Protesis de Rehabilitacion.

November 24, 2022 | Author: Anonymous | Category: N/A
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xi

 

\)2/) `8cl8 ")$)(%#$A,%&(), #/#*#1%+, #/#(%$71&(+,88888888888888888888888 88888888888888888888888888888888888888888 8888888888888888888 f` \)2/) `8ce8 "+,%+, 4# *)%#$&)/#,8 88888888888888888888888 8888888888888888888888888888888888888888888888 8888888888888888888888888888888888888888888888 88888888888888888888888 fc \)2/) `8ci8 "+,%+, 4# '')2$&()(&718 )2$&()(&718 8888888888888888888888 888888888888888888888888888888888888888888888 8888888888888888888888888888888888888888888888 88888888888888888888888 fd \)2/) `8cf8 "+,%+ 4# #/#*#1%+, 1+$*)/&T)4+,8 8888888888888888888888 888888888888888888888888888888888888888888888 88888888888888888888888888 888 fl \)2/) `8cg8 "+,%+ 4# #/#*#1%+, #/#(%$71&(+, 88888888888888888888888888888888 888888888888888888888888888888888888888888888888888 8888888888888888888 fe \)2/) `8dh8 "+,%+, &14&$#(%+,8 888888888888888888888888888888888888888888888 8888888888888888888888 8888888888888888888888888888888888888888888888 888888888888888888888888888888 8888888 fe \)2/) `8d_8 "+,%+ %+%)/#,8 888888888888888888888888888888888888888888888888888888888888888888888888888888888 fi \)2/) `8d`8 B$+%+(+/+ 4# 0$.#2), mB$.#2) _n 888888888888888888888888888888888888888888888888 8888888888888888888888888 88888888888888888888888888 888 gd \)2/) `8dc8 B$+%+(+/+ 4# 0$.#2), mB$.#2) `n8 88888888888888888888888888888888888888888888888 888888888888888888888888 88888888888888888888888888 888 gl \)2/) c8_8 ")$)(%#$A,%&(), 4# 0)(%#, #6)/.)4+,8 888888888888888888888888888888888888888888 88888888888888888888888 8888888888888888888 gf \)2/) c8`8 "+*0)$)(&71 4# /), ()$)(%#$A,%&(), 4#/ 0$+%+%&0+ (+1,%$.&4+ (+1 >:DbJ? : H #/ 4&,#X+ 0$+0.#,%+8 888888888888888888888 88888888888888888888888888888888888888888888 888888888888888888888888888888888888888888 8888888888888888888 gg \)2/) d8_8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 0)$) #/ *74./+ _8 8888888888888888888888888 _he \)2/) d8`8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# #$;+1+*A) m*74./+ _n8  88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _he \)2/) d8c8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ ($&% #$&+ 4# )3.,%# m*74./+ _n888 _he \)2/) d8d8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# 4.$)2&/&4)4 m*74./+ _n8  88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hi \)2/) d8l8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# #,%)2&/&4)4 m*74./+ _n8  88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hi \)2/) d8e8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ ($&% #$&+ 4# (+,%+ m*74./+ _n8 888 _hi \)2/) 0#,+ #,0#(A'&(+ #,0#(A'&(+ 4#/ 0)$)($&%#$&+ #/ *74./+ `8 8888888888888888888888888 _hi \)2/) d8i8 d8f8 L6)/.)(&71 L6)/.)(&71 4#/ 4#/ 0#,+ 4# )4)0%)2&/&4)4 m*74./+ `n8 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hf \)2/) d8g8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ (+1%$+/ m*74./+ `n8 88888 _hf \)2/) d8_h8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# (+,%+ m*74./+ `n8 8 _hf \)2/) d8__8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# '.1(&+1)/&4)4 m*74./+ `n8 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hf \)2/) d8_`8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# $#,&,%#1(&) m*74./+ `n8 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hg \)2/) d8_c8 L6)/.)(&71 4#/ 0#,+ #,0#(A'&(+ 4#/ ($&%#$&+ 4# %)*)X+ m*74./+ `n8  88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 _hg

xii

 

1"#%3"N) *)1+ 0.#4# 6#$,# )'#(%)4) 0+$ 0)%+/+;A), %$).*)%+/7;&(), Hu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o#Y%#1,&71 4)(%&/)$ #1 /), %$#, ')/)1;#, 4# /+, 4#4+, 4# /) *)1+5 ,&1 &1(/.&$ #/ 0./;)$5 #1 .1 $)1;+ )$%&(./)$ #1%$# h H eh ;$)4+,8 L,%# 0$&*#$ 0$+%+%&0+ 0$#,#1%) .1 0#,+ 4# dlh ;$)*+,5 %# .1) 4&*#1,&71 4# _l (* Y g (* Y e (* H '.1(&+1) (+1 .1) '.#1%# 4# _` @ H l J8 N) (+1,%$.((&71 4# .1 0$&*#$ 0$+%+%&0+ 0#$*&%&7 &4#1%&'&()$ $#-.#$&*%+, 4# 4&,#X+ H +0%&*&T)(&71 4#,($&%+, #1 #,%# %$)2)3+8 N) #6)/.)(&71 4#/ 0$&*#$ 4&,0+,&%&6+ ,# $#)/&T7 ) 0)$%&$ 4# 0$.#2), #1 0)$%&(&0)1%#, ,)1+, -.# 1+ 0$#,#1%)2)1 1&1;.1) 0)%+/+;A)8 "+1,&4#$)$ $#-.#$&*%+, (+*+ )*0/&)$ #/ $)1;+ 4# '/#Y+o#Y%#1,&715 *#3+$)$ /) )4)0%)2&/&4)4 ) 4&'#$#1%#, *#4&4), )1%$+0+*K%$&(), 4# /) *)1+ # &1(/.&$ .1 ,&,%#*) *+4./)$ &1%#$()*2&)2/# 0)$) /), *)1+, 4#$#(C) # &T-.&#$4) /# 4)1 .1) *)H+$ '.1(&+1)/&4)4 )/ 4&,0+,&%&6+ 0$+0.#,%+8 J,A5 #/ ,&,%#*) 0.#4# ),&,%&$ 4# *#3+$ *)1#$) #/ 0$+(#,+ 4# $#(.0#$)(&71 #1 4&'#$#1%#, )0/&()(&+1#, 4# $#C)2&/&%)(&71 'A,&()8 (JUJTHJ] PUJBAQ O#C)2&/&%)(&715 7$%#,&,5 4#4+,8 

xiii

 

':#+1'$+ \C# C)14 *)H 2# )''#(%#4 2H %$).*)%&( 0)%C+/+;&#, )14u+$ &13.$&#, %+ %C# 0#$&0C#$)/ 1#$6+., ,H,%#*8 O#C)2&/&%)%&+1 ),,&,%#4 2H *#(C)%$+1&( 4#6&(#, ()1 $#,%+$# %C# '.1(%&+1)/&%H +' )1 &13.$#4 /&*2 +$ 0$#6#1% %C# 4#;#1#$)%&+1 +' %C# C)14 *+%+$ )00)$)%.,8 \C# 0$#,#1% ,%.4H 4#,($&2#, %C# 0$+0+,)/ +' $#4#,&;1 )14 +0%&*&T)%&+1 +' )1 #Y+,S#/#%+1 '+$ C)14 $#C)2&/&%)%&+15 2),#4 +1 ) *+4./)$ )14 #$;+1+*&( (+1'&;.$)%&+18 D#,&;1 0)$)*#%#$, )$# 4#'&1#4 '$+* #1;&1##$&1; ($&%#$&) )14 C)14o*+6#*#1% S&1#*)%&( ;.&4#/&1#, '+$ 0),,&6# 3+&1% $#C)2&/&%)%&+18 \C# (+1(#0%.)/ 4#,&;1 )14 0$+4.(% ,0#(&'&()%&+1, )$# 4#%#$*&1#4 ), 0)$% +' ) (+**.1&%Ho#1;);#*#1% 0$+3#(%5 &1 (++0#$)%&+1 t&%C 0$+'#,,&+1)/, &1 0CH,&+%C#$)0H )14 0CH,&()/ $#C)2&/&%)%&+1 )$#),8 \C# $#4#,&;1 &, ()$$ +.% '$+* ) '&$,% 2.&/% 0$+%+%H0# ()0)2/# +' %$)1,*&%%&1; '/#Y&+1 )14 #Y%#1,&+1 *+6#*#1%, %+ %C# %C$## 0C)/)1;#, +' %C# C)14 '&1;#$,5 1+% &1(/.4&1; %C# %C.*25 &1 ) 3+&1% $)1;# 2#%t##1 h )14 eh 4#;$##,8 \C# (+1,%$.(%&+1 +' %C# '&$,% 0$+%+%H0# #1)2/#4 ., %+ &4#1%&'H 4#,&;1 )14 +0%&*&T)%&+1 $#-.&$#*#1%, 4#,($&2#4 &1 %C&, 0)0#$8 "+1,&4#$&1; $#-.&$#*#1%, ,.(C ), #Y%#14&1; %C# $)1;# +' '/#Y&+1o#Y%#1,&+15 &*0$+6&1; %C# )4)0%)2&/&%H %+ 4&''#$#1% )1%C$+0+*#%$&( *#),.$#*#1%, +' %C# C)14 )14 &1(/.4&1; )1 &1%#$(C)1;#)2/# *+4./)$ ,H,%#* '+$ %C# $&;C% )14 /#'% C)14 ;&6# ) ;$#)%#$ '.1(%&+1)/&%H %+ %C# 0$+0+,#4 4#6&(#8 \C.,5 %C# ,H,%#* ()1 2#%%#$ ),,&,% %C# $#(+6#$H 0$+(#,, &1 4&''#$#1% 0CH,&()/ $#C)2&/&%)%&+1 )00/&()%&+1,8 ?A^_VHO]Q O#C)2&/&%)%&+15 +$%C+,&,5 '&1;#$,8

xiv

 

5/*#"6) 7 $)-#+1%$$*8- /" %-' 81+"#*# 3"$'+18-*$' ('1' 1"9':*&*+'$*8- /" &)# /"/)# +1*.'&4-0*$)# /" &' 3'-); *-+1)/%$$*8L1 $#/)(&71 ) /) $#C)2&/&%)(&71 (+16#1(&+1) (+16#1(&+1)/5/5 #/ .,+ 4# 7$%#,&, *#()%$71&(), &1($#*#1%) /) %),) 4# $#(.0#$)(&71 *+%+$) 4# 0)(%#, ($71&(+, p_q8 L,%# %&0+ 4# 4&,0+,&%&6+, 4&,0+,&%&6+ , 4#2#1 0#$*&%&$ #/ ,#;.&*%+ 4# %$)H#(%+$&), 1)%.$)/#, ;#1#$)4), 0+$ /+, 4#4+, 4# /) *)1+8 @)$&+, 4&,0+,&%&6+, 0$#,#1%)1 .1 $)1;+ )$%&(./)$ -.# $#,%$&1;# /) '/#Y+o#Y%#1,&71 %+%)/ 4# /+, 4#4+, p`5 cq8 V1+ 4# /+, *)H+$#, $#%+, #1 #/ 4#,)$$+//+ 4# 7$%#,&, 0)$) $#C)2&/&%)(&71 4# /+, 4#4+, 4# /) *)1+ #, /) #$;+1+*A)8 N) *)H+$A) 4# 4&,0+,&%&6+, 4# $#C)2&/&%)(&71 1+ &1(/.H#1 #1 ,., *#()1&,*+, /) ()$)(%#$A,%&() 4# )4)0%)$,# ) 4&,%&1%), *#4&4), )1%$+0+*K%$&(), pdq8 ]%$+ ')(%+$ &*0+$%)1%# #1 #/ 4&,#X+ 4# *#()1&,*+, 0)$) $#C)2&/&%)(&71 #, /) *+4./)$&4)48 N+, *#()1&,*+, 4&,#X)4+, 4#2#1 0#$*&%&$ )4)0%)$,# %)1%+ ) /) *)1+ &T-.&#$4) (+*+ 4#$#(C)8 B+$ %)1%+5 #/ %$)2)3+ 0$+0.#,%+ 0/)1%#) #/ 4#,)$$+//+ 4# .1 *#()1&,*+ -.# ,# )4)0%# ) 4&6#$,), *#4&4), )1%$+0+*K%$&(), 4# /+, 4#4+, %$&')/I1;&(+, 4# /) *)1+5 1+ ;#1#$# $#,%$&((&+1#, #1 #/ $)1;+ )$%&(./)$ 1)%.$)/ 4# /+, 4#4+, 4# /) *)1+5 # &1(/.H) .1 ,&,%#*) *+4./)$ -.# '.1(&+1# 0)$) /) *)1+ 4#$#(C) # &T-.&#$4)8

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  "+*0)$)$ #/ $)1;+ ) )$%&(./)$ $%&(./)$ 0#$*&%&4+ 0+$ #/ 4&,0+,&%&6+ 4&,#X)4+5 (+1 #/ +2%#1&4+ #1



#/ *+4#/+ (&1#*I%&(+ &*0/#*#1%)4+8 1

 

LE 3'1$) +"81*$) LELE (UJDIAJbCADIV OAU NHVTUAbJ N+, 4#4+, 4# /) *)1+ 0.#4#1 6#$,# )'#(%)4+, 0+$ #1'#$*#4)4#, %$).*)%+/7;&(), Hu+ /#,&+1#, #1 #/ ,&,%#*) 1#$6&+,+ 0#$&'K$&(+8 O#C)2&/&%)(&71 H '&,&+%#$)0&) ,+1 '.14)*#1%)/#, 0)$) $#(.0#$)$ /) *+%$&(&4)4 H ,#1,&2&/&4)4 &1%#;$)/ 4# /+, 4#4+, %$&')/I1;&(+, 4# /) *)1+5 #1 (+$$#,0+14#1(&) )/ %&0+ 4# )'#((&71 #1 %$)%)*%+ plq8 N) $#C)2&/&%)(&71 ),&,%&4) 0+$ 7$%#,&, *#()%$71&(), 0#$*&%# $#(.0#$)$ /) '.1(&+1)/&4)4 4# .1 *&#*2$+ /#,&+1)4+ H #6&%) /) 4#;#1#$)(&71 4#/ )0)$)%+ *+%$&T 4# /) *)1+ peq8 L/ +23#%&6+ 4# #,%# %$)2)3+ #, 4&,#X)$ H (+1,%$.&$ .1) 7$%#,&, 0)$) $#C)2&/&%)(&71 4# /+, 4#4+, %$&')/I1;&(+, 4# /) *)1+8 L1 #/ (),+ 4# (#1%$+, 4# '&,&+%#$)0&) H $#C)2&/&%)(&71 'A,&() #1 L(.)4+$5 #Y&,%# /) 1#(#,&4)4 4# $#4.(&$ (+,%+, +0#$)%&6+, *#4&)1%# #/ .,+ 4# 4&,0+,&%&6+, ).%+*)%&T)4+, 4# 2)3+ (+,%+8 L/ (#1%$+ 4# '&,&+%#$)0&)5 $#C)2&/&%)(&71 H %#$)0&) 'A,&() P:ML\:P]v #, /) +$;)1&T)(&71 (+/)2+$)4+$) #1 #/ 0$+H#(%+ 4# 6&1(./)(&71 4#/ (.)/ #,%) &1&(&)%&6) '+$*) 0)$%#8 V1 0$+H#(%+ 4# 6&1(./)(&71 ,+(&)/ 0$#%#14# )%#14#$ 0$+2/#*), 4# /) ,+()45 (+1 /) 0)$%&(&0)(&71 4# .1) #1%&4)4 #Y%#$1) ) /) .1&6#$,&4)4 H #,%.4&)1%#, #1 )(%&6&4)4#, (/)$)*#1%# $#/)(&+1)4), (+1 ,. ()$$#$) 3.1%+ ) /) ;.A) 4# 0$+'#,+$#,8 P:ML\:P]v5 (+1 #/ +23#%&6+ 4# )*0/&)$ ,. ()0)(&4)4 4# )((&71 0)$) /) )H.4) ) 0+2/)(&+1#, 6./1#$)2/#,5 &4#1%&'&() #1 /) $#4.((&71 4# (+,%+, +0#$)%&6+, /) 0$&1(&0)/ *+%&6)(&71 *+%& 6)(&71 0)$) ,. 6&1(./)(&71 )/ 0$+H#(%+8 "+*+ 0)$%# 4#/ 0$+H#(%+ 4# 6&1(./)(&71 B@?o`h_ioh__5 #/ %$)2)3+ 0$+0.#,%+ ,# (+*0/#*#1%)$I (+1 +%$+, 0$+H#(%+, 4# %&%./)(&71 4#,)$$+//)4+, #1 /) Z)(./%)4 4# :1;#1&#$A) >#(I1&()5 (+1 #/ +23#%&6+ 0$&1(&0)/ 4# 0$+4.(&$ #/ 0$+%+%&0+ &1&(&)/ 4# .1 #Y+#,-.#/#%+ 0)$) $#C)2&/&%)(&71 4# *)1+8 N+, 0$+H#(%+, (+1 /+, (.)/#, #,%# %$)2)3+ 4# %&%./)(&71 %# $#/)(&71 &1(/.H#1a #/ 4&,#X+ H (+1,%$.((&71 4# .1 #Y+#,-.#/#%+ 0)$) $#C)2&/&%)(&71 4#/ 4#4+ 0./;)$5 #/ #,%.4&+ (&1#*I%&(+ 4# /) *)1+5 #/ (+1%$+/ 4# .1 #Y+#,-.#/#%+ 0)$) $#C)2&/&%)(&71 0),&6) H )(%&6) 4# *)1+5 H /) *#4&(&71 4# '.#$T), #1 /), ')/)1;#, 4# /+, 4#4+, 4# /) *)1+8

LEZE 0ADAHJUCOJOA] OA bJDVQ JDJIVbaJ ^ NJIVUVRaJ] LEZELE 'DJIVbaJ OA OA UJ bJDV LEZELELE

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ZEdE (HA]ADIJPCfD ^ ]AUAPPCfD OA JUIAHDJICBJ] ZEdELE 3fOGUV] OA UJ fHIA]C]  J 0)$%&$ 4#/ )1I )1I/&,&, /&,&, '.1(&+1)/ ,# 4#%# 4#%#$*&1)$+1 $*&1)$+1 ` *74 *74./+, ./+, (+ (+1 1 /+, (.)/#, 4#2#$I (+1%)$ /) 7$%#,&, 0)$) 4#4+, %$&')/I1;&(+,8 L,%+, *74./+, 3.1%+ (+1 ,. '.1(&71 0$&1(&0)/ H /), $#,0#(%&6), ,.2'.1(&+1#, ,# *.#,%$)1 #1 /) \)2/) `8_8

ZEdEZE #VUGPCVDA] 3fOGUV L D# )(.#$4+ (+1 #/ 4&);$)*) '.1(&+1)/5 #,%# *74./+ (.#1%) (+1 c ,.2'.1(&+1#,a   J3.,%)$ 7$%#,&, ) /) *.X#()



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26

 

ZEdEZELE '`G]IJH fHIA]C] J UJ bGiAPJ 'UIAHDJICBJ L N) )/%#$1)%&6) _ *+,%$)4) #1 /) Z&;.$) `8e H Z&;.$) `8i &1(/.H# #/ ,+0+$%# 0)$) )3.,%)$ /) 7$%#,&, ) /) *.X#()8 L,%) )/%#$1)%&6) 0$#,#1%) #1 ,. 2),# .1) #,0+13) 0)$) *#3+$)$ #/ (+1%)(%+ (+1 /) ,.0#$'&(&# 4# /) 0&#/8 J4#*I,5 &1(/.H# (+$$#), -.# 0.#4#1 ,#$ )3.,%)4), 0)$) -.# ),A #/ ,+0+$%# -.#4# '&3+8

Z&;.$) `8e8 J3.,%# *.X#() r J/%#$1)%&6) _ m@&,%) &,+*K%$&()n8 mZ.#1%#a B$+0&)n

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27

 

Z&;.$) `8f8 J3.,%# *.X#() r J/%#$1)%&6) ` m@&,%) &,+*K%$&()n8 mZ.#1%#a B$+0&)n

Z&;.$) `8g8 J3.,%# *.X#() r J/%#$1)%&6) ` m@&,%) /)%#$)/n8 mZ.#1%#a B$+0&)n

ZEdEZEZE 1ARGUJH hDRGUV bGiAPJ L1 /) Z&;.$) `8_h ,# 0$#,#1%) #/ *#()1&,*+ 0)$) $#;./)$ /) 0+,&(&71 4# /) *.X#()8 L,%# *#()1&,*+ &1(/.H# %$#, 0)$%#, 0$&1(&0)/#,8 N) 0$&*#$) H *I, /)$;) #, /) -.# ,#$6&$I (+*+ .1&71 )/ ,+0+$%# #1 /) *.X#()8 N) ,#;.14) #, /) #1()$;)4) 4# ,#$ /) .1&71 )/ ,+0+$%# 4# /) *)1+8 Z&1)/*#1%#5 /) %#$(#$) +(.0) ,. #,0)(&+ #1%$# /), 4+, 0&#T), )1%#$&+$#, H ,&$6# 0)$) 4)$/#, $+%)(&718 L1 (+13.1%+ #,%) ,+/.(&71 0#$*&%# 4)$/# $+%)(&71 #1 '/#Y+o#Y%#1,&71 H )24.((&71o)4.((&71 ) /) *.X#()8

Z&;.$) `8_h8 >#()1&,*+ 0)$) $#;./)$ I1;./+ *.X#()8 mZ.#1%#a B$+0&)n 28

 

ZEdEZEdE '`G]IJH fHIA]C] J UJ bJDV B)$) )3.,%)$ (+$$#(%)*#1%# (+$$#(% )*#1%# /) 7$%#,&, ) /) *)1+ ,# 0$#,#1%) /) ,+/.(&71 ,+/.(& 71 #1 /) Z&;.$) `8__ H Z&;.$) `8_`8 L,%# ,+0+$%# ,# &1(+$0+$) #1 /) *)1+ *#4&)1%# .1) (+$$#) 4# 6#/($+8  J4#*I,5 0$#,#1%) 0$#,# 1%) .1) ,.0#$'&(& ,.0#$'&(&# # 4# #,0+13) 0)$) * *#3+$)$ #3+$)$ /) #$;+ #$;+1+*A) 1+*A) 4#/ 4&,0+, 4&,0+,&%&6+8 &%&6+8

Z&;.$) `8__8 ?+0+$%# *)1+ m@&,%) &,+*K%$&()n8 mZ.#1%#a B$+0&)n

Z&;.$) `8_`8 ?+0+$%# 4# *)1+ m@&,%) /)%#$)/n mZ.#1%#a B$+0&)n

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29

 

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30

 

'UIAHDJICBJ Z

Z&;.$) `8_d8 >74./+ _ r )/%#$1)%&6) `8 mZ.#1%#a B$+0&)n

@#1%)3),a   N) (+$$#) 4# 6#/($+ /# 4) .1) *)H+$ #,%)2&/&4)4 H )3.,%# ) /) 7$%#,&, 4#2&4+ ) ,.



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31

 

ZEdEdELE 1ARGUJH RAVbAIHaJ OAU bAPJDC]bV 'UIAHDJICBJ L N) )/%#$1)%&6) _ *+,%$)4) #1 /) Z&;.$) `8_l 0$#,#1%) .1 4&,#X+ 4# 4+, #,/)2+1#, 0)$) #'#(%.)$ #/ *+6&*%+ 4# '/#Y+o#Y%#1,&71 4# /+, 4#4+,8 L/ 0$&*#$ #,/)271 (.#1%) (+1 d ,#((&+1#, *+,%$)4), *+,%$)4), #1 /) Z&;.$) `8_e N) ,#((&71 _ *I, * I, 0$7Y&*) ) /) 0)$%# ,.0#$&+$ 4# /) *)1+ 0#$*&%# $#)/&T)$ #/ *+6&*%+ 4# )24.((&71 H )4.((&71 ) /+, 4#4+, %$&')/I1;&(+,8 L1 #,%) ,#((&71 #, 4+14# ,# #,%)2/#(# /) (+1#Y&71 (+1 /) ,.2'.1(&71 d m%$)1,*&%&$ *+6&*%+ ) /+, 4#4+, %$&')/I1;&(+,n8 N), +%$), %$#, ,#((&+1#, 0$#,#1%)1 .1 *#()1&,*+ -.# 0#$*&%# $#;./)$ ,., 4&*#1,&+1#,8 >#4&)1%# 4+, %+$1&//+, m.2&()4+ #1 /) 0)$%# ,.0#$&+$ 4# /), ,#((&+1#, ` H dn /) ,#((&71 c -.#4) )3.,%)4) #1%$# /), ,#((&+1#, ` H d8 B)$) ).*#1%)$ #/ %)*)X+ 4#/ #,/)271 #, 1#(#,)$&+ 4#,)3.,%)$ /+, %+$1&//+, H 4#,0/)T)$ /) ,#((&71 c8 "+1 #/ '&1 4# $#4.(&$ /+, ;$)4+, 4# /&2#$%)$ H (+1%$+/)$ #/ *+6&*%+ 4# /) ')/)1;# 0$+Y&*)/ #,%# ,&,%#*) &1(/.H# .1 *#()1&,*+ 4# ,#;.&*%+ 4# %$)H#(%+$&)8 L,%# *#()1&,*+ )(%F) (.)14+ #/ ,&,%#*) 4# #,/)2+1#, $#)/&T) /) '/#Y&71 4#/ 4#4+8 ".)14+ #/ 4#4+ ,# #1(.#1%$) '/#Y&+1)4+ #1 (&#$%+ I1;./+5 /) ,#((&71 ` 4#/ #,/)271 _ ;#1#$) .1 (+1%)(%+ (+1 /) ')/)1;# 0$+Y&*)/8 L,%# (+1%)(%+ $#,%$&1;# #/ *+6&*%+ *+6&* %+ 4# 4&(C) ')/)1;#8 L,%# ,&,%#*) #,%I .2&()4+ #1 #/ #Y%$#*+ 4# /) ,#((&71 `8 B)$) (+1,#;.&$ /) )4)0%)2&/&4)4 4# #,%# ,&,%#*) ) 4&'#$#1%#, *#4&4), ,# .%&/&T) c #/#*#1%+,8 L,%+, #/#*#1%+, ,# *.#,%$)1 #1 /) Z&;.$) `8_i

Z&;.$) `8_l8 ?&,%#*) 0)$) $#;./)$ ;#+*#%$A) 4#/ *#()1&,*+ r )/%#$1)%&6) ` m6&,%) &,+*K%$&()n8 mZ.#1%#a B$+0&)n 32

 

Z&;.$) `8_e8 ?&,%#*) 0)$) $#;./)$ ;#+*#%$A) 4#/ *#()1&,*+ r )/%#$1)%&6) ` m6&,%) /)%#$)/n8 mZ.#1%#a B$+0&)n

Z&;.$) `8_i8 ?&,%#*) 4# )(%.)(&71 0),&6) r )/%#$1)%&6) ` m6&,%) /)%#$)/n8 mZ.#1%#a B$+0&)n

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33

 

Z&;.$) `8_f8 ?&,%#*) 0)$) $#;./)$ ;#+*#%$A) 4#/ *#()1&,*+ r )/%#$1)%&6) c m6&,%) &,+*K%$&()n8 mZ.#1%#a B$+0&)n

Z&;.$) `8_g8 ?&,%#*) 0)$) $#;./)$ ;#+*#%$A) 4#/ *#()1&,*+ r )/%#$1)%&6) c m6&,%) /)%#$)/n8 mZ.#1%#a B$+0&)n

ZEdEdEZE $VDAjCfD OA bAPJDC]bV J UV] OAOV] IHC\JUhDRCPV]

Z&;.$) `8`h8 L/#*#1%+ 0)$) (+1#Y&71 4#/ *#()1&,*+ ) /+, 4#4+, %$&')/I1;&(+,8 mZ.#1%#a B$+0&)n

34

 

L/ #/#*#1%+ *+,%$)4+ #1 /) Z&;.$) `8`h 0#$*&%# (+1#(%)$ #/ *#()1&,*+ 4# #,/)2+1#, ) /), ')/)1;#, 4# /+, 4#4+, %$&')/I1;&(+,8 B)$) )3.,%)$/+5 #,%# #/#*#1%+ %# .1) ()6&4)4 4+14# /) ')/)1;# 4&,%)/ #1%$) H -.#4) (+1 )0$&#%#8 J4#*I,5 #1 #,%) ()6&4)4 ,# #1(+1%$)$I1 #1(+1%$)$I 1 /+, ,#1,+$#, Z?O 1#(#,)$&+, 0)$) *#4&$ /) '.#$T) -.# #3#$(# #/ 4#4+8

ZEdEdEdE $VDIHVU OAU ]C]IAbJ L/ *74./+ ` $#-.&#$# 4# 4+, 6)$&)2/#, 4# (+1%$+/ 0$&1(&0)/#, 0)$) (+1%$+/)$ #/ ,#;.&*%+ 4# /), %$)H#(%+$&), 4# '/#Y+o#Y%#1,&71 4# /+, 4#4+, %$&')/I1;&(+,8 L,%), 6)$&)2/#, 4# (+1%$+/ ,+1a @)$&)2/# 4# (+1%$+/ _a (+1%$+/ 4# /) 0+,&(&71 4# /), ')/)1;#, @)$&)2/# 4# (+1%$+/ `a (+1%$+/ 4# '.#$T) #3#$(&4) 0+$ #/ 4#4+

Z&;.$) `8`_8 ?#1,+$ 4# '/#Y&718 mZ.#1%#a p`lqn

L/ 0$&*#$ 0)$I*#%$+ #, 1#(#,)$&+ %)1%+ #1 #3#$(&(&+, 0),&6+, (+*+ )(%&6+,8 N) 0+,&(&71 4# ()4) ')/)1;# ,# (+1%$+/) #1 '.1(&71 4#/ I1;./+ 4# ()4) .1) 4# ,., )$%&(./)(&+1#,8 B)$) (+1,#;.&$ #,%+ ,# .%&/&T) .1 ,#1,+$ 4# '/#Y&71 mZ&;.$) `8`_n )(+0/)4+ #1 ()4) )$%&(./)(&718 N) '+$*) 4# .2&()$ ()4) .1+ 4# #,%+, ,#1,+$#, #, *#4&)1%# #/ #/#*#1%+ *+,%$)4+ #1 Z&;.$) `8``8 L,%# #/#*#1%+ #,%I #/)2+$)4+ 4# .1 *)%#$&)/ #/I,%&(+ -.# ,# )3.,%) )/ 4#4+ 0)$) 0#$*&%&$ ) /) )$%&(./)(&71 '/#Y&+1)$,# ,&1 0$+2/#*) ) /) 6#T -.# /# ,&$6# 4# ,+0+$%# )/ ,#1,+$8 D#2&4+ )/ %)*)X+ 4#/ ,#1,+$ H %+*)14+ #1 (.#1%) #/ (+,%+ ,# +0%) 0+$ (+/+()$ .1 ,#1,+$ #1 /) ')/)1;# D:B H >"B #1 /+, 4#4+, ` H d H .1 ,#1,+$ #1 /) ')/)1;# B:B #1 /+, 4#4+, c H l8

35

 

Z&;.$) `8``8 L/#*#1%+ 0)$) )(+0/)$ #/ ,#1,+$ 4# '/#Y&718 mZ.#1%#a B$+0&)n

L/ ,#;.14+ 0)$I*#%$+ -.# (+1%$+/)$ #, 1#(#,)$&+ ,+/+ 0)$) #3#$(&(&+, )(%&6+,8 )(%&6 +,8 N) *)1#$) 0)$) (+1%$+/)$ /) '.#$T) #3#$(&4) 0+$ #/ 4#4+ #, (+1 #/ .,+ 4# ,#1,+$#, 4# '.#$T) + Z?O dh` mZ&;.$) `8`cn8 V1+ 4# #,%+, ,#1,+$#, ,# .2&() #1 /) 0)$%# ,.0#$&+$ 4# /) ')/)1;# H (+1%$+/) /) #Y%#1,&71 4#/ 4#4+8 ]%$+ ,#1,+$ #,%I .2&()4+ #1 /) 0)$%# &1'#$&+$ H (+1%$+/) /) '/#Y&71 4#/ 4#4+8 N) *)1#$) 4# )3.,%)$/+, #1 ()4) 4#4+ #, ) %$)6K, 4#/ #/#*#1%+ *+,%$)4+ #1 /) Z&;.$) `8`h8 L,%# #/#*#1%+ ,# )3.,%) )/ 4#4+ ;$)(&), )/ *&,*+ %&#*0+ -.# &1(+$0+$) )*2+, ,#1,+$#, 4# '.#$T)8 N) *)1#$) #1 /) -.# ,# )(+0/) ) /) *)1+ ,# *.#,%$) #1 /) Z&;.$) `8`d8

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36

 

Z&;.$) `8`d8 L/#*#1%+ 0)$) )(+0/)$ #/ ,#1,+$ 4# '/#Y&718 mZ.#1%#a B$+0&)n

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37

 

Z&;.$) `8`e8 >#()1&,*+ 0)$) ;#1#$)$ *+6&*%+ 4# 4#4+, %$&')/I1;&(+, r )/%#$1)%&6) _ m6&,%) ,.0#$&+$n8 mZ.#1%#a B$+0&)n

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38

 

Z&;.$) `8`f8 >#()1&,*+ 0)$) ;#1#$)$ *+6&*%+ 4# 4#4+, %$&')/I1;&(+, r )/%#$1)%&6) ` m6&,%) ,.0#$&+$n8 mZ.#1%#a B$+0&)n

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39

 

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110

 

 

yF= yF1; else else    xF = xF2; yF = yF2; end    end rF = [xF yF 0]; % PAR E alpha1=atan((yF-yA)/(xF-xA)); BF=((BC+CD)^2+(DE+EF)^2-(2*(BC+CD)*(DE+EF)*cos(alpha3)))^0.5; phi7=acos((-(BC+CD)^2+BF^2+(DE+EF)^2)/(2*(DE+EF)*BF)); phi9= pi-alpha3-phi7; phi10=alpha2-phi9;  AF=((xF-xA)^2+(yF-yA)^2)^0.5; phi11=acos((-(BF^2)+AF^2+AB^2)/(2*AB*AF)); phi8=pi-phi11-phi10; phi12=pi-phi7-phi8; % PAR E xE = xF + EF*cos(alpha1+phi12); yE = yF + EF*sin(alpha1+phi12); rE = [xF yF 0]; % PAR D xD = xE + DE*cos(alpha1+phi12); yD = yE + DE*sin(alpha1+phi12); rD = [xD yD 0]; % PAR C xC = xD + CD*cos(pi-alpha3+phi12+alpha1); yC = yD + CD*sin(pi-alpha3+phi12+alpha1); rC = [xC yC 0]; % PAR B xB = xC+(BC*cos(pi-alpha3+phi12+alpha1)); yB = yC+BC*sin(pi-alpha3+phi12+alpha1); rB = [xB yB 0]; %PAR G syms xG  xG yG  yG  eqnG1 = (xG-xF)^2+(yG-yF)^2-FG^2==0; eqnG2 = (xH-xG)^2+(yH-yG)^2-GH^2==0; solG = solve([eqnG1 eqnG2],[xG yG]); xGpos = solG.xG; yGpos = solG.yG; xG1 = double(eval(xGpos(1))); xG2 = double(eval(xGpos(2))); yG1 = double(eval(yGpos(1))); yG2 = double(eval(yGpos(2))); if if xG1>xH  xG1>xH xG = xG1; yG= yG1; else    else xG = xG2; yG = yG2; end    end rG = [xG yG 0]; phi4 = atan((yB-yC)/(xB-xC)); for for beta2=  beta2= beta2:-2.5*(pi/180):-90*(pi/180) beta3 = beta3 - 1.4444*(pi/180); % DEDOS %MCP  %MCP   xJ = 0; yJ = 0; rJ = [xJ yJ 0]; %PIP    %PIP xK = JK*cos(beta1); yK = JK*sin(beta1); rK = [xK yK 0]; %DIP %DIP    xL = xK + KL*cos(beta1+beta2); yL = yK + KL*sin(beta1+beta2); rL = [xL yL 0]; %PAR I xI = xL + LI*cos(beta1+beta2+beta3); yI = yL + LI*sin(beta1+beta2+beta3); rI = [xI yI 0]; %PAR H xH = xL + LH*cos(beta1+beta2+beta3+beta4); yH = yL + LH*sin(beta1+beta2+beta3+beta4); rH = [xH yH 0]; contadorh=contadorh+1; vectorh(contadorh,:)=[rH]; % ESLABONES % PAR A

xA = -0.01; yA = 0.025;

111

 

 

rA = [xA yA 0]; % PAR F syms xF  xF yF  yF  %JH= ((xJ+xK+xL+0.002)^2+(yJ+yK+yL+0.012)^2)^0.5 eqnF1 = (xF-xH)^2+(yF-yH)^2-FH^2==0; eqnF2 = (xF-xA)^2+(yF-yA)^2-AF^2==0; solF = solve([eqnF1 eqnF2],[xF yF]); xFpos = solF.xF; yFpos = solF.yF; xF1 = double(eval(xFpos(1))); xF2 = double(eval(xFpos(2))); yF1 = double(eval(yFpos(1))); yF2 = double(eval(yFpos(2))); if if xF1>xA  xF1>xA xF = xF1; yF= yF1; else else    xF = xF1; yF = yF1; end    end rF = [xF yF 0]; % PAR E alpha1=atan((yF-yA)/(xF-xA)); BF=((BC+CD)^2+(DE+EF)^2-(2*(BC+CD)*(DE+EF)*cos(alpha3)))^0.5; phi7=acos((-(BC+CD)^2+BF^2+(DE+EF)^2)/(2*(DE+EF)*BF)); phi9= pi-alpha3-phi7; phi10=alpha2-phi9;  AF=((xF-xA)^2+(yF-yA)^2)^0.5; phi11=acos((-(BF^2)+AF^2+AB^2)/(2*AB*AF)); phi8=pi-phi11-phi10; phi12=pi-phi7-phi8; if if xF>xA  xF>xA % PAR E xE = xF + EF*cos(alpha1+phi12); yE = yF + rE = [xF yF 0]; % PAR D xD = xE + DE*cos(alpha1+phi12); yD = yE + rD = [xD yD 0]; % PAR C xC = xD + CD*cos(pi-alpha3+phi12+alpha1); rC = [xC yC 0]; % PAR B xB = xC+(BC*cos(pi-alpha3+phi12+alpha1)); rB = [xB yB 0]; else    else % PAR E xE = xF - EF*cos(alpha1+phi12); yE = yF rE = [xF yF 0]; % PAR D xD = xE - DE*cos(alpha1+phi12); yD = yE rD = [xD yD 0]; % PAR C xC = xD - CD*cos(pi-alpha3+phi12+alpha1); rC = [xC yC 0]; % PAR B xB = xC-(BC*cos(pi-alpha3+phi12+alpha1)); rB = [xB yB 0]; end end    %PAR G syms xG  xG yG  yG  eqnG1 = (xG-xF)^2+(yG-yF)^2-FG^2==0; eqnG2 = (xH-xG)^2+(yH-yG)^2-GH^2==0;

EF*sin(alpha1+phi12); DE*sin(alpha1+phi12); yC = yD + CD*sin(pi-alpha3+phi12+alpha1); yB = yC+BC*sin(pi-alpha3+phi12+alpha1);

EF*sin(alpha1+phi12); DE*sin(alpha1+phi12); yC = yD - CD*sin(pi-alpha3+phi12+alpha1); yB = yC-BC*sin(pi-alpha3+phi12+alpha1);

solG = solve([eqnG1 eqnG2],[xG yG]); xGpos = solG.xG; yGpos = solG.yG; xG1 = double(eval(xGpos(1))); xG2 = double(eval(xGpos(2))); yG1 = double(eval(yGpos(1))); yG2 = double(eval(yGpos(2))); xG = xG1; yG = yG1; rG = [xG yG 0]; phi4 = atan((yB-yC)/(xB-xC));

112

 

 

B)$) 4#%#$*&1)$ #/ *+4#/+ (&1#*I%&(+ (+1 /), *A1&*), *#4&4), )1%$+0+*K%$&(), 4# .1 4#4+ %$&')/I1;&(+ 4# /) *)1+ ,# .,) #/ (74&;+ )1%#, 0$#,#1%)4+5 0#$+ ()*2&)14+ /+, ,&;.%#, 6)/+$#,a

%% Coordenadas pares cinematicos  AB = 0.039; BC = 0.0265; CD = 0.032; DE= 0.032 ;EF = 0.0415; FG=0.03; GH=0.03; FH=0.056; % [m] [m]    JK = 0.022; KL=0.015; LI=0.01; LH=(0.012^2 + 0.01^2)^0.5; beta4 = atan(0.01/0.012); JH= 0.045;  AF=0.088;

113

 

 

'DAjV ***E $8/*0) "- 3'+&': ('1' "& $4&$%&) /"& +)1Y%" 7 &'# .%"1>'# (1"#"-+"# "- &' :'#" /"& #*#+"3' /" "#&':)-"#

"74&;+ 4#%#$*&1)$(+1 #/ %+$-.# H /), '.#$T), #1)1%$+0+*K%$&(),8 /) 2),# 4#/ ,&,%#*) 4# #,/)2+1#, 0)$) .1 4#4+0)$) #1 #Y%#1,&71 /), *IY&*), *#4&4), %% Coordenadas pares cinematicos  AB = 0.039; BC = 0.0265; CD = 0.032; DE= 0.032 ;EF = 0.0415; FG=0.03; GH=0.03; FH=0.056; % [m] [m]    JK = 0.064; KL=0.039; LI=0.03; LH=(0.017^2 + 0.015^2)^0.5; beta4 = atan(0.015/0.017); JH= 0.045;  AF=0.13; %phi1 = 0.4*pi; % 90 grados [rad] alpha2 = 135*(pi/180); % [rad] alpha3 = 120*(pi/180); % [rad] phi2 = pi-alpha2; % [rad] phi3 = pi-alpha3; % [rad] phi5 = 41*(pi/180); % [rad]  [rad]  phi6 = (pi-(phi5))/2; % [rad]  [rad]  beta1 = 0*(pi/180); % Angulo MCP [rad] beta2 = 0*(pi/180); % Angulo PIP [rad]  [rad]  beta3 = 0*(pi/180); % Ángulo DIP [rad] [rad]    % DEDOS %MCP xJ = 0; yJ = 0; rJ = [xJ yJ 0]; %PIP xK = JK*cos(beta1); yK = JK*sin(beta1); rK = [xK yK 0]; %DIP xL = xK + KL*cos(beta1+beta2); yL = yK + KL*sin(beta1+beta2); rL = [xL yL 0]; %PAR I xI = xL + LI*cos(beta1+beta2+beta3); yI = yL + LI*sin(beta1+beta2+beta3); rI = [xI yI 0]; %PAR H xH = xL + LH*cos(beta1+beta2+beta3+beta4); yH = yL + LH*sin(beta1+beta2+beta3+beta4); rH = [xH yH 0]; % ESLABONES % PAR A xA = -0.01; yA = 0.025; rA = [xA yA 0]; % PAR F syms xF  xF yF  yF  %JH= ((xJ+xK+xL+0.002)^2+(yJ+yK+yL+0.012)^2)^0.5 eqnF1 = (xF-xH)^2+(yF-yH)^2-FH^2==0; eqnF2 = (xF-xA)^2+(yF-yA)^2-AF^2==0; solF = solve([eqnF1 eqnF2],[xF yF]); xFpos = solF.xF; yFpos = solF.yF; xF1 = double(eval(xFpos(1))); xF2 = double(eval(xFpos(2))); yF1 = double(eval(yFpos(1))); yF2 = double(eval(yFpos(2))); xF = xF2; yF= yF2; rF = [xF yF 0]; % PAR E alpha1=atan((yF-yA)/(xF-xA)); BF=((BC+CD)^2+(DE+EF)^2-(2*(BC+CD)*(DE+EF)*cos(alpha3)))^0.5; phi7=acos((-(BC+CD)^2+BF^2+(DE+EF)^2)/(2*(DE+EF)*BF));

phi9 pi alpha3 phi7; phi10=alpha2-phi9;

114

 

 

 AF=((xF-xA)^2+(yF-yA)^2)^0.5; phi11=acos((-(BF^2)+AF^2+AB^2)/(2*AB*AF)); phi8=pi-phi11-phi10; phi12=pi-phi7-phi8; % PAR E xE = xF + EF*cos(alpha1+phi12); yE = yF + EF*sin(alpha1+phi12); rE = [xF yF 0]; % PAR D xD = xE + DE*cos(alpha1+phi12); yD = yE + DE*sin(alpha1+phi12); rD = [xD yD 0]; % PAR C xC = xD + CD*cos(pi-alpha3+phi12+alpha1); yC = yD + CD*sin(pi-alpha3+phi12+alpha1); rC = [xC yC 0]; % PAR B xB = xC + (BC*cos(pi-alpha3+phi12+alpha1)); yB = yC + BC*sin(pi-alpha3+phi12+alpha1); rB = [xB yB 0]; %PAR G syms xG  xG yG  yG  eqnG1 = (xG-xF)^2+(yG-yF)^2-FG^2==0; eqnG2 = (xH-xG)^2+(yH-yG)^2-GH^2==0; solG = solve([eqnG1 eqnG2],[xG yG]); xGpos = solG.xG; yGpos = solG.yG; xG1 = double(eval(xGpos(1))); xG2 = double(eval(xGpos(2))); yG1 = double(eval(yGpos(1))); yG2 = double(eval(yGpos(2))); xG = xG2; yG = yG2; rG = [xG yG 0];

%% Velocidades  w1= -1.0471; %[rad/s] %[rad/s]     w1 = [0 0 w1]; % [rad/s] [rad/s]    [m/s]    vA = [0 0 0]; % [m/s] vJ = [0 0 0]; % [m/s] [m/s]    [m/s]    vK = [0 0 0]; % [m/s] vL = [0 0 0]; % [m/s] [m/s]    % Vel B rBA = rB-rA; vB = vA+cross(w1,rBA); vBn = sqrt((vB(1))^2+(vB(2))^2+(vB(3))^2); % Vel C rCA = rC-rA; vC = vA+cross(w1,rCA); vCn = sqrt((vC(1))^2+(vC(2))^2+(vC(3))^2); % Vel D rDA = rD-rA; vD = vA+cross(w1,rDA); vDn = sqrt((vD(1))^2+(vD(2))^2+(vD(3))^2); % Vel E rEA = rE-rA; vE = vA+cross(w1,rEA); vEn = sqrt((vE(1))^2+(vE(2))^2+(vE(3))^2); % Vel F rFA = rF-rA; vF = vA+cross(w1,rFA); vFn = sqrt((vF(1))^2+(vF(2))^2+(vF(3))^2); %Vel H syms w2z syms  w2z   w3z   w3z  rHF = rH-rF; rHL = rH-rL;  w2zs = w2z;  w3zs = w3z;  w2s = [0 0 w2zs];  w3s = [0 0 w3zs]; eqnvC = vF+cross(w2s,rHF)-vL-cross(w3s,rHL)==0; eqnvCx = eqnvC(1); eqnvCy = eqnvC(2);

solvC = solve([eqnvCx,eqnvCy],[w2z,w3z]);

115

 

 

 w2z = (eval(solvC.w2z));  w3z = (eval(solvC.w3z));  w2 = [0 0 w2z];  w3 = [0 0 w3z]; vH = vB+cross(w2,rHF); % Vel G rGF = rG-rF; vG = vF+cross(w2,rGF); vGn = sqrt((vF(1))^2+(vF(2))^2+(vF(3))^2);

%% Aceleraciones  wd1 = [0 0 0]; % [rad/s^2] [rad/s^2]    aA = [0 0 0]; % [m/s]  [m/s]  [m/s]    aJ = [0 0 0]; % [m/s] [m/s]    aK = [0 0 0]; % [m/s] aL = [0 0 0]; % [m/s] [m/s]    % Aceleración B aB = aA+cross(wd1,rBA)+cross(w1,cross(w1,rBA)); aBn = cross(wd1,rBA); aBt = cross(w1,cross(w1,rBA)); % Aceleración C aC = aA+cross(wd1,rCA)+cross(w1,cross(w1,rCA)); aCn = cross(wd1,rCA); aCt = cross(w1,cross(w1,rCA)); % Aceleración D aD = aA+cross(wd1,rDA)+cross(w1,cross(w1,rDA)); aDn = cross(wd1,rDA); aDt = cross(w1,cross(w1,rDA)); % Aceleración E aE = aA+cross(wd1,rEA)+cross(w1,cross(w1,rEA)); aEn = cross(wd1,rEA); aEt = cross(w1,cross(w1,rEA)); % Aceleración F aF = aA+cross(wd1,rFA)+cross(w1,cross(w1,rFA)); aFn = cross(wd1,rFA); aFt = cross(w1,cross(w1,rFA)); % Aceleración H: syms wd2z syms  wd2z     wd3z wd3z  wd2zs = wd2z;  wd3zs = wd3z;  wd2s = [0 0 wd2zs];  wd3s = [0 0 wd3zs]; eqnaC = aF+cross(wd2s,rHF)+cross(w2,cross(w2,rHF))-aL-cross(wd3s,rHL)cross(w3,cross(w3,rHL))==0; eqnaCx = eqnaC(1); eqnaCy eqnaC(2); solaC == solve([eqnaCx,eqnaCy],[wd2z,wd3z]);  wd2z = double(eval(solaC.wd2z));  wd3z = double(eval(solaC.wd3z));  wd2 = [0 0 wd2z];  wd3 = [0 0 wd3z]; aH = aF+cross(wd2,rHF)+cross(w2,cross(w2,rHF)); aHn = cross(wd2,rHF); aHt = cross(w2,cross(w2,rHF)); % Aceleración G aG = aF+cross(wd2,rGF)+cross(w2,cross(w2,rGF)); aGn = cross(wd2,rGF); aGt = cross(w2,cross(w2,rGF)); % Aceleración centros de masa: aC1 = aB/2; aC2 = (aB+aC)/2; aC3 = (aC+aD)/2; aC4 = (aD+aE)/2; aC5 = (aF+aE)/2; aC6 = (aF+aG)/2; aC7 = (aG+aH)/2;

%% Análisis de Fuerzas:

% Centro de masa rC1 = (rB+rA)/2;

116

 

 

rC2 = (rB+rC)/2; rC3 = (rC+rD)/2; rC4 = (rD+rE)/2; rC5 = (rF+rE)/2; rC6 = (rF+rG)/2; rC7 = (rH+rG)/2; % Gravedad g = 9.8; % [m/s^2]  [m/s^2]  % Masa eslabones  m1  m2  m3  m4  m5  m6  m7

= = = = = =

0.004; 0.002; 0.002; 0.004; 0.004; 0.004;

% % % % % %

[kg] [kg]    [kg]    [kg] [kg] [kg]    [kg]    [kg] [kg] [kg]    [kg] [kg]   

% Dimensiones geoméricas eslabones h12 = 0.012; % Altura [m]  [m]  d12 = 0.008; % Espesor [m]  [m]  fe = 10; % Módulo de la fuerza [N] Fe = [fe*sin(beta3) fe*cos(beta3) 0] ; % [N] [N]    % Peso de los G1 = [0 -m1*g G2 = [0 -m2*g G3 = [0 -m3*g G4 = [0 -m4*g G5 = [0 -m5*g G6 = [0 -m6*g G7 = [0 -m7*g

eslabones (Fuerza gravitacional): 0]; 0]; 0]; 0]; 0]; 0]; 0];

% Momento de inercia de masa con respecto al centro de gravedad: Ic1 = m1*(AB^2+h12^2)/12; % [kgm^2] [kgm^2]    Ic2 = m2*(BC^2+h12^2)/12; % [kgm^2] [kgm^2]    [kgm^2]    Ic3 = m3*(CD^2+h12^2)/12; % [kgm^2] Ic4 = m4*(DE^2+h12^2)/12; % [kgm^2] [kgm^2]    Ic5 = m5*(EF^2+h12^2)/12; % [kgm^2] [kgm^2]    Ic6 = m6*(FG^2+h12^2)/12; % [kgm^2] [kgm^2]    [kgm^2]    Ic7 = m7*(GH^2+h12^2)/12; % [kgm^2] % Fuerzas de Inercia: Fin1 = m1*aC1; % [N]  [N]  Fin2 = m2*aC2; % [N]  [N]  Fin3 = m3*aC3; % [N]  [N]  Fin4 = m4*aC4; % [N]  [N]  Fin5 = m5*aC5; % [N]  [N]  Fin6 = m6*aC6; % [N]  [N]  Fin7 = m7*aC7; % [N]  [N]  % Momentos de Inercia: Min1 = wd1*Ic1; % [N] [N]    Min2 = wd1*Ic2; % [N] [N]    [N]    Min3 = wd1*Ic3; % [N] Min4 = wd1*Ic4; % [N] [N]    Min5 = wd1*Ic5; % [N] [N]    [N]    Min6 = wd2*Ic6; % [N] Min7 = wd2*Ic7; % [N] [N]    % Ecuaciones de Newton-Euler: syms F12xz  F12xz F12yz F12yz   F23xz  F23xz F23yz F23yz   F34xz  F34xz F34yz  F34yz F45xz F45xz   F45yz F45yz   F56xz F56xz   F56yz F56yz   F67xz  F67xz F67yz F12x = F12xz; F12y = F12yz; F23x = F23xz; F23y = F23yz; F34x = F34xz; F34y = F34yz; F45x = F45xz; F45y = F45yz; F56x = F56xz; F56y = F56yz; F67x = F67xz; F67y = F67yz; % Eslabón 2: F23 = [ F23x F23y 0 ]; F32 = -F23; F12 = [ F12x F12y 0 ]; eqnF2 = G2+F12+F32-Fin2==0; eqnF2x = eqnF2(1);

eqnF2y = eqnF2(2);

117

 

 

% Eslabón 3: F34 = [ F34x F34y 0 ]; F43 = -F34; eqnF3 = G3+F23+F43-Fin3==0; eqnF3x = eqnF3(1); eqnF3y = eqnF3(2); % Eslabón 4: F45 = -F45; [ F45x F45y 0 ]; F54 eqnF4 = G4+F34+F54-Fin4==0; eqnF4x = eqnF4(1); eqnF4y = eqnF4(2); % Eslabón 5: F56 = [ F56x F56y 0 ]; F65 = -F56; eqnF5 = G5+F45+F65-Fin5==0; eqnF5x = eqnF5(1); eqnF5y = eqnF5(2); % Eslabón 6: F67 = [ F67x F67y 0 ]; F76 = -F67; eqnF6 = G6+F56+F76-Fin6==0; eqnF6x = eqnF6(1); eqnF6y = eqnF6(2); % Eslabón 7: eqnF7 = G7+F67+Fe-Fin7==0; eqnF7x = eqnF7(1); eqnF7y = eqnF7(2); % Solución Preliminar: solu = solve([eqnF2x,eqnF2y,eqnF3x,eqnF3y,eqnF4x,eqnF4y,eqnF5x,eqnF5y,eqnF6x,eqnF6y,eqnF7x,eqnF7y],[F12x z,F12yz,F23xz,F23yz,F34xz,F34yz,F45xz,F45yz,F56xz,F56yz,F67xz,F67yz]); F12xs F12ys F23xs F23ys F34xs F34ys

= = = = = =

double(eval(solu.F12xz)); double(eval(solu.F12yz)); double(eval(solu.F23xz)); double(eval(solu.F23yz)); double(eval(solu.F34xz)); double(eval(solu.F34yz));

F45xs F45ys F56xs F56ys F67xs F67ys

= = = = = =

double(eval(solu.F45xz)); double(eval(solu.F45yz)); double(eval(solu.F56xz)); double(eval(solu.F56yz)); double(eval(solu.F67xz)); double(eval(solu.F67yz));

F12s F23s F34s F45s F56s F67s

= = = = = =

[ [ [ [ [ [

F12xs, F23xs, F34xs, F45xs, F56xs, F67xs,

F12ys, F23ys, F34ys, F45ys, F56ys, F67ys,

0 0 0 0 0 0

]; ]; ]; ]; ]; ];

rAC1 = rA-rC1; rBC1 = rB-rC1; F21=-F12s; F01 = -F21-G1+Fin1; Mm = Min1-cross(rBC1,F21)-cross(rAC1,F01);

118

 

 

B)$) 4#%#$*&1)$ #/ %+$-.# H /), '.#$T), #1 /) 2),# 4#/ ,&,%#*) 4# #,/)2+1#, (+1 /), *A1&*), *#4&4), )1%$+0+*K%$&(), 4# .1 4#4+ %$&')/I1;&(+ #1 #Y%#1,&71 ,# .,) #/ (74&;+ )1%#, 0$#,#1%)4+5 0#$+ ()*2&)14+ /+, ,&;.%#, 6)/+$#,a %% Coordenadas pares cinematicos  AB = 0.039; BC = 0.0265; CD = 0.032; DE= 0.032 ;EF = 0.0415; FG=0.03; GH=0.03; FH=0.056; % [m] [m]    JK = 0.022; KL=0.015; LI=0.01; LH=(0.012^2 + 0.01^2)^0.5; beta4 = atan(0.01/0.012); JH= 0.045;  AF=0.088;

Z&1)/*#1%#5 0)$) #,%)2/#(#, #/ %+$-.# H /), '.#$T), 0)$) .1 4#4+ #1 '/#Y&71 ,# 4#2#1 ()*2&)$ #/ 6)/+$ 4# /+, ,&;.%#, I1;./+,a 2#%) _a oghy 2#%) `a oghy 2#%) ca oehy

119

 

 

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Carácter del  movimiento principall principa

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Impacto ligero

Impacto medio

Impacto pesado

Uniforme Impacto ligero Impacto medio Impacto pesado 

1.00 1.10 1.25 1.50

1.25 1.35 1.50 1.75

1.50 1.60 1.75 2.00

1.75 o mayor 1.85 o mayor 2.00 o mayor 2.25 o mayor

 

mZ.#1%#a pd`qn

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.JPIVH OA OCDhbCPV ™›  

K    =

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v

√ 

vt 

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(Unidades acostumbradas en Estados Unidos)

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√ 

200vet 

v

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(Unidades SI)

 A

donde  A  = 50 + 56(1 −  B )

 

2/3

 

 B   = 0.25(12 − Q ) v

mZ.#1%#a pd`q5 pdcqn

"+1 /), #(.)(&+1#, )1%#$&+$#, ,# +2%# eœ  * WL++TW 

.JPIVH OA IJbJiV NVH \UAjCfD ™   B)$) .1 0),+ 4# (+$+1) 4# `d ,#;F1 JM?:uJJ pdcqa

™ * žL žL Ÿ  120

 

 

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mZ.#1%#a pd`q5 pdcqn

 

 J,A /) #(.)(&71 0)$) #,%)2/#(# ¡ ¢ #, /) ,&;.%# pd`q5 pdcqa ¡ ¢  * ¡ £¤  E +L++NR , t  

H ,# +2%# .1 ¡ ¢  * WLM[+ 

(GDIV OA PVDIJPIV ADIHA ADRHJDA] ™ ¥   B)$) #1;$)1#, (71&(+, $#(%+, ej  #@ y¦/ / _ pd`q5 pdcq8

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Número de dientes del engrane acoplado 13

100

15

20

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3 0 35 40 45 50 30

100

  o    i   r 90   c    t    é

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90

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60

0. 18

0. 20

0. 22

0.24

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0.30

Factor geométrico,  J  (  (Y  J )

0.32

0.34

0.36

0.48

0.40

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.JPIVH OA IAbNAHJIGHJ ™«   ?#;F1 JM?:uJJ 0)$) .1) %#*0#$)%.$) 4# %$)2)3) #1%$# h H _`h y" ,# %# .1 em  4# _ pd`q5 pdcq8

.JPIVH OA PVD\CJTCUCOJO OA HA]C]IADPCJ J UJ \UAjCfD ™¬  ^ \JPIVH OA PVD\CJTCUCOJO NVH NCPJOGHJ ¬  

 

Factores de  confiabilidad del acero* 

Requerimientos de aplicación

C R   (Z  R (   Z  Z)  Z 

Menos de una falla en 10 000 Menos de una falla en 1 000 Menos de una falla en 100 Menos de una falla en 10 Menos de una falla en 2  

† K R   (Y  R (   Y Z  Z) 

1.22 1.12 1.00 0.92

1.50 1.25 1.00 0.85‡

0.84

0.70§

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.JPIVH OA PVHVDJbCADIV OA HA]C]IADPCJ J UJ NCPJOGHJ  ¥  

C   xc  =  Z   xc  =

1.5

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2.0

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mZ.#1%#a pd`q5 pdcqn

 

122

 

 

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1.14 1.7 1.12

1.6

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    Z    (

   1

1.5

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  e    d   r   o    t   c   a    F

   2

    B     B

    H     H

    P     G     B     B

1.4

1.08

1.3 1.06 1.2 1.04

    H     H  ,   a    d   a    l   u   c    l   a   c   a   z   e   r   u    d   e    d   n    ó    i   c   a    l   e    R

Cuando 1.02

 H   BP

 H   B

1

 H   BG

 H   B

2

< 1.2

use C  H  ( Z   Z W ) = 1 1.00

0

2

4

6

8

10

12

14

16

18

20

Relación de reducción de engranes, N   / n ( z  z2 /   z1)

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123

 

 

'DAjV =E 9)+%+$ D" _i_i\h_`, ON ZJVNbJ=LO Series 1717 ... SR Values at 22°C and nominal voltage 1717 T 1 Nomina Nominall vol voltag tage e   U N N     R  2 Termi Terminal nal res resist istanc ance e 3 Efficie Efficiency ncy,, max max..   ηmax. 4 No No-l -loa oad d sp speed eed   n 00   5 No-load No-load current, current, typ. (w (with ith shaft shaft ø 1,5 mm)   I 00   6 Stal Stalll ttor orqu que e   M H H     M RR   7 Fricti Friction on tor torque que 8 Speed Speed ccon onst stan antt   k nn     k EE   9 Bac Back-EM k-EMF F con consta stant nt 10 Torqu Torque e co const nstant ant   k M M   11 Cur Curren rentt ccons onstan tantt   k II   12 Slope Slope o off n-M n-M cu curve rve   Δn  /    ΔM  13 Rot Rotor or induct inductance ance   L 14 Mechanical Mechanical time consta constant nt   τ mm   15 Ro Roto torr inert inertia ia   J  16 Ang Angula ularr accelera acceleratio tion n   α mmax. ax.     R tth1 h2  17 The Therma rmall resist resistanc ance e h1 /   R tth2  18 19     20 21

22 23 24 25 26 27 28  

w1

 

Note:

 

006 SR 6 4,3 69 14 000 0,046 5,34 0,18 2 410 0,414 3,96 0,253 2 620 65 16 0,58 92

012 SR 12 17,1 70 14 000 0,023 5,38 0,18 1 210 0,829 7,92 0,126 2 600 260 16 0,59 92

The diagram indicates the recommended speed in relation to the available torque at the output shaft for a given ambient temperature of 22°C.

The nominal voltage (U N) curve shows the operating point at nominal voltage in the insulated and thermally coupled condition. Any points of operation above the curve at nominal voltage will require a higher operating operating voltage. Any points below the nominal voltage curve will require less voltage.

V Ω

% min-¹ A m Nm m Nm min-¹ /V mV/min-¹ mNm/A A/mNm min-¹ /mNm µH ms gcm² ·10³rad/s²

2 / 210

s

-30 ... + +8 85 (optional version +125 sintered bearings (standard) 1,5 1,2 0,2 20

-55 ... +125)

°C °C

ball bearings, preloaded (optional version) 1,5 5 0,5 10

mm N N N

0,03 0,015 0,2 0 steel, black coated 18 clockwise, viewed from the front face 16 000 1 NdFeB

M N N   I N N   n N N  

1,2 0,7 0, 10 790

     

2,1 0,63 6 540

mm mm g min-¹

2,1 0,32 6 570

2,1 0,19 4 570 R th2  th2  value  value

n [min-1]

21 000 18 000

2,0

3,5

2,2 0,16 6 540

m Nm A min-¹

has been reduced by 0%. 1717T024SR 1717T024SR (Rth2 -50%) Intermittent operation Operating point at nominal value

Watt

0,5

15 000 The diagram shows the motor in a completely insulated as well as thermally coupled condition (Rth2 50% reduced).

024 SR 24   68,8 70 14 000 0,011 5,36 0,17 602 1,66 15,9 0,063 2 610 1 040 16 0,59 92

K /W

Rated values are calculated with nominal voltage and at a 22°C ambient temperature. The

Note:

018 SR 18 50,1 68 12 300 0,013 4,66 0,18 709 1,41 13,5 0,074 2 640 760 16 0,58 80

4,5 / 27

w2 

The Therma rmal l time tim e cons constan tantt range:   τ   / τ  Operating Opera ting temper temperature ature – motor – winding, max. permissible S Sh haft bearings Shaft load max.: – with shaft diameter – radial at 3 000 min -¹ (  (3 3 mm from bearing) – axial at 3 000 min -¹ – axial at standstill Shaft play:   ≤ – radial – axial   ≤ Housing material Mass Direction of rotation Speed Speed up to   n m max. ax. Number of pole pairs Magnet material

Rated values for continuous operation   29 Ra Rate ted d to torq rque ue 30 Rated current current (thermal (thermal limit) limit) 31 Ra Rate ted d spe speed ed  

003 SR 3 1,07 1, 69 69 14 000 0,091 0, 5,37 0,18 4 820 0,207 1,98 0,505 0, 2 610 17 16 0,59 92 92

                               

5,0

UN

12 000   9 000   6 000 3 000 M [mNm]

0 0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Recommended operation areas (example: nominal voltage 24V)

For notes on technical data and lifetime performance refer to “Technical Information”. Edition 2017

© DR. FRITZ FAULHABER GMBH & CO. KG Specifications subject to change without notice.

mZ.#1%#a pd`qn 124

 

 

  O#4.(%+ _iu_ dgda_ ZJVNbJ=LO

Series 17/1 17/1 stainless steel steel

Housing material Geartrain material Recommended max. input speed for: – continuous operation   Backlash, at no-load Bearings on output shaft Shaft load, max.: – radial (6,5 mm from mounting face)   – axial   Shaft press fit force, max. Shaft play – radial (6,5 mm from mounting face)   – axial Operating temperature range Specifications   Number of gear stages Continuous torque Intermittent torque Mass without motor, ca. Efficiency, max. Direction of rotation, drive to output

8 000 min-¹ ° sintered bearings

≤ 2

≤ 5 N ≤ 3 N ≤ 100

 

8 000 min-¹ ° ball bearings, preloaded

≤ 2

 

N

 

≤ 0,06 mm ≤ 0,  0,1 mm

 

≤ 75 ≤ 12 ≤ 35

   

mNm mNm g %

1 550 800 28 90 = 3,33:1 4,5:1

L2 [m  [ mm] = length without motor L1 [  [m mm] = length with motor 1624T...S 1717T...SR 1724T...SR 1727U...CXR 1741U...CXR 1628T...B AM1524...-55

18,6 42,4 35,6 42,6 45,8 59,8 46,6 35,0

2 550 800 35 80 =

mm = 0 mm - 30 ... + 100 °C

3 550 800 42 70 =

11:1 15:1 20:1

23,7 47,5 40,7 47,7 50,9 64,9 51,7 40,1

N N N

≤ 0,03

 

- 30 ... + 100 °C

Reduction ratio 1) (rounded)

1)

17/1 K stainless steel steel

4 550 800 49 60 =

37:1 44:1 50:1 68:1 81:1 91:1

5 550 800 56 50 =

123:1 148:1 167:1 178:1 200:1 240:1 270:1 304:1 365:1

28,8 52,6 45,8 52,8 56,0 70,0 56,8 45,2

412:1 494:1 593:1 667:1 750:1 800:1 900:1 1 013:1 1 367:1

33,9 57,7 50,9 57,9 61,1 75,1 61,9 50,3

39,1 62,9 56,1 63,1 66,3 80,3 67,1 55,5

 The reduction ratios are rounded, the exact values are available on request or at www.faulhaber.com. Orientation with respect to motor terminals not defined

For more combinations see table. Example of combination with 1717...SR

3x

M2  3 deep

ø17 ±0,1

 0

-0,01

ø9 -0,015

ø4 -0,018

 0

ø9 -0,01

 0

3,5 -0,05

3x 120°

8 ø14

11,3 ±0,3 L2 ±0,3

17/1

Edition 2017

mZ.#1%#a pddqn

10,75 ±0,3

13,5 ±0,3 14 ±0,3

L1 ±0,8

For notes on technical data and lifetime performance refer to “Technical Information”.

+0,2  0

17/1 K

© DR. FRITZ FAULHABER GMBH & CO. KG Specifications subject to change without notice.

125

 

 

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