Informe 2 Brazo Robotico

 

UNIVERSIDAD NACIONAL DE INGIENERÍA FACULTAD DE INGENIERÍA MECÁNICA

DINÁMICA DE SISTEMAS MULTICUERPO - (MT 516)  SEGUNDO INFORME MANIPULADOR ROBÓTICO DE 4 GRADOS DE LIBERTAD

ALUMNOS: LUQUE APAA DE!VIS

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VILLALVA RIVERA $AVIER $EREM!

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SECCIÓN: A DOCENTE: CALLE FLORES IVAN ARTURO L%&' 5 * +,%*&./* "#10

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Facultad de Ingeniería Mecánica

1 E$ES E$ES DE DE COOR COORDEN DENADA ADAS S

FIGURA N°1 PRIMER EJE DE COORDENADAS

FIGURA N°2 SEGUNDO EJES DE COORDENADAS

2 DINÁMICA DE SISTEMAS MULTICUERPO MT 516

 

Facultad de Ingeniería Mecánica

FIGURA N°3 TERCER EJE DE COORDENADAS

FIGURA N°4 CUARTO EJES DE COORDENADAS

3 DINÁMICA DE SISTEMAS MULTICUERPO MT 516

 

Facultad de Ingeniería Mecánica

FIGURA N°5 QUINTO EJES DE COORDENADAS

" CINEMA CINEMATICA TICA DIRECT DIRECTA A Donde:   

d1 = 10!!" #3= 153!!" #4 = 103!!"

2"1 T#$%# de &#'(! &#'(!e)'o* e)'o*

I

2

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4 DINÁMICA DE SISTEMAS MULTICUERPO MT 516

 

Facultad de Ingeniería Mecánica

T#$%# 1 P#'(!e)'o* Den#+,)-.#')en$e'/

"" MA MATRI TRI DENA DENAVIT VIT-7ARTENBERG -7ARTENBERG cos θ1   0

 A  1 =

 A  2 =

[ [

 3

 A =

[ [

 A  4 =

T 1=

T 2=

[ [

senθ1

  senθ 1

  −cos θ

  0

0

1 0

0

cos θ2

  −senθ

senθ2

  cos θ2

1

  0

  d1

0

0

  0

1

2

0

0

0

0

0

0

1

0

0

0

0

1

cos θ3

  −senθ

senθ3

  cos θ3

0

3

0

] ]

  a 3∗ cos θ3   a 3∗ senθ3

0

0

1

0

0

0

0

1

cos θ4

  −senθ

senθ 4

  cos θ 4

4

0 0

0

0

1

0

0

0

0

1

cos θ1   0

senθ 1 0

  0

  senθ1   0   −cos θ 1   0

1 0

0

0

0

] ]

  a 4∗cos θ 4   a 4∗senθ 4

  d1 1

]

∗   −cos θ ∗senθ senθ ∗ senθ   −senθ ∗senθ

cos θ 1 cos θ 2 2

1

se sen n θ2 0

  cos θ 2 0

1

2

1

2

senθ 1   −cos θ1   1 0

  d1 1

5 DINÁMICA DE SISTEMAS MULTICUERPO MT 516

0 0

]

 

Facultad de Ingeniería Mecánica

[

T 3 =

c ( θ1 )∗c ( θ 2)∗c (θ3 )−c ( θ1 )∗s ( θ2)∗s ( θ3 ) c ( θ2 )∗c ( θ 3)∗s (θ1 )− s ( θ 1)∗s ( θ2)∗s ( θ3 ) c ( θ2)∗s (θ3 )+ c ( θ3 )∗s ( θ2) 0

−c ( θ )∗c ( θ )∗ s ( θ )− c ( θ )∗c ( θ )∗ s ( θ ) −c ( θ )∗s ( θ )∗ s ( θ )− c ( θ )∗ s ( θ )∗s ( θ ) c ( θ )∗ c ( θ )− s ( θ )∗ s ( θ ) 1

2

3

1

3

2

2

1

3

3

1

2

2

3

2

3

0

s ( θ 1) −c ( θ1) 0 0

a 3∗c (θ1)∗c ( θ2 )∗c ( θ 3)− a 3∗c ( θ1)∗s ( θ2 )∗ s ( θ 3) a 3∗c ( θ2)∗c ( θ3 )∗s ( θ 1)− a 3∗s ( θ1)∗s ( θ2 )∗s ( θ3) d 1+ a 3∗c ( θ3)∗s ( θ 2) 1

6 DINÁMICA DE SISTEMAS MULTICUERPO MT 516

]

 

[

)∗(( c ( θ )∗c (θ )∗ s (θ )+ c (θ )∗c ( θ )∗s (θ )) −c ( θ )∗(c (θ )∗s (θ )∗s ( θ )−c (θ )∗ c (θ )∗c (θ ))−s (θ )∗ −c (θ )∗(s (θ )∗ s( θ )∗s (θ )−c (θ )∗c ( θ )∗s (θ ))−s (θ )∗ )∗(( c (θ )∗s (θ )∗s (θ )+ c (θ )∗s (θ )∗s (θ )) T   4 4= c ( θ )∗(c ( θ )∗s ( θ )+ c ( θ )∗s ( θ ))+ s ( θ )∗(c (θ )∗c ( θ )− s ( θ )∗ s ( θ )) 4

1

2

3

1

2

3

4

1

2

3

1

3

2

4

1

2

3

2

3

1

4

2

1

3

3

3

2

4

2

3

3

2

4

2

3

2

3

0

s ( θ 4)∗ )∗(( c ( θ1)∗s ( θ2 )∗s (θ 3)− c (θ1 )∗c (θ 2)∗c ( θ3))− c ( θ 4 )∗(c (θ1 )∗c (θ 2)∗s (θ3 )+ c (θ1)∗c (θ3 )∗s ( θ2)) s ( θ4 )∗ )∗(( s( θ1)∗s (θ2 )∗s (θ 3)− c (θ2 )∗c (θ3 )∗s (θ1))− c ( θ 4 )∗(c (θ2 )∗ s (θ 1)∗s (θ3 )+ c ( θ3 )∗s (θ 1)∗s (θ2 )) c ( θ4 )∗(c ( θ 2)∗c ( θ3)− s ( θ2 )∗s ( θ 3))− s ( θ 4 )∗(c ( θ2 )∗ s ( θ 3)+ c ( θ 3)∗s ( θ2 )) 0

s ( θ 1) − c ( θ1 ) 0 0

a 4 c ( θ4 )( c ( θ 1) s ( θ2 ) s ( θ 3)− c ( θ1 )c ( θ 2) c ( θ3 ))−a 4 s ( θ4 )( c ( θ1 ) c ( θ2) s ( θ3 )+ c ( θ1 ) c ( θ3) s ( θ 2))+ a 3 ( θ1 ) c ( θ 2) c ( θ3 )−a 3 c ( θ 1) s ( θ2 ) s ( θ 3) a 4 s ( θ4 )( c ( θ 2) s ( θ1 ) s ( θ 3)+ c ( θ 3) s ( θ1 ) s ( θ2))− a 4 c ( θ 4 )( s ( θ1 ) s (θ 2) s ( θ3 )−c ( θ 2) c (θ3 ) s ( θ1))+ a 3 c ( θ2 ) c ( θ 3) s ( θ1 )−a 3 s ( θ 1) s ( θ2 ) s ( θ 3) a 1 + a 4 c ( θ 4 )( c ( θ2 ) s ( θ 3)+ c ( θ 3) s ( θ2 ))+ a 4 s ( θ 4 )( c ( θ2 ) c ( θ 3)− s ( θ2 ) s ( θ 3))+ a 3 c ( θ2 ) s ( θ 3)+ a 3 c ( θ 3) s ( θ2 ) 1

 

Facultad de Ingeniería Mecánica

]

 

 CINEMA CINEMATIC TICA A INVERS INVERSA A

FIGURA N° S,*)e!# de% $'#o &#'# ,ne!(),# ,n+e'*#

Donde:

√ 



2

2



 

R=  x +  y r = R − L 4



 

s = Z − L 1



 

q 4=−( q 2+ q 3 )

 

.#%%#ndo 3: 2

2

2

3

r + s − L 2 − L = D cos ( q 3 )= 2∗ L 2∗ L 3

 

Facultad de Ingeniería Mecánica

S, D  1 en)one* e% $'#o e* !6 &ee7o8 de %o on)'#',o *e &'o*,/e # #%%#' 3: q 3 =atan 2 ( √ 1− D , D ) 2

F,/" 12 S,*)e!# de% $'#o 92 6 93



  alfa = atan 2 ( L 3∗sen ( q 3 ) , L 2+ L 3∗cos ( q 3 ) )



  beta =atan 2 ( s ,r )

.#%%#ndo 2: q 2= beta−alfa

 

Facultad de Ingeniería Mecánica

F,/"13 S,*)e!# de $'#o 928 93 6 94 .#%%#ndo 4: q 4=−(q 2 + q 3 )

F,/"14 O',/en de oo'den#d#* de% $'#o .#%%#!o* 1: q 1= atan 2 ( y , x )

 

Facultad de Ingeniería Mecánica

 

Facultad de Ingeniería Mecánica

 

Facultad de Ingeniería Mecánica