Upload
nikola
View
256
Download
0
Embed Size (px)
Citation preview
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 1/22
“ВИСОКА ТЕХНИЧКА ШКОЛА СТРУКОВНИХ СТУДИЈА „НОВИ БЕОГРАД“
Семинарски рад
- Kinematika robota-
Студент: Никола Тешић Професор: др. Весна Шотра бр.индекса: 183/12
Јун 2015
0
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 2/22
2. G!"#$%&' % (%)"'#%(' "*')%+"' $!,!#' R!"#$%&"' ($')*&"& +&'"&#$,& "&./,!" $')'# , / (' 4#, $# ($&+*&4 4$6
+*7&8 9' & "&./, #$3#3$ $')'# 3 #7$, &4/ !+*')/, "&./,!" #' %&"' /($&
4&,/,#, , ')/,#, /&'(.'4/& ('"'7& ,! #&'$,& "&./,!"8 ;#," %&"' 4&,/,#, +&'"&#$,3"/,(3*<,'/,. $')'# ('&)/' %&"' ')$4,#, *3&7& ', & 7*3 3 ($#,/," $&*,!<,"8= '7,$3 ,!*+/ ' ,/&"#,<, +'7'$,%&"' ' )$!,/, , 3)$!/3 3 !+*')'7," "&./,!" , ('!*,
7&!3 #!78 '$,/'" )$!,/'" ($&/'>&/ $4/'+ ($&4"
?''" $!"#$/ ,/&"#,& /7,>& %&"' & )7,#, (,#/&" '4$&@,7/ ('*'6 , $&#/ $')'#
($&' #'!7/,. 3/3#$>/,. , ('*>/,. ''$4,/#8 ?3 & ')$43& , /,/ ($&$3/7/ $&#/
,! &4/,. ''$4,/# 3 4$3+& '4/'/' 4,$&#/, , ,/7&$!/, ($')*&" ,/&"#,& $')'#8
2.1. !-)!)% -#'!% %+ #!$%& "*')%+'"'
?&'$, "&./,!" ' ')*# /3& , #&./,& ($'37 ,#&"& #&* "&@3')/' ('7&!/,. $!/,"
#,('7," 7&!8 A! '7& 7&'" >,$'& ')*#, ,!73%, %&"' '/& ('"'7& ', 3 ),#/, ! ($'37/&
$')'#,&8 B$, #'"& !4$6%&"' '4$&@&/, /,7' #$'+'#, 3 4&,/,<," #,. ('"'7 ,#'7$&"&/'
%&"' & $3'7'4,#, #,"& 4 ')>/&/ )343 >#' &4/'#7/, , /,8 B$7' ('#$&)/' & ($'3,#,#,('7& 7&! #&* ' ')$!33 "&./,!" !#," $!*,,#& #$3#3$& "&./,!" ', & 7*3 3
$')'#,<,8
2.1.1. (0456 79
9,/&"#,, ($ ('4$!3"&7 47 "&@3')/' ('7&!/ #&*8 = !7,/'#, '4 /,/ 7&!,7/ # 47
4&* ,/&"#,& ($'7& 4&*,"' / '4$&@&/& *&8 C ),"' #& *& "'+*, 4&,/,#, $!"'#$,%&"'"'+3%& /,/& 7&!& 47 #&*8
B'"#$%&"' ($7' &4/' *')'4/' #&*'8 D/' "'6& 4 & $&%& / >&# /&!7,/,. $!*,,#,. /,/:
"'6& 4 & $&%& #$/*#'$/' 436 ' E F ! , "'6& 4 & ')$%& '' 7& '4 #,. ' G7,4, *,3 281H
4*& ," #$, "'+3%& '4/'/' *')'4/& #$/*<,& , #$, *')'4/& $'#<,&8 A! #'+ !*33&"' 4 & ('#$&)/' >&# 7&*,,/ G'$,#,%&"' ,!$! ($"&#$,H 4 ), & &4/'!//' '4$&4,' ('*'6 #&*: #$,
($"&#$ 4 ), & '4$&4,*' #$/*#'$/' $&#/& , #$, 4 ), & '4$&4,*' $'#<,'/' $&#/& '4/'/'
'$,&/#<, #&*8
1
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 3/22
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 4/22
Sl. 2.3. Izgled kinematički paro!a
L
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 5/22
Sl. 2.4. "ota#ioni $a% i translatorni $b% zglob
Sl. 2.&. 'ančani sistem tela
2.1.2.(0456 ;0<
M,!'7& #&* ('7&!/,. ,/&"#,," ($'7," /!,7"' ,/&"#,," */<,"8D74& %&"'
('4$!3"&7#, 4 3 7&!& ')*, $'#<,'/,. ,*, #$/*#'$/,. !+*')'78 N.&"#, $36,% ,!"&@3 47
($&4#7* ),*' ', '4 !+*')'7 G*82858H8N*'6&/,, !+*')7, $!*63 & / !+*')'7& (&#& *& ,!"&@3',. & /*!& $#, &+"&/#,8
9,/&"#,, */<, 3 ('&)/' 76/, 3 $')'#,<, !#' >#' "&./,!" 7'+ $')'# ($&4#7* 3 #7$,
&4/ ,/&"#,, */<8 M *,<, 28O ($&4#7*&/' & /&'*,' "/,(3*<,'/,. $')'# , .&"#, 3 ($,!/, '4+'7$3%, ,/&"#,, */<,8
N7' #&*' &*&"&/# */< /!,7%&"' &+"&/#'" */<8 N&+"&/#& */< "#$"' $3#,"/&4&'$"),*/," #&*,"8 P/< & 4*& #', '4 /,! !+*')'7 , &+"&/#8 ;+*')'7, 3 ')&*&6&/,
&+"&/#, 12 888
R!"'#$,%&"' /&& '4 ('4&* ,/&"#,,. */<8 9,/&"#,& */<& "'6&"' ('4&*,#, / ($'#& ,
$!+$/#&8 B$'# */< ('4$!3"&7 "' &4/ /,! &+"&/# ($, &"3 7, &+"&/# ," 47!+*') ($&#.'4/, , /$&4/, "' ('*&4/, 3 /,!3 ," &4/ !+*')8 ?7, */<, ($,!/, 3 / *,<,
28O8 = *33 4 ($7, &+"&/# */< /,& 7&!/ ! ('4*'+3 7&% & *')'4/ G*8 285H #4 , # &+"&/#
," "' &4/ !+*') G'/ /$&4/,H *, #' & *3 ', ! ($#,/3 $')'#,3 /,& ),#/8
R!+$/# */< ('4$!3"&7 4 )$ &4/ &+"&/# */< /', #$, ,*, 7,>& !+*')'7 G&4/ ($&#.'4/, ,47 ,*, 7,>& /$&4/,.H8 C*& */< & +$/ G*8 28QH8
K
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 6/22
Sl. 2.(. Primeri manipula#ioni robota sa odgo!arajućim kinematičkim lan#ima
Sl. 2.). Sema razgranatog lan#a
= ($#,/," $&*,!<," $')'#,. ,#&" $!+$/#, */<, & $&%3 / ($,"&$ '4
/#$'('"'$/,. .'43%,. $')'# G*8 28H8
a% b%
5
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 7/22
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 8/22
Sl. 2.1. Manipula#ioni robot u zadatku monta/e
2.1.3. -470 =;9>9? 604569@ ;0<
R/,& "' 37&*, 4&,/,<,3 )$' #&(&/, ! &4/ ,/&"#,, ($8 N*&4&%, #73 4&,/,<,3 4'*!,"'
4' #'+ 4 & )$' #&(&/, *')'4& !+*')/'+ ,/&"#,'+ */< &4/ )$'3 "'+3%,. /&!7,/,.
$&#/ #'+ */< '4/'/' &4/ )$'3 /&!7,/,. ($"&#$ ('#$&)/,. 4 ), & &4/'!//''4$&4,' ('*'6 <&*'+ */<8 B'"#$%&"' ,/&"#,& */<& !+*')'7," J *& $'#<,'/," ,*,
#$/*#'$/,"8
N*8 28118P/< #$, #&(&/ *')'4&
T' & 3 (,#/3 '#7'$&/, */< #4 & ! 4&,/,/& ('*'6 ('#$&)/' !/#, ('"&$/ 3 7,"
!+*')'7," */< 4*& ! ', 3+' & ')$/3# 7, $'#<,'/, !+*') , '*,, & ('"&$ 3 7'"
#$/*#'$/'" !+*')38 M,"& '4 #7,. */< !+*')'7, 3 "&@3')/' /&!7,/, , ('"&$-/ 3
!+*')'7," "'+3 ),#, ($',!7'*/8 M ($,"&$ '4 */< / *,<, 2811 ('#$&)/' & !/#, 3+*'7&
, , ,!436&/& L ( #7 ,/&"#,, */< ," #$, #&(&/ *')'4&8 U'6&"' !*3,#, 4 & '4
'#7'$&/,. */< )$' #&(&/, *')'4& &4/ )$'3 !+*')'78
Sl. 2.12. Primer zat!orenog lan#a
9'4 !#7'$&/,. */< ($')*&" & *'6&/,,8 I$' #&(&/, *')'4& */< /,& &4/ )$'3 !+*')'78
B'"#-$"' "&./,!" ($,!/ / *,<, 28128 D7 !#7'$&/, */< ," (&# !+*')'7 7, (' &4/," $'#<,'-/," #&(&/'" *')'4&8 ; '4$&@,7/& ('*'6 '7'+ */< ('#$&)/' & !/#,
3+*'7& , #8 4'7'*/' & !/#, 47 ($"&#$8 C*& */< ," 47 #&(&/ *')'4& ,' ," (&#
!+*')'78 B$')*&" !#7'$&/,. */< %&"' 4&#*/,& ')$4,#, 3 '4&*3 K85 3 '"& +'7'$,"'
' ,/&"#,<, , 4,/",<, /&,. * !#7'$&/,. */<8
Q
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 9/22
2.2.G!"#$%&' "')%ABC'D%!)%* $!,!#' N4 %&"' '(>#& /*,!& ,/&"#,,. */< $&/3#, "&./,!"," ', & 7*3 3 ($#,/,"$&*,!<," "/,(3*<,'/,. $')'#8 T/*,!,$%&"' #$3#3$3 V$3&V , V>&V $')'#8 ;#," %&"'
($'4,3#'7#, )$' #&(&/, *')'4& "/,(3*<,'/'+ $')'#8 C&,/,%&"' 7&#'$& ', '4$&@33
+&'"&#$,3 $')'# , / $3 ('!#, ('#3( ($'$3/ ('*'6 "&./,!" $')'# , ('*'6$4/'+ ($&4"
2.2.1. "0;0 690E@F< 07F;<909@ 9>94
Sl. 2.13. Minimalna kon+igura#ija i 0aka robota
U,/,"*/ '/,+3$<, ('4$!3"&7 "&./,!" #$, !+*') '4/'/' #$, #&(&/ *')'4&8 M#73 ",/,"*/3 '/,+3$<,3 /4'7&!3& & #'!7/, !7$>/, "&./,!" $')'# ', %&"'
3*'7/' /!,7#, >8 M *,<, 281L .&"#, & ($&4#7*&/ ('4&* */< / ",/,"*/3
'/,+3$<,3 , >38 N*&4, 4 ",/,"*/ '/,+3$<, ')3.7# !+*')'7& N1 N2 , NL , &+"&/#& 1 2 ,L > & /4'7&!3& , 4$6, '4$&@&/, )$' !+*')'7 , &+"&/# G/ ($,"&$ K 5 , OH8 M!,7
",/,"*/ '/,+3$<, ('#,& '#34 >#' 7, "/,(3*<,'/, $')'# ('&43& #7 "&./,!"8
U,/,"*/ '/,+3$<, &#' & 4&,/,>& ' "&./,!" #$, #&(&/ *')'4& ', 7$>,
('!,<,'/,$/& #8 4'7'@&/& >& / 6&*&/' "&#' 3 $4/'" ($'#'$38 9/,& %&"' 7,4&#, 4 & ('4 ('"'" ('!,<,'/,$/ '),/' ('4$!3"&7 ('*'6 "'+ 7$. >& $')'# G# T / *,<, 281LH8
?' / # ('*'6 ('$&4 ",/,"*/& '/,+3$<,& 3#,3 , &+"&/#, "& >&8 D#34 & "'6& $&%,
4 ",/,"*/ '/,+3$<, '4$&@3& ('*'6 '$&/ >& G# W / *,<, 281LH !&4/' >'"7$>, ('!,<,'/,$/& 7$. G# T / *,<, 281LH8
U,/,"*/ '/,+3$<, & "&./,!" #$, !+*') '4 ',. 7, "'6& ),#, $'#<,'/, ,*, #$/*#'$/,8
D!/,"' R $'#<,'/, ? #$/*#'$/, !+*')8 N4 "'6&"' 37&#, '!/7/& "&./,!" /*&4&%, /,/: / ($,"&$ R?? '!/7 "&./,!" #$, !+*') G, #$, #&(&/ *')'4&H '4 ',. &
($7, $'#<,'/, 4$3+ 47 #$/*#'$/8 N4 %&"' '$,#&%, 37&4&/' '!/7/& ')$4,#, /&>%&
.&"& ",/,"*/& '/,+3$<,& $')'#8
H B$7'3+'/ ,*, ??? .&"8 U,/,"*/ '/,+3$<, ($7'3+'/& ,*, ??? .&"& ," #$,
#$/*#'$/ !+*')8 M *,<, 281K ($,!/ & ($,"&$ '77& ",/,"*/& '/,+3$<,& , #' ,!+*&4
$')'# , /&+'7 .&"#, ($,!8
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 10/22
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 11/22
B'"#$"' ???-.&"3 ($,!/3 / *,<, 281K , $!"'#$,"' ># & #' >#' '+$/,7 "'+3%/'# 4
7$. W #,+/& 3 ),*' '3 #3 ($'#'$8 D+$/,&/& ('#,& '#34 >#' ('"&$/& ),*' '+ &+"&/#
$'! '4+'7$3%, !+*') /,& '+$/,&/'8 M ($,-"&$ '4 *,!/ !+*') N1 (' >,(, X1X2 37&4&/, 3
"&./,, +$/,/,<, GX1 , X2H8 A '4 '#*,. !+*')'7 436,/ ,!7*&/ ,*, 37*&/ &+"&/#'+$/,&/ & "'" 436,/'" &+"&/# ( & 3 '/#$3<,, 37'4& +$/,/,<,8 N ')!,$'" /
'77 '+$/,&/ $4/, ($'#'$ ???-$')'# ),' ), ($7'3+'/, ($,!/ / *,<, 28 158 D#34 ,
/!,7 ($7'3+'/ .&"8 C ), ),*' /,& #$&) ,#%, 4 .'$,!'/#*/ >,( X 1X2 /,& &+"&/# 7&% ($&4#7* 4&' /&('",/& ('4*'+& &+"&/# 1 & 7&$#,*/, #3)8
Sl. 2.1(. ilindrična minimalna kon+igura#ija
)H W,*,/4$,/ ,*, R??-.&"8 U,/,"*/ '/,+3$<, <,*,/4$,/& ,*, R??-.&"& ," #$, !+*') '4
',. & ($7, $'#<,'/, 4$3+ 47 #$/*#'$/8 M *,<, 281O ($,!/ & ($,"&$ '77& ",/,"*/&'/,+3$<,& , #' ,!+*&4 $')'# , /&+'7 .&"#, ($,!8 M *,<, 28O G<H ($,!/ & '> &4/ ($,"&$
R??-.&"&8
M!,7 <,*,/4$,/ .&" ('#,& '#34 >#' ('"&$/ 3 !+*')'7," N1 N2 , NL #/' '4+'7$3
''$4,/#" ! , <,*,/4$,/'+ ''$4,/#/'+ ,#&" >#' & 7,4, 3('$&@,7/&" *,& 281O , 281Q
GH8 = 4*&" # %&"' 7,4&#, 4 & , $4/, ($'#'$ '77'+ $')'# <,*,/4$,/8
10
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 12/22
Sl. 2.1). ilindrični koordinatni sistem i radni prostor
R!"'#$,"' 4 $4/, ($'#'$ R??-.&"& $')'#8 D+$/,&/ & '74& 7*3 !)'+ '+$/,&/&
436,/& &+"&/# 2 , L #& & '/, "'+3 ,!7*,#, G'4/'/' 37*,#,H ,! '4+'7$3%,. !+*')'7 "' 4''4$&@&/& "&$&8 ; ')$#/& 3 !+*')3 N1 "#$%&"' 4 /,& '+$/,&/' "4 , #3 "'+3 4 & ('7&
'+$/,&/8 N ')!,$'" / 37&4&/ '+$/,&/ $4/, ($'#'$ <,*,/4$,/'+ $')'# ,!+*&4' ), ' /
*,<, 281Q G)H8 <H N&$/ ,*, RR?-.&"8 U,/,"*/ '/,+3$<, &$/& ,*, RR?- .&"& ," #$, !+*') '4 ',. 3
($7 47 $'#<,'/ #$&%, #$/*#'$/,8 M *,<, 28O G)H ($,!/ & ($,"&$ &$/'+ $')'# , /&+'7
.&"8 M *,<, 2811 4# & '> &4/ "'+3% .&" &$/'+ $')'#8 ?$&% "'+3% RR?- .&" 4# & / *,<, 281 GH8
Sl. 2.1*. S+erna minimalna kon+igura#ija
B'"&$/ 3 !+*')'7," '4 RR?-.&"& ($,)*,6/' '4+'7$3 ''$4,/#" &$/'+ ''$4,/#/'+,#&" G*, 281 )H ( '#34 /!,7 &$/ .&"8 B$,"&%3&"' 4 ('*(/& /,& ('#(3/'8 M
.&"" *, 281 , 2811 7,4,"' 4 ), ('"&$/ 3 !+*')'7," N1 N2 , NL '4+'7$* ('#(3/'
''$4,/#" , $ &4,/' ' ), 436,/ &+"&/# 2 ),* &4/ /3*, ,*, )$ ' "*8
R!"'#$,"' $4/, ($'#'$ RR?-.&"& $')'#8 T' 37&4&"' +$/,/,& ! ","*/' , ",/,"*/'
,!436&/& 3 !+*')3 NL "#$"' 4 3 ')$#/ 3 !+*')'7," N1 , N2 )&! '+$/,&/ #4 & $4/,
($'#'$ $')'# &4/ >3(* *'(# G*, 281S H8 T' ('#'& +$/,/,<, ', '4$&@33 $/& #&
11
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 13/22
')$#/ 3 !+*')'7," N1 , N2 #4 & $4/, ($'#'$ &4/ ,& '(,/& *'(#&8 Y&4/ ($,"&$ & 4# /
*,<, 281S G)H8
Sl. 2.1,. "adni prostor s+erne minimalne kon+igura#ije
4H R?R , ?RR.&"&8 D7& 47& .&"& ')$@3&"' !&4/' !#' >#' 3 '/'" ')*,3 3 '"& & '),/'
($#,/' $&*,!33 ,"3 ,#, $4/, ($'#'$8 N.&"& 3 ($,!/& / *,<, 2820 GH G)H &4/
'/$&#/ ($,"&$ $')'# / *,<, 2821 GH8
12
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 14/22
Sl. 2.2. ""sema $a% i ""sema. $b%
R4/, ($'#'$ R?R , ?RR-.&"& $')'# & >3(*, 7* ' >#' & ($,!/' / *,<, 2821 G)H8
&H P## ,*, RRR-.&" U,/,"*/ '/,+3$<, *##& ,*, RRR- .&"& ," #$, $'#<,'/ #&(&/
*')'4&8 Y&4/ ($,"&$ ($,!/ & / *,<, 28O GH / *,<, 2822 4# & '> &4/ ($,"&$8
M!,7 *##, $')'# ('#,& '4 $#&$,#,/'+ V*#V ', & 3'7 / '7' .&", GP / *,<, 2822H8
A/& ! '73 '  .&"3 $')'# $&%3 & , 4$3+, /!,7, ' / ($,"&$ !+*7#, ,*, /#$'(',4/,$')'#8 A!47',%&"' ('&)/' &4/3 '4 "'+3%,. RRR-.&"8 B$,!/ & / *,<, 282L , !)'+ *,/'#,
'7&'7'" $3'" /!,7 & /#$'('"'$/ G'7&'*,H .&"8
Sl. 2.21. Primer ""robota i radni prostor
Sl. 2.22. 'aktasti ili """robot
1L
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 15/22
R4/, ($'#'$ RRR-.&"& $')'# !7,, '4 "'+3%/'#, ')$#/ 3 7'" !+*')38 T' ), ')$#/ ),* )&! '+$/,&/ '/4 ), $4/, ($'#'$ ),' *'(# ,, & ('*3($&/, '4$&@&/ 436,/'" $3&8 9'
')$#/ 3 !+*')'7," /,3 /&'+$/,&/ #' %& $4/, ($'#'$ ),#, &4/ 4&' *'(#& *'6&/'+ ')*,
G*, 282KH8
U'$"' ('"&/3#, '> &4/ $#&$,#,/ *3 *##& .&"& ",/,"*/& '/,+3$<,&8 ?.&" ($,!/ & / *,<, 2825 !7%&"' & TNZT8 N.&" (' >7&4'" $')'#3 "$& TNZT ',
& /('!/#,,8 N.&" & / *,<, ($,!/ 3 47& 7$,/#& '& & $!*,33 (' /,/3 4&*'7/ ('+'/,. "'#'$8 C' ('+'/ '!/&/' & / *,<, #$&*,<"8 ; '73 .&"3 & $#&$,#,/'
4 4$6, &4/ !#7'$&/, */< ')*, ($*&*'+$"8
Sl. 2.23. ntropomor+na """ sema Sl. 2.24. "adni prostor laktastog
robota
1K
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 16/22
Sl. 2.2&. S5sema
2.2.2. +H0 I0J ; H6 9>94
= '4&*3 28281 $&&/' & 4 & "&./,!" "/,(3*<,'/'+ $')'# "'6& ('4&-*,#, / 47 4&*: #!78
",/,"*/3 '/,+3$<,3 , !7$>/, "&./,!" ,*, >3 $')'# G*8 281LH8 U,/,"*/ '/,+3$<,
4'7'4, >3 3 6&*&/, 4&' $4/'+ ($'#'$ '4/'/' ('!,<,'/,$ '$&/ >&8 R!"'#$,"' 4#$3#3$3 !7$>/'+ "&./,!" ,*, >& $')'#8
;7$>/, "&./,!" $')'# #', & '4 '4$&@&/'+ )$' !+*')'7 / $3 & ($,7$>%3&
#'!7/, !7$>/, 3$&@ G&/+*8 &/4-&&<#'$H8 ;+*')'7, >& 3 (' ($7,*3 $'#<,'/,8 M *,<, 282O ($,!/ & .&" "&./,!" >&8 ? W '!/7 '$&/ >& , #3 & 3<$#/ (*',< ' &
37$>%3& ! 7$. ",/,"*/& '/,+3$<,& ' & 3<$#/ ,($&,4/'8 W&*,/ & "'6& *&(' +*&4#,
' & *, 282O 3('$&4, *," 281K , 281O +4& 3 ($,!/& ",/,"*/& '/,+3$<,&8
Sl. 2.2(. Sema 0ake robota
? I '!/7 ('*'6 +4& & #'!7/, !7$>/, 3$&@ 37$>%3& ! "&./,!" >&8 ?' &
3<$#/' 3 ')*,3 (*',<& / '' & /*!& !7$#/, ! 37$>%7-/&8 ;7$>/, 3$&@ 3<$#/ &
,($&,4/' 3 ')*,3 .7#*&8 J$. !7$>/'+ 3$&@ '!/&/ & #'" T8
15
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 17/22
Sl. 2.2). 6!ataljka robota
U&./,!" >& ," &4/ 47 ,*, #$, !+*') , ,#' #'*,' #&(&/, *')'4&8 I$' !+*')'7 !7,, '4
/"&/& #8 '4 !4# ', %& $')'# ')7*#,8 N ')!,$'" / #' 4 ",/,"*/ '/,+3$<, ," #$,#&(&/ *')'4& #' !/, 4 %& $')'# 33(/' ,"#, &#,$, (&# ,*, >&# #&(&/, *')'4&8 D4$&@,7/&
)$' #&(&/, *')'4& ', & ('#$&)/ ! ')7*/& '4$&@&/'+ !4# & ('&)/ ($')*&" , ' #'"&%& ),#, $&, /,&8 I,%& $&, ' $')'#," ', ,"3 7,>& '4 >&# #&(&/, *')'4&8
R!"'#$,%&"' (,#/& !7$>/'+ 3$&@ $')'#8 D(>#& $&&/' 3 (,#/3 & 3$&@ ', /&('$&4/'
,!7$>7 !4# ', & ('#7*&/ ($&4 $')'#8 T' & ('#7*&/ !4# ($&/'>&/ /&'+ ($&4"&#
#4 & !7$>/, 3$&@ #'!7/ .7#*8 D),/' & .7#* <$# 3 ')*,3 *&># ' / *,<, 282Q8?' & !#' >#' 3 .7#*& &#' 3($7' #7'+ ')*,8 ?7 .7#* ," &4/ #&(&/ *')'4&
.7#/& #8 #,/&8 B*',<'" I .7#* & 37$>%3& ! "&./,!" >&8
[7#* "&@3#," /& "'$ 4 )34& ')*, *&>#8 ; /&& ($,"&/& ('+'4/& 3 .7#*&
733"," ,*" ' / ($,"&$ ! ($&/'>&/& *,"'78
T' & ('#7* !4# $)/ ($/&" #4 & !7$>/, 3$&@ (,>#'* ! ($/& ' &!4# / ($,"&$ ##' !7$,7/& #4 & !7$>/, 3$&@ 3 ')*,3 !7$,7,. *&>#8 = $!/,"4$3+," ($,"&/" ('7*3& & $!*,,#, !7$>/, 3$&@,8 U&@3#," &#' & '$,#, #&$",/ .7#*
('4$!3"&73%, ('4 #," 7& 7$#& !7$>/,. 3$&@8 B'4 .7#*'" & ('4$!3"&7 &#' , <&'
('*&4-/, &+"&/# */<8 M ($,"&$ 3 !4#3 ($&/'>&/ /&'+ ($&4"&# '$,#,%&"' ,!$!.7#*& ('4$!3"&7#, .7#*3 , $4/, ($&4"&# !&4/'8
C*& > $')'# #', & '4 "&./,!" >& GWI / *,"H , !7$>/'+ 3$&@ '4/'/'.7#*& GIT / *,"H8 U&./,!" >& !&4/' ",/,"*/'" '/,+3$<,'" ')&!)&@3& 4
7$. .7#*& GTH 4'@& 3 6&*&/, ('*'6 , 4 .7#* !3!"& 6&*&/3 '$,&/#<,3 3 ($'#'$38 ;7$>/,
3$&@ G.7#*H /&('$&4/' ,!7$>7 ('#7*&/, !4#8
9' >#' "'6&"' 7,4&#, > ,/43#$,'+ "/,(3*<,'/'+ $')'# /&" "/'+' *,/'#, >'"
'7&8 U&@3#," #$&) $&%, 4 & '4 &(&$,"&/#*/,. ($'#&#,,. $')'# 3 ('*&4/& 7$&"& , '4
,/43#$,,. 7& &>%& '$,#& *'6&/& >& '($&"*&/& 7&%," )$'&" ($#,38
D .7#*" , !7$>/," 3$&@," 3'(>#& 7,>& %&"' +'7'$,#, 3 +*7, 5 '7& /,+&8
2.2.3. "9@FK09=4 640 9>94 L >9 =470 =;9>9?
C&#*/,& %&"' /*,!,$#, "'+3%/'# $&#/ , ('&)/' #'!7/'+ 3/<,'/*/'+ $&#/ $')'#8
U/,(3*<,'/, $')'# "' ('"#$*, ' '#7'$&/, */< )&! +$// 3 '"& 3 &+"&/#, ('7&!/,
!+*')'7," J *& ', 4'!7'*73 &4/3 #$/*<,3 ,*, $'#<,38 ?7 "&./,, ,#&" ,"'/'*,' #&(&/, *')'4& '*,' ," !+*')'78 T' ," / !+*')'7 ,#&" %& ,"#, / #&(&/, *')'4&
)&! ')!,$ / #' 4 *, & / 7&%& ,*, "/& '4 O8 J,4&%&"' 3'$' !>#' & '7 7$&4/'# O ),#/8 C*&$')'# ' "&./,, ,#&" "'6& 4 & $&%& / / /&!7,/,. /,/8 B$, #'"& & 3!,"3 3 ')!,$
$&#/ 7,. &+"&/#8 J,4&%&"' /,& 4 & ! ($'$3/ 4,/",& ('#$&)/' 7'4,#, $3/ ' '7,.
/ /&!7,/,. "'+3%/'#, $&#/8
1O
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 18/22
N4 %&"' "&@3#," ')$#,#, (6/3 / $&#/ ' ,"3 /&3 3/<,3 3 '#7$&/3 '4$&@&/'+
"/,(3*<,'/'+ !4#8 B'"#$"' "'+3%/'# $&#/ .7#*& $')'# #' & ('*&4/, &+"&/#
*/<8 B'"#$"' $&#/ "' &4/'+ #&* ('*&4/&+ 3 */<3 /& <&*'+ */<8 D!/,"' /.
)$' #&(&/, *')'4& .7#*& 3 ($'#'$38 B$7' !*33&"' 4 .7#* ' #&*' 3 ($'#'$3 "'6&
,"#, /7,>& >&# #&(&/, *')'4& #$, #$/*<,& , #$, $'#<,&8 C*& 8
9' .7#* /,& *')'4/ 7&% */<&" 7&!/ ! ('4*'+3 #' /&/' $&#/& "'6& ),#, '+$/,&/''7'" *//'" 7&!'"8 ?' ! )$' #&(&/, *')'4& .7#*& "'6&"' $&%, 4 & "/, ,*, &4/
)$'3 #&(&/, *')'4& */< #8:
Sl. 2.2*. 7esingularni i singularni meanizam
T/*,!,$"' !>#' & /& 8 D7 /&&4/'# 3+&$,>& 4 & 3 ",*3 3/<,'/*/'+
$&#/ /&, #&(&/ *')'4& */< "'6& ,!+3),#,8 M)'*& & #' ')/,#, 3! /&'*,' '/$&#/,.
($,"&$8 M *,<, 282 ($,!/& 3 47& ",/,"*/& '/,+3$<,& ???-#,( / 73 & /4'7&!3&> &4/," !+*')'" #8 &4/," #&(&/'" *')'4&8 N7, '4 '7,. */< ," (' &#,$, !+*') , '
"&./,, ,#&" ," &#,$, #&(&/ *')'4&8 C*& / \ K8 N #/'7,># $&#/ .7#*& #7$, #'&
4$3+,&8 = *33 GH .7#* #'@& ," K #&(&/ *')'4&8 ?4 & /. \ K #8 /. \ / , /,7,.
+3),# /&"8 = *33 G)H .7#* ," "' #$, #&(&/ *')'4& #8 /. \ L , 8 ?' & '#34 >#'
#/'7,># $&#/ .7#*& #$/*<,& N2 , NL /,3 /&!7,/& 7&% ($',!7'4& &4,/#7&/ &&# ,
('/>3 & ' &4/ #$/*<,8 C*& &4/ '4 # 47 #&(&/ *')'4& & +3),8 ?$&) $&%, 4 & '+3),#3 "'6& +'7'$,#, "' #/'7,># ('"&$/ .7#*&8 T' / ,/#&$&3& ('"&$/& <&*'+
*/< #8 $&#/& 7,. &+"&/# #4 #& 47& #$/*<,& /& "'+3 4 & &4,/& !)'+ &+"&/#
,!"&@3 /,. G&+"&/# )$' 2H ', ," /&' 7'& ('436/' $&#/&8 X3),# #8 $!*, / , /. /#&
'#34 >#' #' ('436/' $&#/& &+"&/# 2 /& 3#,& / $&#/& .7#*&8 N&+"&/# "'6& *,!,#, $'!
!+*')'7& N2 , NL .7#* , 4*& ",$'7#,8
M *,<, 282S8 ($,!/ 3 47 /&>#' 4$3+, ($,"&$ +3),# #&(&/, *')'4&8 P/< GH &
#7*&/ '4 47 #&* ($, &"3 3 !+*')'7, N1 , N2 &$,/, #8 7, 4'7'*7 (' #$, $&*#,7/ ')$#
#4 */< ," / \ L ] L \ O #&(&/, *')'4&8 B'*&4/, &+"&/# */< G#&*' )$8 2H "&@3#," ,"
#&(&/, *')'4& &$ & #/'7,># /&+'7'+ $&#/ &4/ #&(&/ *')'4& +3), G')$#/& #&*
1 '' '& GAHH8
1Q
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 19/22
Sl. 2.2,. 'an#i sa s+eričnim zglobo!ima
?$'&+"&/#/, */< &$,/," !+*')'7," G*8282S)H ," /\L]L]L\S #&(&/, *')'4&8 B'*&4/,
&+"&/# ( ," /. \ O #&(&/, *')'4& &$ & #$, #&(&/ *')'4& +3)& G')$#/ '' ' GAH GAAH ,
GAAAHH8
a% b%
Sl. 2.3. 7esingularan i singulalaran polo/aj robota
U&./,!"& '4 ',. & /. ^ / #8 '4 ',. & +3)& /&, #&(&/, *')'4& /!,7"' ,/+3*$/,""&./,!"," '/& '4 ',. +3),# /&" #8 /. \ / /!,7"' /&,/+3*$/,"8 = ($,"&$3 *,&
282) ($,!/ 3 47 "&./,!" &4/ ', & #*/' /&,/+3*$/ , 4$3+, ', & #*/'
,/+3*$/8 U&@3#," 3'),&/' & 4 3 "&./,!", $')'# /&,/+3*$/, '," 3 /&," ('&)/,"
('*'6," 4 ('#3 ,/+3*$/,8 B'"#$"' ($,"&$ $')'# ($,!/'+ / *,<, 28L08 9'4 '7'+
*/< & / - O8 94 & $')'# /4& 3 ('*'63 GH #4 /&+'7 .7#* "'6& 4 & ('"&$ , ')$%& 37," ($7<," G#$, #$/*<,& , #$, $'#<,&H #8 / . \O \ / ( & "&./,!" /&,/+3*$/8 U&@3#,"
4 & $')'# 3 ('*'63 G)H #4 .7#* /& "'6& 4 & ')$%& '' 7'& '& G*H8 C*& / . ^ / ,"&./,!" & ,/+3*$/8 ?$&) '> ,#%, 4 7, $')'# ,, */< ," 7,>& '4 O #&(&/, *')'4& G/ _
OH "'$ 37& ),#, ,/+3*$/ &$ & 8 B,#/& ,/+3*$/'#, & 76/' &$ 4 & /4& 3
,/+3*$/'" ('*'63 $')'# 7''" .7#*'" /& "'6& /($7,#, '/& ('$&#& '& ), ,/& "'+'
', "'+3 ),#, ('#$&)/,8
1
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 20/22
T/*,!,$"' 4 "'+3%/'# $')'# 4 ')7, '4$&@&/& "/,(3*<,'/& !4#&8C&,/,>,"' ($7' /&&
/&'(.'4/& ('"'7&8
- B'!,<,'/,$/& ('4$!3"&7 4'7'@&/& 7$. .7#*& 3 6&*&/3 #3 $4/'+ ($'#'$8
Sl. 2.31. Potpuna orijenta#ija
- B'#(3/ '$,&/#<, .7#*& ('4$!3"&7 ('#7*/& .7#*& 3 #/' '4$&@&/, 3+*'7/, ('*'6
3 ($'#'$38 B'#(3/ '$,&/#<, "'6& & ('"#$#, / *&4&%, /,/8 ;.#&7 & 4 & '4$&@&/ '
.7#*& ,*, $4/'+ ($&4"&# ('*'(, 6&*&/," ($7<&" 3 ($'#'$3 , '> & !4& 3+' ')$#/
.7#*& '' #'+ ($7<8 N*, 28L1 ,*3#$3& ('#(3/3 '$,&/#<,38 D3 ($&4"&# G`H #$&) ('*'(,#,
($7<&" '#7'$ G`aH , '> ($&4"&# ')$/3#, '' '& ! 3+' 4 ), & ,(3(&/& / )'/' #$/,
($&4"&# ('#7,*' /($" 6*&) 3 '#7'$38 ?4 & #& ($&4"&# "'6& 37&#, 3 '#7'$8
C&*,",/ '$,&/#<, ('4$!3"&7 "' 4 & '4$&@&/ ' .7#*& ,*, $4/'+ ($&4"&# ('*'(,
6&*&/," ($7<&" 3 ($'#'$38
R!*, ,!"&@3 4&*,",/& , ('#(3/& '$,&/#<,& ($,!/ & / *,<, 28L28 / ($,"&$3 ($&/'>&/
'/#&/&$ #&/'>%38= *33 GH 76/' & &4,/' 4 ' G`H)34& 7&$#,*/ '4/'/' 3 (,#/3 &
4&*,",/ '$,&/#<,8 = *33 G)H 76/ & /& "' ' G`H /&+' , ' G``H ' "'$ !3!&#,6&*&/, ($7<8 94 & ($7< G`H '4$&@&/ '/4 ('*'6 ($7< G``H "'6& ),#, 4&,/,/ 3+*'"
')$#/ '' '& G`H8 = (,#/3 & ('#(3/ '$,&/#<, '/#&/&$8M&>#' *,/' "'6&"' 3',#, , 3
!4#3 ($,!/'" / *,<, 28L18 = (,#/3 & ('#(3/ '$,&/#<, !)'+ ,#3$&/'+ 4&* (' 436,/,<,*,/4$ ', #$&) 4 & ('*'(, )'/," 6*&)'" / $36/'" '#7'$38 94 #7'+ ,#3$&/'+ 4&*
/& ), ),*' #8 4 ), & <,*,/4$,/ ($&4"&# 37*,' 3 <,*,/4$,/ '#7'$ #4 ), ),*' 4'7'*/' ('*'(,#,
'& ($&4"&# , '#7'$ '4/'/' 4'7'*/ ), ),* 4&*,",/ '$,&/#<,8
1S
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 21/22
Sl. 2.32. -elimična i potpuna orijenta#ija
C*& 4 +'7'$,"' ' '$,&/#<,, #4 $!",>*"' ' &4/'" ($7<3 3 ($'#'$3 , 3+*3 ')$#/ ''
/&+8 ?7 ($,#3( & ('+'4/ &$ 3 ($#,/'" 4&,/,/3 !4# 3+*7/'" "'6&"' 3',#, /&3
'3 ,, & ($7< 76/ 3 '/$&#/'" !4#38 C'7'*/' & ('"#$#, ($,"&$& / *," 28L18 ,
28L2 , *' 3',#, ),#/& ($7<& G`H8 N*,/' & ($,"&$," / *,<, 28L8R!/,"' 4 ('"V7$.V .7#*&8? ('" ('4$!3"&7 '4$&@&/3 !4#3 #3 .7#*& ,*, /&'+ 4$3+'+ !7$>/'+
3$&@8
?' & 37& '/ # ,& & 4'7'@&/& 3 '4$&@&/, ('*'6 ),#/' 3 '/$&#/'" !4#38 M ($,"&$ ($,
.7#/3 ($&4"&# ),#/' & ('!,<,'/,$#, #3 T ($,!/3 / *,<, 282Q8 94 & $4/, ($&4"&# 37*,
3 '#7'$ ),#/' & ('!,<,'/,$#, 7$. ($&4"&# G# T / *,<, 28L18H8 = *33 $)/ ($/&" ('!,<,'/,$ & 7$. (,>#'* ! ($/& 3 *33 !7$,7/ 7$. !7$,7,. *&>#8
D!/,"' /! )$' #&(&/ , *')'4& ', & ('#$&)/ ! ,!7$>&/& '4$&@&/'+ "/,(3*<,'/'+
!4#8
; 7*@,7/& !4# ('!,<,'/,$/ ('#$&)/' & L #&(&/ *')'4& #8 /! \ L8
; 7*@,7/& !4# ('!,<,'/,$/ !&4/' 4&*,",/'" '$,&/#<,'" ('#$&)/' & L ] 2'4/'/' 5 #&(&/, *')'4& G/! \ 5H8
; 7*@,7/& !4# ('!,<,'/,$/ !&4/' ('#(3/'" '$,&/#<,'" ('#$&)/' & L ] L
'4/'/' O #&(&/, *')'4& G/! \ OH8
C ), $')'# "'+' 3(&>/' ,!7$>,#, ('#7*&/, !4# ('#$&)/' & , 4'7'*/' 4 )34& 8D),/' & /. \ / 3 *33 +'7'$,"' ' $&43/4/#/'#, $')'# 3 '4/'3 / ('#7*&/,
!4#8 C*& $&43/4/#/'# ('4$!3"&7 V7,>V #&(&/, *')'4& .7#*& G/.H 3 '4/'3 /
/"/, )$' ('#$&)/ ! ,!7$>&/& !4# G/!H8
D 7,>3 #&(&/, *')'4& "'6&"' +'7'$,#, , 3 *33 ,/+3*$/'#,8 ?4 & / _ /. '4/'/'
"&./,!" G/H ," 7,> 3 '4/'3 / .7#*3 G/.H8 A 3 '7'" *33 "'+*, ),"' +'7'$,#, '
$&434/#/#'#,8 U&@3#," ' & $')'# ,/+3*$/ "' 3 /&," ('*'6," #4 ,!)&+7"' #&$",/$&43/4/#/'#, &$ "&./,!" /,& /"&$/' ($'&#'7/ 4 ," 7,> #&(&/, *')'4& 7&% & # 7,>
('*&4,< "/,7/ "'+3%/'#, $&#/ .7#*& GV+3)*&/&V #&(&/, *')'4&H >#' ($&4#7*
/&6&*&/3 ,#3<,38 T' & ( $')'# ($'& /"&$/' #' 4 #*/' )34& ,/+3*$/ , 4 ,"7,> #&(&/, *')'4& / ($,"&$ $')'# *,& 282) #4 '$,#,"' #&$",/ $&43/4/#/, $')'#8 N*,/'
& $')'#," ', ,"3 / _ O , ', 3 37& ,/+3*$/, !)'+ ( 4*& , $&43/4/#/,8
20
8/16/2019 Seminarski Rad-Kinematika Robota
http://slidepdf.com/reader/full/seminarski-rad-kinematika-robota 22/22
94 & 3 (,#/3 /"&$/ $&43/4/#/'# #4 & '),/' $4, ' /&'*,' <,*&7 ', & 6&*& ('#,%,8
Y&4/ '4 <,*&7 & ('#,!/& 7&*,,. )$!,/ , #4 & '),/' ($'! #!78 ($*&*/, #&(&/, *')'4&
G*8282)H8 C$3+, <,* & ,!)&+7/& /&6&*&/& ,/+3*$/'#,8 94 $')'# 4'@& 3 ,/+3*$/, ('*'6 #8
/. #$(, +3),# #4 & #,7,$ 7,> #&(&/, *')'4& "&./,!" ,"& & '),/' +3),# "'6&'"(&/!,$#,8 ?$&%, <,* ($'&#'7/ $&43/4/#/,. $')'# & #7$/& ('')/'#, ,!)&+7/
($&($&8 ?4 $')'# "'6& 4 !'),@& ($&($&3 4 ($, #'"& /&+'7 .7#* !4$6, ('!,<,3 ,
'$,&/#<,3 /&'(.'4/3 ! ,!7$>&/& !4#8 =3(/' '4 7,. /"&$/' $&43/4/#/,. $')'# ($')*&"7,> #&(&/, *')'4& $!$&>7 & 37'@&/&" 4'(3/,. !.#&7 '," & 3('>*7 7,>8
M&>#' 4$3+,, ($')*&" 7* & 4 & $')'# , .7#* ," /. #&(&/, *')'4& /+63& 3!4#3 ', & "'6& ')7,#, , "/& G4*& /! ^ /.H8 ?4 & ($')*&" 7,> #&(&/, *')'4& $&>7
37'4*&/&" $!*,,#,. $,#&$,3" '(#,"*/'#,8
M'/ '7,. 4&,/,<, , 4,3, ' ,/+3*$/'#, , $&43/4/#/'#, 37&4,"' /& '+$/,&/ ',.
%&"' & 3 '7' /,!, 3+*7/'" 4$6#,8 C/>/, $')'#, ($&#&6/' & ($'! ' /&,/+3*$/,
'4/'/' ,/+3*$/, 3 "' 3 /&," (&<,*/," ('*'6,"8 C*& 3 /'$"*/'" $43 & /. \ / ,
!#' +'7'$,"' ' #&-(&/," *')'4& $')'# /& ($&<,!,$3%, 4 *, ",*,"' / "&./,!" ,*, .7#*38
D7' 76, ! 8 ?4 '$,#,"' '!/3 / ('4$!3"&7"' /. \ /8 9'4 $')'# / _ O #&(&/,*')'4& ('4$!3"&7%&"' /. \ O , '$,#,%&"' #&$",/ $&43/4/#, $')'#8 C/ & $')'#, 3+*7/'"
($'! #' 4 ,"3 K5 ,*, O #&(&/, *')'4&8 R')'# &#,$, #&(&/ *')'4& "'6& 4 ')7, ('!,<,'/,$/& ! ># & ('#$&)/' #$, #&(&/ *')'4& ($&'#*," $#," #&(&/'" *')'4& 7$>,
4'(3/ $&#/ >#' & 4'7'*/' ! ,!7$>&/& /&,. &4/'#7/,,. "/,(3*<,'/,. !4# 3
($,8 ?' 3 '),/' !4<, ($&/'>&/ ($&4"&# '(*36,7/ ($& , *,/'8 R')'# (&# #&(&/,*')'4& "'6& 4 ,!7$>, !4# ('!,<,'/,$/ !&4/' 4&*,",/'" '$,&/#<,'"8 ?3 (43 /
($,"&$ !4<, ($&/'>&/ #&/'#, G*828L2H &4/'#7/,, !4<, "'/#6& !7$,7/ , *,/'8
R')'# >&# #&(&/, *')'4& 3 ($,/<,(3 "'6& 4 ,!7$>, ),*' 7 "/,(3-*<,'/, !4# &$ & '/37& "'6& 7&#, / ($')*&" ('!,<,'/,$/ !&4/' ('#(3/'" '$,&/#<,'"8 ?' 3 / ($,"&$
*'6&/,, !4<, ($&/'>&/ G*828L2)H "'/#6& G*828L1H !7$,7/ , *,/'8
21