D$ng Anh Tudn v^ Dtg T9P chi KHOA HOC & CONG NGHE 176(16): 71 -75
TINH TOAN THIET KE ROBOT LEO DAY SU* DUNG CO CAU BON KHAU BAN LE
D^ng Anh Tu^n, Duong Pham Tu6ng Minh
Trudng Dgi hoc Ky thugt Cong nghiep — DH Thdi Nguyen T O M T A TBai bao de xuat phuang phap tinh loan va phan tich dgng hgc cho robot di chuyen tren day SJJ dung CO ciu bfin khSu ban 16. B5ng phuang phap giai t(ch, mo hinh dong hgc cua robot dugc dua vko khao sat cdc thong s6 nhu do nghiSng thdn, vjin toe di chuyin trung binh, vj Ui vk quj dao ch§n ciia robot. Dya v^o kit qua da tinh toan, cac thong s6 kich thuac phii hgp dugc dua nhSm dam bao kha nSng di chuyin on djnh vk can bang ca cau. Cfing suat can thiet cho dgng ca cOng dugc xac dinh sii dung phuang phap dl chuyin kha di dam bao dieu kien di chuyen deu ciia robot.
K€t qua tinh toan ung dung thiet ke mo hlnh thuc de danh gia kha nang lam viec.
TCi' kh6a:C(7cdj( bdn khdu; phuang phdp gidi tich, dgng hoc; dgng luc hgc; Matlab GlOl THIEU
Co cau ban khau la mot trong nhOng co cau nguyen ly may dau tien duo'c thiet ke va si>
dung. Do ket cau dem gian va tinh chat chuyen dong da dgng, ta co the tim thay hinh anh cua cac co cau b6n khau trong hau het cac ITnh vuc trong cupc song, ke ca trong sinh hpc (cu the la cac chuyen dgng phong sinh hgc) hay cac ket cau kJ thuat [1]). Co cau bon khau ban le dug-c iing dung rong rai trong thiet ke cac bo phan may, bien chuyen dgng ciia quay khau dan thanh cac chuyen dpng phuc tap cua khau dau ra (Hinh 1).
4 khdu bdn li Mpt s6 hiln the cua co cau bon khau ban le dupe phan tich, nghien cuu va dugc xem nhu la cac mo hlnh co sa dl xay dung nen cac bp phan may sii dung ph6 biin trong cupc song (bp ph|in giam chan banh xe tau hoa, khung xe d^p, dau nghiln da, tay kep robot...[3]).
Mpt so CQ c3u robot di chuyen tren nen phang duac 6k xu5t va thiit kl chay thu nhu co cau Jansen, Klann,... da dupe nghien cuu vl dong hpc [4], hay ca cau Jansen da dirpc phan tich
danh gia cac thfing sfi de dira ra nhgn xet ve chuyen dpng, ma sat voi nen de xac djnh cfing suat dfing ca... [5] tren ca so cac co cau nay, Amanda Ghassaei de xuat ket cau va che tao thir nghiem co cau di chuyen mai va so sanh mfi hinh thu dugc vcfi mo hinh Theo Jansen v6 kich thuac mo hlnh, quy dao chuyin dpng chan, vj tri khoi tam cac khau [6] ... Nhii'ng co cau nay deu co dac diem chung la trong mpt khoang chu ky chuyen dgng ciia khau dan, quy dao cua mpt diem tren co cau thuc hien chuyin dpng chay ngang dong vai tro diem ty tren mat dat de ca co cau di chuyen ve phia truoc (Hinh 2).
Tel. 0985 059022. Email: anhtuan679@gmail ci
Hinh 2. Cdc dgng ca cdu di chuyen (tir trdi sang phdi). Ca cdu Jansen; Ca cdu Klann;
Ca cdu Ghassaei
Co cau di chuyen dang treo ngupc co quj dao
ctia diem chan va phan than nam ve hai phia
khac nhau cua phan chuyen dfing thang, cho
phep CO cau co the chuyen dpng khi treo
ngugc nha cic chan bam tua tren mpt thanh
hogc dSy treo co dinh. Dii chuyen dpng khong
diJng banh xe nhung ca cauco the di chuyen
nhe nhang va cho phep treo tai vol khoi lugng
71
Duong Pham Tuong Minli va Dig Tap chi KHOA HOC & CONu N u n c , Ion. Co kha nhilu mfl hinh thiet ke dya theo
nguyen ly chuyen dong c o cau dang nay, nhung chua co nghien ciJu nao tap trung vao qua trinh tinh toan cu the cho cac truang hgp chiu tai cdng n h u danh gia dp fin dinh trong qua trinh leo day ciia c a cau.
PHAN TICH D O N G HOC C O CAU Tren c o so mo hinh c o cau dupe de xuat nhu Hinh 3, qua trinh phan tich dpng hpc c a cdu voi cac gia trj dau vao la kich thuoc cac khau dugc thuc hien voi cac npi dung gfim: Phan tich vi tri c o cau xac dinh cac thong so dpng hoc CO can (van tflc, gia toe...):
a ) f ^ ^ _ 5 ! i ^ ^ , j / ^ _^ _ ^ b)
Hinh 3. Ket cdu robot treo dang 2D (a) .3D (b) vd luge dd ca cdu (c)
Xay dung phuong trinh chufli dpng cho nhanh truac (nhom khau I' 2, 3 , 4) va sir dung phuong phap sfl phuc de b i i n dfli ve he phuang trinh: l^-i- 1^+ 1^^ = 1^
O l e J i ' + L e J ' " - H | „ e ^ ' " = Le"" (1) i l^sinq^- l3|Sinq3= I, sinq,-!-l^sinq^
il4COsq4- IjiCOsq,^ liCosq,-!- IjCOsq^
Trong do, I, la vector xac djnh khau va 9|la goc tao boi I, voi chieu duong true x.
Giai he phuong trinh (2) ta xac dinh dugc g i i tri 83, 64 theo goc quay cua khau dan 62.
Tiep tuc tinh toan cho nhom c o cau bon kliau 7, 2, 5, 6 va ap dung cflng thiic Euleur de biin dfii ve he phuong trinh: I7 + I3 + I5, = 1^
» l^e^"' + 1^6^"' + lj,e"'> = l,e"" (3)
I L s i n q 5 - l 5 , s i n q 5 = l^sinq,-!- l^sinq^
<=>i (4) i lg cos q^ -15, cos qs = 1, cos q, + 1^ cos q^
Tiep tuc giai he p h u a n g trinh nay ta xac dinh d u g c gia tri 85, % theo goc khau dan 9?.
Vai CO cSu d u p e khao sat co Ii=l7=30; l2=10;
I3i=l5i=l32=l52=l4=l6=40 va 81=67=0°, ta thu dugc do thi bien doi ciia van toe goc cac khau (o>3,(D4,co5,a)6), gia tri ciia cac thong so nay ti le thuan voi van tflc goc khau dan (ra2), va ta CO t h i bilu dien do thi bien doi ti sfl truyen ik2=C0k/(B2 dugc mfl ta nhu Hinh 4.
Hlnh 4, Dd thi thay doi ti sd truyen (1/^2) g^^^ cde khdu 0)1, vd 0)2 theo gdc quay cua khdu ddn 62 Vi tri cac diem C (ben trai) va E (bSn phai) dugc xac dinh theo cac vector thanh phan:
R ^ - i ^ + i ^ + i ^ , R l = i l + i ^ + l ^ vai quy dao chuyen dflng dugc mfl ta trong Hinh 5.
Hinh 5, Quy dao cdc diim C (trdi) vd E (phai)
Hinh 6. Tung dd cdc chan vd quy dgo di chuyen theo phuang y cua ca cdu Bai toan ve chuyen dpng cua c a c i u Uen quan den trang thai di c h u y i n cua c o c i u tai thcri diem cac chan (cu t h i la 2 chan truoc va 2 chan sau ciia c a cau) ty len day treo, trong do vi tri tyday moi phia d u g c x a c dmh theo moi quan he: y,n,„,= min(yctri,; ycpi,a,) va y,,^= min
Dang Anh Tuan va Dig Tap chi KHOA HQC & CONG NGHE 176(16): 71-75 (yEtrai ; yEphai)- Tu do, dp nhSp nho cua than
robot (quy dao di chuyen phuang y) dugc xac dinh theo Hinh 6.
Ket qua thu dugc tren d6 thj tuong ung vai cac goc khau din 82 la 91° va 271° (lech pha 180°). Dua vao ket qua tren d6 thi va kilm nghiem chuyen dpng mo hinh, ta co bang tong hgp cac thai diem lam viec ciia mfii chan:
Bang 1.
62 Chan truoc
Chan sau Sd chan tyday
Trang thai ly ddy ciia cdc chdn 0°-i-9P 91°+271° 271'>^360°
tphai Mrai lipliai
2 2 2
Khi CO cau di chuyen lufin chi co 2 chan tiep xuc vai day. Can cu vi tri ciia cac chan, dfl nghieng ciia than dugc xac djnh va mfl ta theo goc lech dang bieu thuc: tan9 - Ay/Ax (vai
4y^\y<ruac-yi.aii\ v a Ax^\x,r„^-X^au\)- K i t qUakhao sat cho thay cp nam trong khoang gia tri [-0,0014°; 0,0014°] anh huang khfing dang kl den chuyen dfing cua toan ca cau.
Dao ham cac phuang trinh (1) va (3), ta dugc phuang trinh van tfic:
l,(>},e^'''~'' +l,,0,e^"'^^ ^l^to^e^^'"'^ (5) f/jOj sin ^j„ +/3,fi'3 sin^3„ = 1^0)^ sin 8^^
[/jOjj cos 5j^ + /jiOj cos^3„ = /,fflj cos 9^
,,,./--^K,,J-'^^-iJ'-'^ ("
(6)
j/jOjj sin 5,„ + /jjO, sin &;„ = l^m^ sin 6^.,
[/jO, C0s5j„ + /i|(M5 C0S6;^ = IftO^ COS^j^ (8)
Vo'i ^Ar = ^- +"7 la phuang ciia cua vector van toe vacoj la van toe goc khau tirang ung.
Giai cac he (6) va (8) xac djnh dugc van tfic goc cac khSu 3, 4, 5, 6. Khi do, van tfic cac dilm C va E tuong ung se la:
1 Vc. = l;'"; sini93+ 031+133)0)810^3 ^g^
r V^^ Ijffl, COsflj + (15,+ Ij,}«75 cos^s
^VE.= l2'a2sm^2+(lii + ls2)'"iSin^5 (,0j
Ca cau chuyen dflng tren day treo ngang nen ta chi khao sat cac gia tri vcx va VEX, tai thoi diem cac chan ty day (van toe ca cau se xac dinh theo van toe cac diem nay). Ket hgp vol sfl lieu trong Hinh 6, ta co do thi van toe ciia cac chan di chuyen nhu Hlnh 7:
Hinh 7. Do thivdn tdc theo phuang x cua cdc
chdn vd van tdc trung binh cua ca cdu Sir dung phucmg phap dfii gia, thay vi khao sat van tfic cac chan vai gia co dinh, ta co cac chan ty tren day co djnh, va ca cau se bj day ve phia truac vol van tflc dung bang van toe trung hlnh cfing cua v§n tflc cac chan C, E v6i Vcoi:au-(Viru(re+Vsau)''2. Mat khac, SC xuit hien su trugt do chenh lech v^n toe tinh ti6n cua 2 chan ty day, vai v,n,o,=|vtni6i;-Vsaul (gia trj do dugc la lO'^coz (rat nho so vai van toe di chuyen ciia co cau v==(S,2-^17,3)G)2 nSn co the bo qua hi£n tupng trupt nay.
PHAN TICH D O N G L U C HOC CO CAU Qua trinh tinh toan dpng lire hpc co cau cho phep xac dinh tai trpng tac dung ISn tirng khSu, khop trong co cau, tir do dua ra ket cau khau phil hpp va thflng so dgng ca can thiet de he lam viec duoc. Tren co sd mo hinh dugc de xuat, tai trpng dugc xac djnh boi khfli lugng ca cau (Ps) dat len day se phan bfl qua cac chan de tac dyng xuong day. Ap dung phuang phap di chuyin kha di dl xac dinh cong suat tren khau dan theo bieu thiic:
^ i ^ + ^ v 7 + ^ i ^ + ^ ^ + ^ ^ = ''.(.(ll) p
Vdfi: Pc.E = "T la phan lire tu day tac dung lai len ca cau, xac djnh theo tong tai trpng PE tac dung tren day va sfi chan ty day i=2. Do cac diem tyday khao sat c6 v^ » V;;» v nen c6
t h l c o i ^ ^ i v I = ^.^ (12)
73Duong Pham Tucmg Minh va Dig Tap chi KHOA HOC & COlNU r ^ u n t G, = —m^g la trpng lugng khau.
P^, = —m, a^, la luc quan tinhciia kliau.
A^g, - - • / i , e , la momen quan tinh cua khau.
Pcb la gia tri cong suat can bang tren khau dan (dpng co) de can bang vai cac thanh phan tac dung cua ngoai luc.
Do kich thuoc cac khau tuong dfli nho, ma tai trpng dat tren c o c i u kha Ion so vai cac thanh phan luc do khau sinh ra (mflmen quan tinh, trpng luc, luc quan tinh..) nen co the bo qua cac thanh phan luc nay. Liic nay phucmg trinh (11) CO the rut gpn ve dang: .P^^ = P^-v^ (12) Ta CO do thi gia tri Pjbtheo goc khau dan 02 va ti le thuan voi toe dp ciia dpng c a CO2 va tai trpng cua ngoai lire P i (Hinh 8).
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\ ~ ^
O'dS)
\ '
Hlnh 8. Do thi cdng sudt dgng ca cdn bdng ca cdu Khi do, cflng suat dfing ca can thiet de robot CO the van hanh khi chiu tai trgng P^:
-Prf, = m a x ( P ^ , ) = \,6o}^.P,^ ( w ) Dfing thoi ta ciing co the xac dinh tai trpng giai han tir thflng so dau vao ciia dgng co. Vi du: vol dpng c a co cong suat 20W, sfl vong quay n=30 vong/phut, c o cau vol kich t h u a c mo hinh da cho se di chuyen tren day voi - _ 1 7 . 3 . 3 0 . 2 p _ , . , „ , . . ..
60 3'i.J3tnim/s) va tai trpng nang gioi h^n (ke ca khfli lugng c o c i u ) co t h i len
1,626.^;,
toiPj- = 3,98(N)
KET LUAN
Bai bao de xuat p h u a n g phap tinh toan va phan tich dflng hpc cho c o ciu robot treo dang
bon khau ban le, c a cau thu dugc co kha nang djch chuyen tren day treo v a i dp on dinh cao.
Khac vai viec giai bang p h u o n g phap hga do (phuang phap lugng giac), viec xay dung mo hinh dang sfi phuc giiip qua trinh tinh toan dugc thuc hien chinh xac va co the tich hgp vai phan mem tinh toan nhu Excel, Matlab, C, ... se cho ket qua nhanh chong. Can cii vao qua trinh phan tich dong hpc qua trinh di chuyen cac chan robot, viec xac djnh cac dilu kien lam viec (van toe di chuyen, dp dao mjit san, vi tri chiu tai trpng...) dugc thuc hien tuong dfli dan gian. Tir ket qua tinh toan thu dugc, CO m a rpng tinh toan vai cac co cau robot dong dang, giiip xac dinh cac thong sfl tong quat nhu cflng suit dpng co, tai trpng tac dung, van tflc di chuyen hay dp fln dinh ciia san.
TAI LIEU T H A M K H A O 1. M. Muller (1996), A Novel Classification of Planar Four-Bar Linkages and its Application to the Mechanical Analysis of Animal Systems, Phil Trans. R. Soc. Land B, 351, 689-720 2. L. Roy, A. Sen, R. P. Chetia and M. J. Borah (2008), "Analysis and Synthesis of Fourbar Mechanism", International Journal of Theoretical and Applied Mechanics, Vol 3(2), pp. 171-186 3. Artobolevsky 1.1. (1975J, Mechanisms in Modern Engineering Design, Vol. I ,Mir Publishers.
4. Kazuma Komoda, Hiroaki Wagatsuma (2016),
"Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms",A/w///6o(/y' ^slem Dynamics, Jun 2017, Vol 40(2), pp. 123-153.
5. Ingram A.J.(2006),^ new type of mechanical -walking machine, Ph.D. thesis. Department of Mechanical and Industrial Engineering Technology, University of Johannesburg, Johannesburg, Department of Physics and Asn-onomy, South Africa.
6. Ghassaei Amanda {201 \),The Design and Optimization of a Crank-Based Leg Mechanism, PhD Thesis, Pomona College.
7. Shigley J.E., Uicker J.J (1981), Theory of machines and mechanisms, McGraw-Hill.
DSng Anh Tuin vd Dtg Tap chl KHOA HQC & CONG NGHE 176(16): 71 - 75
S U M M A R Y
D E S I G N R O P E C L I M B I N G R O B O T USING F O U R B A R M E C H A N I S M Dang Anh Tuan', Duong Pham Tuong Minh
Thai Nguyen University ofTechnology The paper proposes a kinematic calculating and analyzing method for robots moving on a wire using a four-bar mechanism. By using analytical methods, the kinematic model of robot is included to examine parameters such as leg tilt, average moving velocity, position and trajectory of robot's leg. Based on the calculated results, suitable size parameters are proposed to ensure the stable and balanced movement of the structure. The power required for the engine is also determined by using a principle of virtual displacement that ensures a uniform movement of the robot. Calculation results are used to design the actual model to evaluate the robot's ability to work.
Keywords; Four-bar mechanism. Analysis, Kinematic, Dynamic, Matlab
Ngdy nhdn bdi: 01/11/2017; Ngdypltdn bifn: 15/11/2017; Ngdy duy?t dang: 05/01/2018 'Tel: 0985 059022, Email. [email protected]<
