//calculate theta 2p=a3*c3 +a2 +s3 *d4;q=d4*c3-a3*s3;float delta =p*p +q*q;float deltac =p*K1 +q*K2;float deltas =q*K1 - p*K2;tt2= atan2(deltas,deltac);float s2=sinf(tt2);float c2=cosf(tt2);//calculate theta 5;19float s23 =sinf(tt2+tt3);float c23 =cosf(tt2+tt3);m=c1*ax+s1*ay;tt5 =acosf(s23*m- c23*az);float c5= cosf(tt5);float s5= sinf(tt5);//calculate theta4m=c1 *ax +s1*ay;n=-s1*ax +c1*ay;if(tt5!=0){tt4 =atan2(n/s5, (c23*m - s23*az)/s5);}else{tt4=0;}//calculate theta 6tt6 =atan2((s23*(c1*sx +s1*sy)+c23*sz)/s5,-(s23*(c1*nx +s1*ny)+c23*nz)/s5);tt1=r2d(tt1);tt2 =r2d(tt2);tt3 =r2d(tt3);tt4 =r2d(tt4);tt5 =r2d(tt5);20tt6 =r2d(tt6);jointVar[0] =tt1;jointVar[1] =tt2;jointVar[2] =tt3;jointVar[3] =tt4;jointVar[4] =tt5;jointVar[5] =tt6;MoveTo (tt1,tt2,tt3,tt4,tt5,tt6);}void CSerialRobot::SolveForwardKinematic(const float tt1,const float tt2,const float tt3,const float tt4,const float tt5,const float tt6,CFrame* frm){float c1 =cosf(d2r(tt1));float c2 =cosf(d2r(tt2));float c3 =cosf(d2r(tt3));float c4 =cosf(d2r(tt4));float c5 =cosf(d2r(tt5));float c6 =cosf(d2r(tt6));////float s1 =sinf(d2r(tt1));float s2 =sinf(d2r(tt2));float s3 =sinf(d2r(tt3));21float s4 =sinf(d2r(tt4));float s5 =sinf(d2r(tt5));float s6 =sinf(d2r(tt6));float d6=ROBOT_D6;float d4=ROBOT_D4;float d2=ROBOT_D2;float a3=ROBOT_A3;float a2=ROBOT_A2;float px=d6*(c5*(c1*c2*s3 + c1*c3*s2) - s5*(s1*s4 - c4*(c1*c2*c3 - c1*s2*s3))) - d2*s1 + d4*(c1*c2*s3 + c1*c3*s2) + a2*c1*c2 - a3*c1*s2*s3 + a3*c1*c2*c3;float py =c1*d2 + d6*(c5*(c2*s1*s3 + c3*s1*s2) + s5*(c1*s4 + c4*(c2*c3*s1 - s1*s2*s3))) + d4*(c2*s1*s3 + c3*s1*s2) + a2*c2*s1 - a3*s1*s2*s3 + a3*c2*c3*s1;float pz =d4*(c2*c3 - s2*s3) - a2*s2 + d6*(c5*(c2*c3 - s2*s3) - c4*s5*(c2*s3 + c3*s2)) - a3*c2*s3 - a3*c3*s2;frm->SetOrigin (CPoint3D(px,py,pz));}Mt s kt qu m phng:- im tc ng cui chy theo ng xon c: 22- Bin dng chy theo ng helixcal:23- M phng gp mt vt:2425KT LUN.Robot cng nghip l mt b phn rt quan trng trong nn sn xut hin i. N gp phn thay th sc lao ng ca con ngi, tng nng sut lao ng v to ra nhng sn phm ngy cng phc tp v p ng nhu cu ngy cng cao ca con ngi. Thng qua n ny, chng em phn no hiu r c tm quan trng . Vi ti tm hiu v robot Puma, mt loi robot cng nghip ph bin v in hnh, nhm phn tch, thit k v m phng c hot ng ca loi robot ny. Cc vn c bn c gii quyt nh tnh ton ng hc thun, ng hc ngc, thit k dng phn mm CAD, v m phng bng Visual C++ v OpenGL. Bn cnh , do thi gian gp rt, vn cn cc vn khc cn tip tc gii quyt. Chng em xin kin ng gp ca cc thy ti c hon thin hn. Mt ln na nhm xin chn thnh cm n s hng dn tn tnh ca thy Nguyn Tun Khoa v thy ng Bo Lm trong thi gian qua. 26PH LC27