proyecto mecanica analitica

8/15/2019 proyecto mecanica analitica

1/21

UNIVERSIDAD DE SAN CARLOS DE GUATEMALA

FACULTAD DE INGENIERÍA

MECÁNICA ANALÍTICA 2

SECCIÓN: N

PROYECTO FINAL MECÁNICA ANALÍTICA 2

INTEGRANTES: CARNET:

GERSON BLADIMIR ANONA CHUNCHÚN 2006-19336

CRISTIAN IVÁN SAMAOA CHÁVE! 2009-"323#

OSCAR CONCOGUA SAGUACHE 2010-"6$%#

GUATEMALA 2" DE OCTUBRE DEL 201"


2/21

INTRODUCCIÓNE& '()*(+,+ ./*+,/ ,/' *. /,/+4 &/' (5/' .+ /((+,/ 7*+ +8('+,+, &/' .(+4'/' +,('/' ' // +& ,/4+ /44+/ /, &/' 7*+ '+ &+ .++,/44; 7*+ +'/' '/, +'+,(&+' +, & (. /(.(, 5/47*+ '(, +&&/' '+4, // 4,'5/4+; 5/4 &/ 7*+ +' .+',+ (5/4,( /54+,.+4 +'*.(4 /./' +'/' +' 54 +,+4 (.+ .+>/ 5/47*+ =*,(/,, &/' +,('/ ' 5/.+4 .('+?4&/' .+ +@/4 ,+4*(&(,./ &)*,/ .+ &/' 54/)4' 54 '(*&4&/' // +& /4(,) M/.+&*(&(./ 54 +'+ 4@/ / &)*,/ /4/ (,+'()./

OBJETIVOS

General

• O+,+4 *, '+ '/4+ // +' +& =*,(/,(+,/ & 5&((>, .+ &/'

.('(,/' +,('/' 54 7*+ +, &/' '()*(+,+' *4'/' '+ ,/' ) 4(/ &&4&/' .+ & ,+4/44+

• C/,/+4 5&(4 54/)4' /, &/' 7*+ '+ 5*+.+, 4+4 '(*&4

+,('/ 5/4 +.(/ .+ *, '/=4+


3/21

Gra&% &e l$'er(a& )e!*n$!a

L/' )4./' .+ &(+4. '/, +& ,+4/ ,(/ .+ +&/(..+')+,+4&(.' (,.+5+,.(+,+' ,++'4(' 54 .+=(,(4 +& +'./ (,+,//; /(,(.+, &/' )4./' .+ &(+4. /, &' //4.+,.'(,.+5+,.(+,+'

E, +&/ +, ./' .(+,'(/,+';+& ,+4/ .+ )4./' .+ &(+4. .+& ('/ '+ 5*+.+, &*&4 +.(,+ +& 4(+4(/.+ G4K&+4-*:

m=3(n−1)−2 j1− j2

D>,.+:

m,; /(&(..

n; ,+4/ .+ +&++,/' +'&/,+'; 44'; 5(+'; + .+ *, +,('/

j1; ,+4/ .+ *,(/,+' .+ 1 )4./ .+ &(+4.

j2; ,+4/ .+ *,(/,+' .+ 2 )4./' .+ &(+4.

Ca&ena !$ne)*($!a

E, *, +*&/ */>(& '+ .+,/(, .+, (,+,4'&.,./ +'+ /((+,/ &' 4*+.' /4(+'

J/.+/' '* + .((.(4 & .+, (,+


4/21

E& '('+ .+ 4,'('(>, F/4./ 5/4:

E& +4)*+;

L @ .+ (/' / @ .+ +&/(..+';

E& +@+ .+ 4,'('(>,;

E& )4*5/ >,(/-.(=+4+,(&; =/4./ 5/4 *, )4*5/ >,(/ *, .(=+4+,(&;

L/' 5&(+4+' / '+(, +' *, *+45/ 4)(./ 7*+ 5/'++ & +,/' ./' ,/./'; '(+,./ '/' &/'5*,/' .+ *,(>, /, /4/' +'&/,+' E& ,+4/ .+ ,/./' &+ . '* ,/4+ &+'&>,: B(,4(/ ./' ,/./'; T+4(4(/ 4+' ,/./'; +,4+ /4/'

M%,$)$en(% &e r%&a&-ra &e -n !-er% r".$&%E' +& '/


5/21

L' +&/(..+' &(,+&+' +, &/' .(=+4+,+' 5*,/' J; ; J '/4+ +& (&(,.4/ +,

4/(>, '+ +, +, &/' +/4+' .+ & =()*4 L +&/(.. &(,+& .+ *&7*(+4 5*,/+'< +, .(4+(>, 5+45+,.(*&4 & &,+ '+ +'+ 5*,/ & 5*,/ .+ /,/ J; 7*++, *&7*(+4 (,',+ +'< +, 4+5/'/; 5/47*+ ,/ .+'&((+,/

U, 5*,/ )+,+4& .+& (&(,.4/; // (+,+ *, +&/(.. /, /5/,+,+/4(/,& +4(& J+4/ &/' 5*,/' J; CM J (+,+, +&/(..+'4+'5+(+,+ +4/ +, J 5/47*+ R0; VR +, +& CM 2R 2R 2V+, J; 7*+ /./' &/' 5*,/' .+& (&(,.4/ (+,+, & ('

L +,+4) (,( /& .+& (&(,.4/ 4/.,+ +':

E12

Ip ω2

D/,.+ I5 +' +& /+,/ .+ (,+4( &4+.+./4 .+ *, +@+ 7*+ 5' 5/4 J '+ 5*+.+

.+/'44 7*+ I5I MR2

& 4++5&4 +, E; '+ (+,+:

E1

2 I ω2

1

2 MR

2ω

2

J+4/ V R; +,/,+':

E1

2 I ω2

1

2 M v

2

E'/ '(),(=( 7*+ & +,+4) (,( /& .+ *, /@+/ +, /((+,/ .+ 4/..*4+'< .. 5/4 & +,+4) (,( .+ 4/(>, +, /4,/ & +,4/ .+ ' &


6/21

+,+4) +'< .. 5/4 & +,+4) (,( .+ 4/(>, +, /4,/ & +,4/ .+ ' & +,+4) (,( .+ 4'&(>, .+& +,4/ .+ ' .+& /@+/ E& /((+,/ .+4/..*4 '/&/ +' 5/'(&+ '( +8('+ 4/+ +,4+ +& *+45/ 4)(./ 7*+ '+ *++ &'*5+4=((+; 7*+ & =*+4 .+ 4/+ 54/.*+ +& /47*+ ,++'4(/ 54 +4 4/.4 +& *+45/ 4)(./ +, /4,/ & +,4/ .+ ' A 5+'4 .+& 4/+ ,/ 54.(. .+

+,+4) +, (,+, 7*+ //

+'&>, =(@/ .+& +,('/ D+ =/4 4+(. '+ .+,/(, (, (,+4'(/,+' . *, .+ &' &+4,(' .+& +,('/ /+,(.' 5/4 (,+4'(>, (,+, '+ *+'4, ./' (,+4'(/,+' .+& +,('/ /, *4/ +'&/,+' *4/ 54+' (,+, +,('/ (+& ,(+& +&+'&>, =(@/ '+ /,+ /, *, 4(*&(>, *, +'&>, /, *, .+'&(.+4 /4/; +, & '+)*,. (,+4'(>, +,('/ ,(+& &,,; +& +'&>, =(@/ '+/,+ /, ./' 4(*&(/,+' '+,./' +'&/,+' >(&+'.+& +,('/:

Mecanismo biela manivela

inversión 1:

M+,('/ ,(+&- &,, (,+4'(>, 2:

http://www.mecapedia.uji.es/mecanismo.htmhttp://www.mecapedia.uji.es/par_cinematico.htmhttp://www.mecapedia.uji.es/eslabon.htmhttp://www.mecapedia.uji.es/mecanismo.htmhttp://www.mecapedia.uji.es/par_cinematico.htmhttp://www.mecapedia.uji.es/eslabon.htm


7/21

Le/ &e Gras0%# E'&++ 7*+ *, +,('/ .+ *4/ 44' (+,+ & +,/' *, 4(*&(>, .+4+/&*(>, /5&+; '( '/&/ '( & '* .+ &' &/,)(*.+' .+ & 44 ,:

S+ 5*+.+ /'+44 (, .+ & &&. .+'()*&.. 4(,)*&4 7*+:

D+ ' '+ .+.*+:

S( '+ '*5/,+ 7*+ & 4(*&(>, AB +' .+ 4+/&*(>, /5&+; +,/,+'

http://es.wikipedia.org/wiki/Mecanismo_de_cuatro_barrashttp://es.wikipedia.org/wiki/Teorema_del_cosenohttp://es.wikipedia.org/wiki/Cosenohttp://es.wikipedia.org/wiki/Inecuaci%C3%B3nhttp://es.wikipedia.org/wiki/Ra%C3%ADz_cuadradahttp://es.wikipedia.org/wiki/Ra%C3%ADz_cuadradahttp://es.wikipedia.org/wiki/Desigualdad_triangularhttp://es.wikipedia.org/wiki/Desigualdad_triangularhttp://es.wikipedia.org/wiki/Mecanismo_de_cuatro_barrashttp://es.wikipedia.org/wiki/Teorema_del_cosenohttp://es.wikipedia.org/wiki/Cosenohttp://es.wikipedia.org/wiki/Inecuaci%C3%B3nhttp://es.wikipedia.org/wiki/Ra%C3%ADz_cuadradahttp://es.wikipedia.org/wiki/Ra%C3%ADz_cuadradahttp://es.wikipedia.org/wiki/Desigualdad_triangular


8/21

F(,&+,+; '+ /(+,+, &' 4+&(/,+' ,++'4(' '*=((+,+' 54 7*+ &

4(*&(>, AB '+ .+ 4+/&*(>, /5&+:

TEOREMA DE LA RA1ON DE VELOCIDADES ANGULARES

E, & =()*4 3-2%; J2" +' +& +,4/ (,',&/ &' ),(*.+'; & '+ 5*+.+ 4+/4.+,4 54 7*+.4


9/21

E'+ '('+ (&*'4 +& +/4+ .+ & 4>, .+ +&/(..+' ,)*&4+' E& +/4+=(4 7*+ & 4>, .+ &' +&/(..+' ,)*&4+' .+ ./' *+45/' *&+'7*(+4 +,/((+,/ 5&,/; +, 4+&(>, /, *, +4+4 *+45/; +' (,+4'+,+ 54/5/4(/,&

&/' '+)+,/' +, &/' 7*+ +& +,4/ (,',, 5/'(( 4(44(; &/ &4)/ .+ & &,+ .+ &/' +,4/';

+& &+/4 .++ 54/4 5/4 ' ('/ 7*+ & 4>, .+ +&/(..+' ,)*&4+' +'5/'(( *,./ +& +,4/ (,',, & /54+,'(>, .+& 54/&+ & 5&(4 +& /./)4, 7*+ '+ 5*+.+,+.(4 &/' +/4+' .(=+4+,( .+ 5/'((>, ', '+ /,'(.+4 & +*(>, .+ & .(=+4+,( .+ +&/(.. 4+&(/,,./&/' 5*,/' A B;

+, ./,.+ &' ./' (,>),(' '/, & ),(*. & .(4+(>, .+& +/4 .(=+4+,( .++&/(.. V BA; // '+ (,.( 44( .+ +'+ '/&/ +, & +*(>, E, & =()*4


10/21

3-6 '+ *+'4 & '/&*(>, )4, D+'5*' .+ +&+)(4 *, +'&54 4+54+'+,4 &/' +/4+' +&/(..; '+ 4, +'& &/' +/4+' V A VB54(+,./ .+ *, /4()+, /, +, &' .(4+(/,+' +'5+(=(.' E& +/4 7*+ '++8(+,.+ +,4+ &/' 5*,/' .+ V A VB +' +& +/4 .(=+4+,( .+ +&/(.. VBA +'/44+/; .+,4/ .+ &/' &(+' .+ +8(*. .+ & )4, ,+4(/4 VBA3RBA / (+,; 3VBA 4RBA

J/4 &/ ,/; & ),(*. ,*4( .+ '+ +,*+,4 (.(+,./ +'& V BA +, &=()*4 3-6; RBA +, & =()*4 3-6; +,(+,./ *(../ .+ 5&(4 .+*.+,+&/' =/4+' .+ +'& 54 &' *,(..+' *, .+ &' 54


11/21

L ),(*. ,/ +' *, '/&*(>, /5&+ .+& +/4 .+ +&/(.. ,)*&4 (, '+ .++ .++4(,4 & .(4+(>, C// '+ (/ ,/4 ,+'; +& +/4 +'5+45+,.(*&4 & 5&,/ .+& 54/5(/ +'&>, 5/47*+ +& /((+,/ +' 5&,/ S(,

+4)/; +'/ ,. .(+ +4 .+ '( '&+ .+& 5&,/ .+ & =()*4 / +,4 &('/

E'/ '+ .++4(, // '+ (&*'4 +, & =()*4 3-6 S+ / +& 5*,/ .+ (' .+*, /'+4./4 +, 4'&(>,; +' .+(4; /(,./'+ /, +& 5*,/ A 5+4/ '(, )(44; '+5*+.+ 4+54+'+,4 & +'&>, // '( )(44 +, /4,/ & 5*,/ A L .(=+4+,( .++&/(.. VBA +' & ,( +&/(.. .++. 5/4 +'+ /'+4./4 .+ ./,.+; &(,+454+4 VBA // (,.(./4 .+ & .(4+(>, .+ 4/(>, .+& 5*,/ B +, /4,/ &

A; '+ +,*+,4 & .(4+(>, .+ 4/ 7*+; +, +'+ +@+5&/; +' /5*+'/ & .+&/((+,/ .+ &' ,+(&&' .+& 4+&/@ A*,7*+ ,/ /, *, ,/(>, +'4(+,+

+/4(&; *, *+, 54, =(,& +, & =/4 1$ 4.W' 4 +, '+,(.//,44(/ & /((+,/ .+ &' ,+(&&' .+& 4+&/@; /, &/ 7*+ '+ (,.( ,/ &),(*. // & .(4+(>,

L /'*4+ .+ 44 &/' .()4' +/4(&+' /, &,+' )4*+''; // +, &=()*4 3-6; =(&( '* &+*4 5+4/ *,./ +& .()4 +' & '/&*(>, )4,; ,/ +' * +8/ J/4 +' 4>, '+ /'*4 /,'4*(4 &'/&*(>, )4+'+ 7*+ VBA '+ 4+54+'+, /, +& +/4 7*+ .+& 5*,/ B & 5*,/ A C/, +' /,+,(>, .+ (.+,(=((>,; ,/ +' ,++'4(/*'4 5*,' .+ =&+ / ,/(/,+' .((/,&+' 7*+ ,. +, , .+ &' ,(' )4,

S(, +4)/; *,/ .+ &/' 5+&()4/' .+ +' /,+,(>, +' 7*+ +& ,&(' /+,4< 5+,'4 7*+ & ,( +' *, '+4(+ .+ X4*/'X )4


12/21

/&(.4'+ .+ 7*+ . 4+ 4. 5*+.+ .++ +'4 5/4 /5&+/ @*'(=(.+.(,+ *, +*(>, +/4(& /44+'5/,.(+,+ L' )4&/ /,'(*+,*, ,( /,+,(+,+ .+ 4+'/&*(>, ,/ *, '*'(*/ .+ *, '+ +>4( (+,=*,..

V/&(+,./ & =()*4 3-6; 5*./ 5+,'4'+ 7*+ +& +/ .+ 7*+ +& +/4 VBA =*+45+45+,.(*&4 RBA +' '(5&+ /(,(.+,( N/ /',+; '( '+ 4++8(, &+*(>, ; '+ /'+44< 7*+ +4 *, 4+'*&./ /&()/4(/; 7*+ 54/(+,+ .+&54/.*/ +/4(& /, +& +/4 E, +& 5'/ '()*(+,+ '+ 54/+4< +'54/5(+..

A/4 7*+ '+ +,/,4./ ; .++4(,/' & +&/(.. '/&* .+& 5*,/ C

E' '+ 5*+.+ 4+&(/,4 +.(,+ &' +*(/,+' .+ & .(=+4+,( .+ +&/(../, &' +&/(..+' '/&*' .+ &/' 5*,/' A B

TEOREMA DE ARON5OLD67ENNEDY DE LOS TRES CENTROS

J/4 &/ 7*+ +'&++ & +*(>, N,,-1W2; +& ,+4/ .+ +,4/' (,',, 3 '+ 4 .+ *, 5*,/ .+&+'&>, 3 7*+ 4++ .+ +&/(.. 54+,+; ('/ .+'.+ +& +'&>, 2 +' *, 54 .+ 5*,/' /(,(.+,+' .+ &/' +'&/,+' 2 3 7*+ 5/'++, & (' +&/(..

'/&*

U, *+, /./ 54 +,+4 54+'+,+ *,; /,=/4+ '+(.+,(=( . 5/&/; '+ 4 *, 4+ 7*+ /,+ +& 54 /44+'5/,.(+,+ .+,+4/' .+ &/' +'&/,+' E, & =()*4 3-1# '+ *+'4 7*+ '+ , &/&(./


13/21

J12; J23; J3" J1" (, *+'4 4+' =&,+'; 5*+'/ 7*+ , ,/ '++,*+,4 J13 J2"

E'/' ./' +,4/' ,/ '+ 5*+.+, +,/,44 5&(,./ ('*&+,+ & .+=(,((>,D+'5*' .+ +,/,44 ,/' +,4/' (,',,; +' .+(4; &/&(,./ &/' 5*,/' 7*+ '('=+, /(+,+ &.+=(,((>,; &/' /4/' '+ &/&(, 5&(,./ +& +/4+ .+ A4/,/&.-+,,+. 7*+/, =4+*+,( '>&/ '+ && +/4+ .+ +,,+. .+ &/' 4+' +,4/' E'++/4+ =(4 7*+ Y&/' 4+' +,4/' (,',,2; +,.4 & .(4+(>, VJ2; 5+45+,.(*&4 RJJ12 J+4/ & +&/(.. .+ J; //5*,/ .+& +'&>, 3; +,.4 & .(4+(>, VJ3; 5+45+,.(*&4 RJJ13 L' .(4+(/,+''/, /+4+,+' /, & .+=(,((>, .+ 7*+ *, +,4/ (,',


14/21

(' /,4.((>, +, &' .(4+(/,+' .+ VJ2 VJ3 54 *&7*(+4 *((>,'+&+(/,. 54 +& 5*,/ J; +,/' 7*+ '+ +&(@ '/4+ & 4+ 7*+ 5' 5/4 J 12 J13

PROGRAMAS PARA PROYECTAR MECANISMOS SAM

SAM S,+'(' A,


15/21

• G+,+4(>, .+ & =*,(>, Á,)*&/ '+ ,++'(, '('=+4 // ,(/ 354+' .+ , ,/ .+ 4'&(>, //

.+ 4/(>,• M*+&&+ ,/ &(,+&

E& *& 5+4(+ +& ,


16/21

• J+4=(& .+ +&/(.. .+ '+)*,./ 2 /4.+,• A@*'./4+' C(/'

E', +' +'5+(&+,+ (& 54 +& /.+&(+,/ .+5+4=(&+' ,/ +', .+& +,('/ =(,&

U, + 7*+ +& +,('/ '+ /,'4*(./ '+ , .+=(,(./ &' +,4.';*&7*(+4 .+ &' '()*(+,+' ,(..+' C(,+,• Á,)*&/'; +&/(.. ,)*&4 +&+4(>,

A.((/,&+,+; SAM 5*+.+ +@+*4 ,


17/21

T/,./ // 5*,/ .+ 54(. +& .('+?/W/5/&/) (,((&; *,/ 5*+.+5/'+4(/4+,+ +@/44 & &(.. +, & *& & 4+/4( .+& 5*,/ .+ *,/5&./4 ()*& & 4+/4( /@+(/; (,./ & )+/+4 .+& +,('/.+,4/ .+ &/' 4,)/' 54+.+=(,(./'

O *,/ 5*+.+ (,((4 +& &/4 5(/ / RMS .+& 54 //4 .+& +,('/;)4+),./ *, ' .+ /5+,'(>, .+@4 7*+ SAM .++4(,+ +& &/4 >5(/.+ & ' '* 5/'((>, .+,4/ .+& 4,)/ 5+4((./ S/&+,+; // +, +& '/.+ & /5(((>, .+ & 4+/4(; *,/ 5*+.+ (, +'5+(=(4 & =*,(>, .+4+=+4+,( (,((4 & .(=+4+,( +,4+ & =*,(>, *& & .+ 4+=+4+,(C*,./ '+ +'< .('+?,./; 5/4 +@+5&/; +7*(5/' 54 .+'44/&&/ ='(/; *,/ +'<*',./ )+,+4&+,+ *, =*+4 54+.+=(,(. // =*,(>, .+ .+'5&(+,/

E& /@+(/ .+ & /5(((>, 5*+.+ '+4 & (,(((>, / 8(((>, .+ *,4(+.. .+ 54/5(+..+' 5(/; RMS; 54/+.(/; .+ & .(=+4+,( +,4+ +&/5/4(+,/ *& /@+(/ .+ *, +,('/; &+' //:

• T4+/4( .+ *, ,/./ /, / '(, 4/,/+4@+ 54+'4(/• C*&7*(+4 ,(.. .+ /((+,/ / =*+4 // =*,(>, .+& (+5/ * /4

,(..

SAM *' &/ >5(/ 54 /.(=(4 &' '()*(+,+' 54/5(+..+' .+,4/ .+ &/'4,)/' .+=(,(./' 5/4 +& *'*4(/:

• G+/+4 .+& +,('/• J4/5(+..+' .+& E&++,/; &+' // '; /,',+ .+& *+&&+;

54/5/4(>, .+ & 4,'('(>,;

E& 54/+'/ .+ /5(((>, +, SAM '+ ' +, *, /./ .+ ./' 5'/'/5*+'/' 5/4:

• E85&/4(>, .+& , +'5+=(

J4(+4/; +& , .+4(. .+ & O5(((>,G+,( L &(' .+ &/' +@/4+' .+ & +85&/4(>, )&/& '+ *+'4 +, +& *.4/.+ &(' E85&/44; +& *& *+'4 +& &/4 .+ & =*,(>, .+ /5(((>, &/'54


18/21

L*+)/; +& .('+?./4 5*+.+ '+&+(/,4 *,/ .+ &/' 4+'*&./' .+ & V+,, .+&E85&/4./4 +5(+ *, /5(((>, &/& E' '7*+. &/& 5*+.+ '4'+ '+ +, & ,( S(5&+8 / +, +& A&)/4(/ E/&*(/ /, *, 4,)/ .+

54, '+&+(/,.

L /(,(>, .+ *, +'4+)( )&/& .+ +85&/4(>, .+ +'4+)( .+/5(((>, &/& /, +& .('+?./4 +, +& *&+ 54 '+&+(/,4 +& +,('/7*+ '+ /5(( 5/'+4(/4+,+ 54++,.+ .4 & +@/4 /5+,'(>, +,4+ &+&/(.. +& &,+ .+&


19/21

S/&(./4' (+,+ '/&*(/,+' 54 (,.*'4(' .+ 5&&(./' (, /,(+,+ /,./' .+ 4+(>,; +.((>, .+ '*5+4=((+' /5&+@';.+,(/'; (,+


20/21

S-s &$#eren(es )+&-l%s;

- S/&(./4' J4+(* 54 .('+?/ .+ 54/.*/ 3D

- S/&(./4' S(*&(/, 54 ,, *,(+4'(..+'

- D4='()' 4+(>, .+ .(*@/' 2D +.((>, DG '(, /'/

- +D4(,)' V(++4 // +44(+,' )4*('

CONCLUSIONES

• E8('+, /./ (5/ .+ +,('/' 7*+ '+ 5*+.+, .('+?4 4+4; 5/4 &/ *&

'+ (,+'()>; ,&(> '+ /*/ &/' /,/((+,/'


21/21

BIBLIOGRAFÍA

• http://es.wikipedia.org/wiki/Grado_de_libertad_(ingenier

%C3%ADa)

• http://es.wikipedia.org/wiki/Cadena_cinem%C3%A1tica• http://www.h.es/ra!ael.sanche"/ingenieriama#inas/car

petaapntes.htm/Apntes%$&ema%$1.pd!
http://es.wikipedia.org/wiki/Grado_de_libertad_(ingenier%C3%ADa)http://es.wikipedia.org/wiki/Grado_de_libertad_(ingenier%C3%ADa)http://es.wikipedia.org/wiki/Cadena_cinem%C3%A1ticahttp://www.uhu.es/rafael.sanchez/ingenieriamaquinas/carpetaapuntes.htm/Apuntes%20Tema%201.pdfhttp://www.uhu.es/rafael.sanchez/ingenieriamaquinas/carpetaapuntes.htm/Apuntes%20Tema%201.pdfhttp://es.wikipedia.org/wiki/Grado_de_libertad_(ingenier%C3%ADa)http://es.wikipedia.org/wiki/Grado_de_libertad_(ingenier%C3%ADa)http://es.wikipedia.org/wiki/Cadena_cinem%C3%A1ticahttp://www.uhu.es/rafael.sanchez/ingenieriamaquinas/carpetaapuntes.htm/Apuntes%20Tema%201.pdfhttp://www.uhu.es/rafael.sanchez/ingenieriamaquinas/carpetaapuntes.htm/Apuntes%20Tema%201.pdf

proyecto mecanica analitica

Documents