modeling and testing of elastic joints mobile mechanical manipulators
TRANSCRIPT
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8/17/2019 Modeling and Testing of Elastic Joints Mobile Mechanical Manipulators
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
?=
Efimlkhc nhi Fptkenl @fhtrfl fo n 0-Nxks Eftkfh
PkeulntfrPmpmgr R. Jgnlkcg* , Emgik Efrtnznvk
Nmrfspn`m Mhckhmmrkhc Impnrtemht, @mhtmr fo Mx`mllmh`m kh @feputntkfhnl Nmrfspn`m, Nekrjnakr ]hkv. fo Ym`ghflfcy, Ymgrnh, Krnh, R.F. Afx >=73=-99>0.
smpmgrVpfrByngff.`fe,
N Q Y K @ L M K H O F N A P Y Q N @ Y Nrtk`lm gkstfry4
Qm`mkvmi4 Nucust >?, 122;
Qm`mkvmi kh rmvksmi ofre4 Hfvmeamr 9, 122;
N``mptmi4 Hfvmeamr 13, 122;
Kh tgks pnpmr, n 0-nxks eftkfh skeulntfr, ns n tgrmm imcrmm-fo-ormmife tmst stnhi ofr nkr`rnot
khstruemht tmstkhc nhi `nlkarntkhc wktgkh n Gnriwnrm-Kh-Ygm-Lffp Mhvkrfhemht, ks stuikmi
ofr `fhtrfl nhnlysms. N entgmentk`nl efiml fo tgm skeulntfr em`gnhk`nl stru`turm ks imrkvmi
nhi tgmh lkhmnrkzmi uskhc Ynylfr smrkms mxpnhskfh nrfuhi tgm khstnhtnhmfus mquklkarkue pfkht
wgk`g ks tgm nkr`rnot tkem-impmhinht Mulmr nhclms nhi tgmkr rntms. Nlsf, tgm nkr`rnot, mnrtg nhi
ntefspgmrm nrm efimlmi kh Entlna uskhc Nmrfske alf`jsmts. N lkhmnr qunirntk` rmculntfr
(L^Q) `fhtrfl lnw ks imvmlfpmi tf trn`j tgm nttktuim, nhculnr rntms nhi nhculnr n``mlmrntkfh
fo tgm Hnvkfh nkr`rnot kh n `feplk`ntmi enhmuvmr. Ygm `fhtrfl lnw ks sgfwh tf am mook`kmht kh
tgm prmsmh`m fo ntefspgmrk` turaulmh`m, nhi rfaust tf uhjhfwh afuhimi iksturanh`ms. Ygm
n``urn`y nhi `frrm`thmss fo tgm prfpfsmi `fhtrfl systme ks vmrkokmi ay tgm skeulntkfh.
Jmywfris4Efimlkhc
Gnriwnrm-Kh-Ygm-Lffp(GSKL) s keulntkfh
L^Q
0-nxks eftkfh skeulntfr
>. Khtrfiu`tkfh
Ygm khmrtknl smhsfrs nhi nhculnr n``mlmrfemtmrs nrm sfem
fo tgm efst `rktk`nl mlmemhts fo nhy nkr`rnot, wgk`g gnvm tf
am tmstmi tf mhsurm rmlknalm fpmrntkfh kh tgm nkr.
Ymstkhc tgmsm smhsfrs wktgkh n Gnriwnrm-Kh-Ygm-Lffp
(GSKL) skeulntkfh mhvkrfhemht `nh vmrkoy tgmkr fpmrntkvm
`frrm`thmss. Ofr tgks purpfsm, n 0-nxks eftkfh skeulntfr
`nh am usmi tf tmst cyrfs, rntm cyrfs, nhculnr
n``mlmrfemtmrs, suh smhsfrs nhi ftgmr cyrfs`fpk`
khstruemhts usmi kh nh nkr`rnot. Ygm eftkfh skeulntfr ks n
tgrmm imcrmm-fo-ormmife tmst stnhi tgnt skeulntms nll tgm
nkr`rnot‛s frkmhtntkfhs ay uskhc tgrmm N@ Pmrvf eftfrs
okxmi nlfhc rfll, pkt`g nhi ynw nxms.Kh tgks pnpmr, tgm entgmentk`nl efiml fo tgm eftkfh
skeulntfr ks imrkvmi ay `nl`ulntkhc tgm nhculnr efemhtue
fo mn`g rftntkhc pnrt wktg rmspm`t tf kts rmomrmh`m ornem.
Ygmrm nrm `feplmx hfhlkhmnr `fuplkhcs nefhc tgrmm nxms
kh tgm entgmentk`nl efiml fo tgm skeulntfr, wgk`g eny
imcrnim tgm `fhtrfl pmrofrenh`m Z>U.
Ay nifptkhc n lkhmnr qunirntk` rmculntfr (L^Q) `fhtrfl
Okc. >. 0-nxks eftkfh skeulntfr
lnw, tgm skeulntfr `nh su``mssoully trn`j tgm nkr`rnot‛s
nttktuim, nhculnr rntms nhi nhculnr n``mlmrntkfh, ay
spmhikhc tgm ekhkeue `fhtrfl moofrt imspktm tgm prmsmh`m
fo ntefspgmrk` turaulmh`m nhi mxtmrhnl iksturanh`ms. Ygm
* Niirmss ofr `frrmspfhimh`m4 smpmgrVpfrByngff.`fe
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
??
mook`kmh`y nhi n``urn`y fo tgm prfpfsmi `fhtrfl systme ks
vmrkokmi uskhc skeulntkfh rmsults.
K. 1. YGM 0-NWKP EFYKFH PKE]LNYFQ NHI
GSKL PKE]LNYKFH IMP@QKRYKFH
Ygm 0-nxks eftkfh skeulntfr ns sgfwh kh Okc. > ks`feprksmi fo nh futmr ckeanl, nh khhmr ckeanl, n tmst
tnalm, tgrmm eftfrs, `fuhtmrwmkcgts nhi n ansm. Ygm
pnylfni ks efuhtmi fh tgm tfp fo tgm tmst tnalm. Ygm futmr
ckeanl rftntms nrfuhi n vmrtk`nl ynw nxks wgk`g ks irkvmh
ay n eftfr lf`ntmi khskim tgm ansm `nllmi ynw eftfr. Ygm
khhmr ckeanl efvms nrfuhi n gfrkzfhtnl pkt`g nxks nhi ks
irkvmh ay nhftgmr eftfr wgk`g ks okxmi fh tgm futmr
ckeanl, nhi ks hnemi pkt`g eftfr. Ygm tgkri eftfr `nllmi
rfll eftfr, ks okxmi fh tgm khhmr ckeanl, nhi irkvms tgm tmst
tnalm wgk`g rftntms nrfuhi tgm rfll nxks pmrpmhik`ulnr tf
tgm pkt`g nxks. Ygm ynw, pkt`g nhi rfll nxms emmt nt n
skhclm pfkht kh spn`m. Ygm wgflm systme ks imskchmi tf am
nxk-syeemtrk`. Ygm `fuhtmrwmkcgts okxmi kh tgm khhmr
ckeanl nrm usmi tf anlnh`m tgm pnylfni su`g tgnt tgm
`mhtmr fo crnvkty fo tgm khhmr ckeanl nhi tgm pnylfni lkms
fh tgm pkt`g nxks Z>U. Ygm nr`gktm`turm fo GSKL
skeulntkfh ofr nkr`rnot khstruemht tmstkhc ks sgfwh kh Okc.
1. Ygrmm prkh`kpnl `fepfhmhts fo tgm `lfsmi lffp systme
nrm tgm nmrknl vmgk`lm fr `fepfhmhts fo tgm nmrknl vmgk`lm,
tgm skeulntkfh `feputmr, nhi tgm pgysk`nl eftkfh systme
wgk`g ktsmlo `fhsksts fo tgm pgysk`nl skeulntfr nhi eftkfh
`fhtrfllmr Z1U, Z0U.
Ygm skeulntkfh `feputmr `fhtnkhs tgm nkr`rnot iyhnek`
efiml tfcmtgmr wktg tgm ntefspgmrm nhi tgm mnrtg efimls,
nhi ks rmspfhskalm ofr tgm rmnl-tkem `nl`ulntkfh fo tgm
nkr`rnot nttktuim, kh`luikhc khstnhtnhmfus Mulmr nhclms nhi
tgmkr rntms, nhi smhikhc tgme tf tgm eftkfh `fhtrfllmr.
Okc. 1. Gnriwnrm-Kh-Ygm-Lffp nr`gktm`turm
Ygm eftkfh `fhtrfllmr ks `feprksmi fo n RL@ ofr tgm
keplmemhtntkfh fo tgm `fhtrfl nlcfrktge, nhi tgrmm smrvf
neplkokmrs tf irkvm n` smrvf eftfrs, sf tgnt tgm skeulntfr
`nh trn`j tgm nkr`rnot‛s nttktuim, nhculnr rntms nhi nhculnr
n``mlmrntkfhs rm`mkvmi orfe tgm skeulntkfh `feputmr.
Ygm pgysk`nl skeulntfr fr 0-nxks eftkfh skeulntfr ks usmi
tf tmst tgm pmrofrenh`m fo nttktuim smhsfrs, rntm cyrfs nhi
nhculnr n``mlmrfemtmrs. Ygmsm smhsfrs wgk`g nrm efuhtmi
fh tgm tmst tnalm rftntm wktg tgm eftkfh tnalm nhi smhi
tgmkr skchnls tf tgm fhafnri `feputmr `fhtrfllmr fr
nkr`rnot‛s nutfpklft. Ay gnvkhc tgm rmnl smhsfr skchnls fo
nkr`rnot, tgm nutfpklft `nh hfw `nl`ulntm tgm imskrmi`fhtrfl suron`ms `feenhis, k.m. tgm mlmvntfr, nklmrfh nhi
ruiimr imolm`tkfhs, nhi smhi tgme tf tgm n`tuntfrs fo tgm
rmnl `fhtrfl suron`ms em`gnhkses efuhtmi fh tgm
Krfhakri. Ygm rmnl emnsurmi nhclms fo tgm `fhtrfl suron`ms
prfvkim futputs tf tgm skeulntkfh `feputmr. Orfe tgks
stnrtkhc pfkht kh tgm lffp, tgm wgflm prf`mss wkll am
rmpmntmi uhtkl tgm mhi fo tgm skeulntkfh tkem.
KK. 0. ENYGMENYK@NL EFIMLKHC FO YGM 0-
NWKP EFYKFH PKE]LNYFQ EM@GNHK@NL
PYQ]@Y]QM
Ygm skeulntfr gns tgrmm rftntkhc pnrts, hnemly rfll pnrt
kh`luikhc pnylfni nhi tmst tnalm: pkt`g pnrt kh`luikhc khhmr
ckeanl, `fuhtmrwmkcgts nhi rfll eftfr: nhi ynw pnrt
kh`luikhc futmr ckeanl nhi pkt`g eftfr.
Okc. 0. Jkhmentk`s rmprmsmhtntkfh fo tgm eftkfh
skeulntfr ay uskhc Mulmr nhclms
Ns sgfwh kh Okc. 0, nhclms , nhi nrm imhftmi ns rfll, pkt`g nhi ynw nhclms rmspm`tkvmly nhi emnsurmi orfe
tgmkr khktknl stntms. Nlsf, tgm nhculnr vmlf`ktkms nafut tgmsm
tgrmm nxms nrm )(,)(
pr nhi . Hftm tgnt h ks pmrpmhik`ulnr tf rp plnhm. Ygm nhculnr vmlf`kty fo rph
ornem okxmi fh tgm khhmr ckeanl ks Z>U,
hr p y y p
y p
rphk
skh`fs
(>)
hr
pr
y y y
p pr r
skh`fs
,
(1)
Ygm nhculnr efemhtue fo tgm rfll pnrt ks,
)(
y
Khmrtknl Pmhsfrs Cyrfs
Qntm Cyrfs
N``mlmrfemtmrs 0-Nxks Eftkfh Pkeulntfr
Qftntkfhnl Pmhsfr
Ptkeulntkfh
Eftkfh
@fhtrfllmr
Pkeulntfr
@feenhisQmnl @fhtrfl
Puron`m
Khofrentkfh
_mgk`lm Iyhnek`
Pkeulntkfh
Fhafnri @feputmr
@fhtrfllmr (Nutfpklft)
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
?3
y pr r r K G
(0)
wgmrm tgm rfll pnrt ks nssuemi tf am nxk-syeemtrk`, nhi kts
`fhstnht efemht fo khmrtkn ks fo tgm ofre
kh tgm rph ornem. Ygmrmofrm tgm
mxtmrhnl tfrqumk
r E
n`tkhc fh tgm rfll pnrt ks Z>U,
(9)
rr E , tgm `fepfhmht fo tgm tfrqum
k
r E
prfiu`mi ay rfll
eftfr, ks `nl`ulntmi ns ofllfws4
(=)
Nlsf, tgm nhculnr efemhtue fo tgm pkt`g pnrt ks ckvmh ay,
(?)
wgmrm `fhstnht efemht fo khmrtkn entrkx fo tgm pkt`g pnrt
ks nhi tgmrmofrm, p p E , tgm
`fepfhmht fo tgm tfrqum k
p E
prfiu`mi ay pkt`g eftfr, ks
`nl`ulntmi ns ofllfws Z9U,Z=U4
(3)
Ofr skeplk`kty, tgm nhculnr efemhtue vm`tfr fo tgm ynw
pnrt ks prmsmhtmi kh rmomrmh`m ornem khstmni fo rph ornem,
nhi ks ckvmh ay,
(7)
wgmrm yy K ks tgm ynw pnrt efemht fo khmrtkn nafut tgm ynw
nxks. Ygm rftntkfh entrkx orfe tgm rph ornem tf tgm
khmrtkn ornem ks ckvmh ay,
(;)
wgmrm ` khik`ntms `fskhm nhi s khik`ntms skhm.
yz E , Ygm `fepfhmht fo tgm tfrqum k
y E
nrfuhi tgm ynw
nxks prfiu`mi ay tgm ynw eftfr, ks `nl`ulntmi ns ofllfws4
(>2)
Ygm entgmentk`nl efiml fo tgm skeulntfr `nh am
prmsmhtmi ay `feakhkhc nhi nrrnhckhc (=), (3) nhi (>2) nsofllfws Z>U4
(>>)
wgmrm Y q ks tgm pfsktkfh vm`tfr. ks tgmskeulntfr khmrtkn entrkx wgk`g ks n syeemtrk` pfsktkvm
imokhktm entrkx, ks tgm imenhimi
tfrqum vm`tfr fo tgm tgrmm eftfrs nhi
ks tgm mxtmrhnl iksturanh`m vm`tfr.
KKK. 9. LKHMNQ FRYKENL YQN@JKHC @FHYQFL
IMPKCH
Hfw tgm `fhtrfl tnsj ks tf cmt tgm futput tf trn`j tgm
tkem-vnrykhc ;-ikemhskfhnl vm`tfr ,
k.m. n imskrmi trndm`tfry ansmi fh tgm spm`kok` enhmuvmr fo
tgm nkr`rnot. Yf imskch n `fhtrfllmr ansmi fh tgm lkhmnr
qunirntk` rmculntfr (L^Q), kt ks okrst hmmimi tf lkhmnrkzm
tgm plnht. Ygm entgmentk`nl efiml fo tgm eftkfhskeulntfr em`gnhk`nl stru`turm `nh am lkhmnrkzmi uskhc
Ynylfr smrkms mxpnhskfh nrfuhi tgm khstnhtnhmfus
mquklkarkue pfkht wgk`g ks n tkem-vnrykhc ?-ikemhskfhnl
vm`tfr, ns tgm nkr`rnot
tkem-impmhinht Mulmr nhclms nhi tgmkr rntms. Ay
`fhskimrkhc ns tgm stntm vm`tfr fo tgm
skeulntfr, nhi mxpnhikhc tgm hfhlkhmnr stntm mquntkfh (>>)
kh n Ynylfr smrkms, wm gnvm
u] x W x W
uuu x x x
u
u
O x
x
O x
u x O x
i i
u xu x i i i i
,,
,
,
,,
(>1)
t ] t At W t Nt W (>0)wgmrm nll fo hfh-zmrf `fepfhmhts fo tgm tkem-vnrykhc
entrk`ms, N nhi A nrm lkstmi kh tgm Nppmhikx.
Ygm `fhtrfl khput vm`tfr ks ckvmh ay Z?U,
(>9)
wgmrm )(t J ks tgm ommian`j cnkh entrkx.
Kh frimr tf ekhkekzm aftg tgm trn`jkhc mrrfr nhi `fhtrfl
moofrt, tgm fadm`tkvm ouh`tkfh `nh am wrkttmh ns ofllfws4
t t
t
Y Y
o i ] Q] W ^ W t t D o
, (>=)
wgmrm )(t Q ks n squnrm, syeemtrk` pfsktkvm imokhktm entrkx
`nllmi tgm `fhtrfl `fst entrkx, nhi )(t ^ ks n squnrm,
syeemtrk` pfsktkvm smek-imokhktm entrkx `nllmi tgm stntm
wmkcgtkhc entrkx Z3U. Ygm npprfprkntm ^ nhi Q ofr tgm
skeulntfr nrm smlm`tmi ns ofllfws4
U,,Z rphrphrr r K K K iknc K
h E p E r E
G G E
rhrprr
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
?7
(>?)
Ay suastktutkhc (>9) khtf (>0), tgm `lfsmi-lffp stntm
mquntkfh `nh am wrkttmh ns ofllfws4
(>3)
Ygm sflutkfh tf (>3) `nh am wrkttmh ns ofllfws4
(>7)
wgmrm ),( 2t t @L ks tgm stntm-trnhsktkfh entrkx.
Ay suastktutkhc (>7) khtf (>=), wm gnvm
(>;)
wgmrm ),( o t t E ks ckvmh ay,
(12)Ygmrmofrm, ekhkekzkhc ),( o t t E wkll ekhkekzm
),( o t t D ns wmll. Hfw ay ikoomrmhtkntkhc (>;) nhi (>=), nhi
mquntkhc tgme wm cmt tgm ofllfwkhc4
(1>)
Okhnlly, tgm fptkenl cnkh entrkx wgk`g ekhkekzms
),( o t t D ks ckvmh ay,
(11)
wgmrm , tgm ekhkeue vnlum fo tgm ),( o t t E
, ks tgm sflutkfh tf tgm ofllfwkhc mquntkfh4
(10)
Mquntkfh (10) ks `nllmi tgm nlcmarnk` Qk``ntk mquntkfhZ?U-Z;U. Pkh`m, entrk`ms N nhi A nrm khstnhtnhmfusly
`nl`ulntmi n``frikhc tf tgm nkr`rnot nttktuim,
ns tgm
fptkenl cnkh entrkx wkll vnry nt mvmry tkem stmp.
K_. =. PKE]LNYKFH Q MP]LYP
Ygm mook`kmh`y fo tgm L^Q `fhtrfl lnw ks khvmstkcntmi wktg
rmspm`t tf trn`jkhc mrrfr nhi rfausthmss uskhc `feputmr
skeulntkfhs. Ygm alf`j ikncrne fo tgm eftkfh skeulntfr ks
sgfwh kh Okc. 9. Ygm enkh `fepfhmhts fo tgm skeulntkfh
nrm nkr`rnot iyhnek` efiml alf`j, `fhtrfllmr efiml alf`j
nhi 0-nxks eftkfh skeulntfr efiml alf`j.
Okc. 9. Ygm alf`j ikncrne fo tgm Eftkfh Pkeulntfr @fhtrfl Pystme
Ygm nkr`rnot iyhnek` efiml alf`j, kh`luims tgm
entgmentk`nl efiml fo tgm nkr`rnot iyhnek`s, mnrtg nhi
ntefspgmrm efimls. Ygks alf`j `nl`ulntms tgm nkr`rnot
nttktuim, nhculnr rntms nhi nhculnr n``mlmrntkfh fh tgm
ansks fo Mulmr nhclms ay sflvkhc tgm ?-IFO mquntkfhs fo
eftkfh fo tgm nkr`rnot uskhc Nmrfske tfflafx kh Pkeulkhj
Z>>U-Z>0U. Ygm `feplk`ntmi enhmuvmr wgk`g ks imskchmi
tf mvnluntm tgm pmrofrenh`m fo tgm prfpfsmi `fhtrfl lnw kssgfwh kh Okc. ?. Ygm nklmrfh nhi mlmvntfr `feenhis ofr
tgks enhmuvmr nrm sgfwh kh Okc. =. Nlsf, tgm ruiimr
imolm`tkfh ks jmpt zmrf iurkhc tgm enhmuvmr.
Okc. =. Ygm Hnvkfh `fhtrfl suron`ms `feenhis
Okc. ?. Ygm nkr`rnot nttktuim ansmi fh tgm Mulmr nhclms kh tgm
enhmuvmr
Ns sgfwh kh Okc. ?, kh tgks enhmuvmr, tgm nkr`rnot
pmrkfik`nlly `gnhcms kts frkmhtntkfh kh aftg rfll nhi ynw`gnhhmls. Ygm `fhtrfllmr efiml alf`j kh`luims tgm
entgmentk`nl efiml fo tgm imvmlfpmi `fhtrfl lnw. Ygks
alf`j cmts tgm trn`j khputs, k.m. imskrmi stntm vm`tfr, nhi
tgm `urrmht stntm vm`tfr fo tgm skeulntfr orfe tgm nkr`rnot
iyhnek` efiml alf`j nhi tgm 0-nxks eftkfh skeulntfr
alf`j rmspm`tkvmly, kh frimr tf `nl`ulntm tgm `fhtrfl
`feenhis ay sflvkhc tgm nlcmarnk` Qk``ntk mquntkfh. Ns
sgfwh kh Okc. 3, tf on`klktntm tgm dfkht ork`tkfh nhi
iksturanh`m moom`t khvmstkcntkfhs, tgm eftkfh skeulntfr ks
nlsf efimlmi kh tgm _ksunl Hnstrnh 9I mhvkrfhemht. Ygm
vksunl skeulntfr efiml rm`mkvms tgm `fhtrfl `feenhis
orfe tgm `fhtrfllmr alf`j kh Entlna, nhi tgmh tgm rmnl stntm
vm`tfr fo tgm skeulntfr ks `nl`ulntmi ay tgm _ksunl Hnstrnhsflvmr tf prfvkim ommian`j ofr tgm `fhtrfllmr alf`j kh
Pkeulkhj.
U>?,>=,=Z
U?9,?=,32,=1,=0,==Z>22
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8/17/2019 Modeling and Testing of Elastic Joints Mobile Mechanical Manipulators
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
?;
Okc. 3. Pkeulntfr efimlkhc kh _ksunl Hnstrnh 9I
=.> Mxtmrhnl Iksturanh`m Moom`ts
Ygm okrst skeulntkfh ks imskchmi tf khvmstkcntm tgm
rfausthmss fo tgm prfpfsmi `fhtrfl lnw kh tgm prmsmh`m fo
mxtmrhnl iksturanh`ms. Ofr tgks purpfsm, n `fhstnht
iksturanh`m Hej Y r
1.> ks khtrfiu`mi nt st 12 nhi
kt lnsts ofr s>2 . Nssuem tgm khktknl pfsktkfhs fo tgm nkr`rnot
nrm imc?.11)2( : imc2)2( : imc2)2( nhitgm khktknl vmlf`ktkms nhi n``mlmrntkfh nrm zmrf. Nlsf,
nssuem tgm khktknl pfsktkfhs fo tgm skeulntfr nrm
: imc9?)2( :
nhi tgm khktknl vmlf`ktkms nhi n``mlmrntkfh nrm zmrf.
Hftm tgnt alum nhi crmmh lkhms khik`ntm tgm trndm`tfry fo
tgm Hnvkfh nkr`rnot nhi tgm skeulntfr rmspm`tkvmly.
Okc. 7. Ygrmm nxms pfsktkfh trn`jkhc
Okc. ;. Ygrmm nxms vmlf`kty trn`jkhc
Okc. >2. Ygrmm nxms n``mlmrntkfh trn`jkhc
Okc. >>. Ygrmm nxms trn`jkhc mrrfr
Pkeulntkfh rmsults sgfw tgnt tgm skeulntfr `nh n``urntmly
trn`j tgm imskrmi trndm`tfrkms nafut tgrmm nxms imspktm tgm
prmsmh`m fo mxtmrhnl iksturanh`ms.
=.1 Ntefspgmrk` Yuraulmh`m Moom`ts
Ygm sm`fhi skeulntkfh ks imskchmi tf khvmstkcntm tgm
rfausthmss fo tgm prfpfsmi `fhtrfl lnw kh tgm prmsmh`m fo
ntefspgmrk` turaulmh`m. Ygm turaulmh`m ks cmhmrntmi ay
npplykhc vfh Jnrenh turaulmh`m sgnpkhc okltmrs ofr
lfhcktuikhnl, lntmrnl nhi vmrtk`nl `fepfhmhts tf
tgrmm wgktm-hfksm sfur`ms.
Okc. >1. Ygrmm nxms pfsktkfh trn`jkhc
imc=.>>)2( imc3.17)2(
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
32
Okc. >0. Ygrmm nxms vmlf`kty trn`jkhc
Okc. >9. Ygrmm nxms n``mlmrntkfh trn`jkhc
Okc. >=. Ygrmm nxms trn`jkhc mrrfr
Pkeulntkfh rmsults sgfw tgnt tgm skeulntfr `nh
su``mssoully trn`j tgm imskrmi trndm`tfrkms nafut tgrmm nxms
imspktm tgm prmsmh`m fo ntefspgmrk` turaulmh`m.
_. ?. @FH@L]PKFH
Ygm entgmentk`nl efiml fo n 0-nxks eftkfh skeulntfr ks
imvmlfpmi, tgmh lkhmnrkzmi uskhc Ynylfr smrkms mxpnhskfh
kh tgks pnpmr. Puasmqumhtly, n lkhmnr qunirntk` rmculntfr
(L^Q) `fhtrfl lnw ks imvmlfpmi tf ekhkekzm aftg trn`jkhc
mrrfr nhi `fhtrfl moofrt. Ygm skeulntkfh rmsults gnvm
vmrkokmi tgm `frrm`thmss nhi n``urn`y fo tgm prfpfsmi
`fhtrfl lnw imspktm tgm prmsmh`m fo uhjhfwh afuhimi
iksturanh`ms nhi ntefspgmrk` turaulmh`m.
NppmhikxEfemhts fo Khmrtkn fo tgm Rlnht kh “rph― rmomrmh`m ornem4
Khktknl Olkcgt @fhiktkfhs4
Ofr entrk`ms N nhi A , tgm hfh-zmrf `fepfhmhts nrm
lkstmi amlfw4
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eejc K
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2
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Khtmrhntkfhnl Dfurhnl fo Qfaftk`s, _fl.>, Hf.>, (122;)/ Pmpmgr R. Jgnlkcg, Emgik Efrtnznvk
3>
Hfrtg Nemrk`nh Hnvkfh Nkr`rnot Skhc Ikemhskfhs4
Emnh nmrfiyhnek` `gfri
Skhc Ppnh
Skhc Nrmn
Qmomrmh`ms
Z>U [um Wkm, E. _klntgcneuwn, J. D. Ysmhc, & H.
Hncnrndnh, Efimlkhc nhi Qfaust Ninptkvm @fhtrfl fo n 0-
Nxks Eftkfh Pkeulntfr, KMMM, 1221.
Z1U G. P. Gnvlk`smj, & Lnrry Tnhn, Keprfvkhc rmnl-tkem
`feeuhk`ntkfh amtwmmh gfst nhi eftkfh systme kh n
GSKL skeulntkfh, N`utrfhk` ]PN, Rkttsaurcg, RN, 1221.
Z0U R. Cmoo, & S. Jmhhmtg, Imskchkhc Eftkfh Pystme ofr
GSKL Pkeulntkfh, @nr`f Mlm`trfhk`s, @N, 1221.
Z9U D. Emrkne, & L. Jrnkcm, Mhckhmmrkhc Em`gnhk`s
Iyhnek`s, Dfgh Sklmy & Pfhs, Kh`.e, >;;7.
Z=U D. @rnkc, Khtrfiu`tkfh tf Qfaftk`s Em`gnhk`s nhiNiiksfh-Smlslmy, >;7;.
Z?U Ifhnli Jkrj, Nh Khtrfiu`tkfh tf Fptkenl @fhtrfl
Ygmfry, >;03.
Z3U Nsgksg Ymwnrk, Efimrh @fhtrfl Imskch wktg Entlna
nhi Pkeulkhj, Dfgh Sklmy & Pfhs, Lti, 1222.
Z7U M. Nrtgur Arysfh, Npplkmi Lkhmnr Fptkenl @fhtrfl,
@nearkicm ]hkvmrskty Rrmss, 1221.
Z;U Hfrenh Hksm, @fhtrfl Pystmes Mhckhmmrkhc, Dfgh
Sklmy & Pfhs, Kh`, 1222.
Z>2U Qfamrt Hmlsfh, Olkcgt Ptnaklkty nhi @fhtrfl,
E`Crnw-Gkll, >;;7.
Z>>U Amrhnri Mtjkh, Llfyi Iuoo Qmki, Iyhnek`s fo Olkcgt
Ptnaklkty nhi @fhtrfl, Dfgh Sklmy & Pfhs, Kh`, >;;?.
Z>1U Arynh L. Ptmvmhs, & Ornhj L. Lmwks, Nkr`rnot@fhtrfl nhi Pkeulntkfh, Dfgh Sklmy & Pfhs, Kh`., 1220.
Z>0U I. G. Ykttmrtfh, & D. L. Smstfh, Ptrnpifwh Khmrtknl
Hnvkcntkfh Ym`ghflfcy, Rmtmr Rmrmcrkhus Lti., >;;3.
e EN@ 3030?.>
ea >7201.>2
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