1mecanismos

8/18/2019 1mecanismos

1/30

UNI – FIM

“AÑO DE LA DIVERSIFICACIÓN PRODUCTIVA Y

FORTALECIMIENTO DE LA EDUCACIÓN”

MECANISMO PARADOJO DE CHÉBYSHEV DEPALANCAS ARTICULADAS

UNIVERSIDAD: UNIVERSIDAD NACIONAL DE INGENIERÍA

FACULTAD: FACULTAD DE INGENIERÍA MECÁNICA

ÁREA ACADEMICA: INGENIERÍA MECÁNICA

CURSO: MECÁNICA DE MÁQUINAS MC-417

SECCIÓN: A

PROFESOR: Ing. J!g" Á#$%&

ALUMNOS 1. A%'!n( D$n$)$ J*n+ T",! 1114/

2. G0"( L(&! C!$23$&n 1415G

3. 6&0&n M&!$n L$2 1184A

4. M"%)*! G&%%&!, A%'"!3 F"!n&n, 1I

. S&%$n&2 C&%$93! J2" L$2 115A

PERIODO ACADMICO: 15 ; II

FEC6A DEPRESENTACIÓN:

4-1-15


2/30

MCANICA DE MÁQUINAS UNI - FIM

!NDICE

INTRODUCCIÓN

CAP!TULO 1" TEMA TEÓRICO

CAP!TULO 2" AN#LISIS DEL MECANISMO

.1. R"

.. G!&, ," 0#$%$,&, ,"% 0")&n$20

.. An%$2$2 )$n"03$)

..1. P! "% 0>3, g!?$) ,"% 0#$0$"n3 !"%&3$# 1

... P! "% 0>3, &n&%@3$) 1

.4. D$&g!&0&2 )$n"03$)2

.5. An%$2$2 )$n"3233$)

.5.1. P! "% 0>3, g!?$) 1

.5.. P! "% 0>3, &n&%@3$) 1

CAPITULO 3" TRABAJO DE INVESTI$ACIÓN

ANE%OS

BIBLIO$RAF!A

Página 2


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INTRODUCCIÓN

Página 3


4/30


TEMA TEÓRICO

Página 4


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#NALISIS DEL MECANISMO

2.1. R&'(&)&*+,-/* &)0&+-, &5 &-,*)6

2.2. $(,6 & 675, &5 &-,*)6

Página 5


6/30


P,"02 )&%)%&! "% g!&, ," 0#$%$,&, ,"% 0")&n$20 2&n, %& 2$g$"n3"

")&)$=n:

GDM n - C 5 - C 4

Dn,":

n : NB0"! ," "2%&'n"2 0=#$%"2

C 5 : NB0"! ,"


7/30


2.3. A*5)) -*&+-6

2.3.1. P6( &5 8+66 9(:-6 &5 67&*+6 (&5,+76

P6)-/* 1

cm 0734.31YCK (15.5367):YC

cm 4002.64YXK (32.2001):YX

cm 1338.189XDK (94.5669):XD

cm 511.34XBK (17.2555):XB

cm 100CDK (50.0000):CD

cm 100BCK (50.0000):BC

cm 4.58ABK (29.2000):ABcm7.55O6DK (27.8500):O6D

cm 100O5CK (50.0000):O5C

cm 3.12O2AK (O2A):O2A

mm6.1500:(O2A)

:mcani!m"#$!Dimn!i"n

(mm)

cm 2K :mcani!m"#$i%nc"n&ig'ac#!ca$a#ac*"

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A-&5&(,-6*&)"

(mm)

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Página 9


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mm6084.5)( 1055.70 YC

:

mm7427.1)( 7842.21 O5C

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mm6236.11)( 2952.145 YX

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mm1374.34)( 7107.426 XD

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mm4158.50)( 1976.630 O6D:

mm2288.6)( 8608.77 XB

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mm0328.0)( 0.4101 BA

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P6)-/* 2

Página 11


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cm 0882.178YDK (89.0441):YDcm 8978.125XCK (62.9489):XC

cm 942.64YXK (32.4710):YX

cm 3776.169XBK (84.6888):XB

cm 100CDK (50.0000):CD

cm 100BCK (50.0000):BC

cm 4.58ABK (29.2000):AB

cm7.55O6DK (27.8500):O6D

cm 100O5CK (50.0000):O5C

cm 3.12O2AK (O2A):O2A

mm6.1500:(O2A)

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cm 2K :mcani!m"#$i%nc"n&ig'ac#!ca$a#ac*"

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13/30


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14/30


(mm)

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mm7.8377)( YD

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mm65.9147)( DO6

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Página 14


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16/30


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2.3.2. P6( &5 8+66 ,*,5;+-6

P&!& %& !"2%)$=n ,"% 0")&n$20

" ,"n3&! &% 0")&n$20 "n 2 ?!0& )0


17/30


V,(,0&n"!&:

⃗r2+⃗r

3=⃗r

1

r2∗ei θ

2

+r3∗ei θ

3

=r 1∗eiθ

1

Página 17


18/30


(¿θ1)(¿θ

3)=r

1∗cos¿

(¿θ2)+r

3∗cos ¿

r2∗cos ¿

(¿θ1)(¿θ

3)=r

1∗sin¿

(¿θ2)+r

3∗sin ¿

r2∗sin ¿

θ3=sin−1(

r1∗sinθ

1−r

2∗sinθ

2

r 3)

θ1=−cos−1 r2

2

+r12

−r32

2∗r2∗r

1

+θ1

⃗r9+⃗r

7=⃗r

1

r9∗ei θ9+r

7∗eiθ7=r

1∗ei θ1

(¿θ1)(¿θ

7)=r

1∗cos¿

(¿θ9)+r

7∗cos¿

r9∗cos ¿

(¿θ1)(¿θ

7)=r

1∗sin ¿

(¿θ9)+r

7∗sin¿

r9∗sin ¿

θ1=sin−1(

r9∗sinθ

9+r

7∗sinθ

7

r1)

Página 18


19/30


r9∗cosθ

9+r

7∗cosθ

7

¿¿

r9∗sin θ

9+r

7∗sin θ

7

¿¿

¿r1=√ ¿

⃗r7+⃗r

4

2=⃗r

5

r7∗ei θ7+

r4

2∗ei θ4=r

5∗e i θ5

(¿θ5)

(¿θ4)=r

5∗cos¿

(¿θ7)+

r 4

2∗cos¿

r7∗cos¿

(¿θ5)(¿θ

4)=r

5∗sin¿

(¿θ7)+r4

2 ∗sin ¿

r7∗sin ¿

θ7=cos−1

r7

2+r5

2−( r42 )2

2∗r5∗r

7

+θ5

r5∗cosθ

5−

r4

2∗cosθ

4

¿¿

r5∗sin θ5−r4

2∗sinθ4

¿¿¿

r7=√ ¿

⃗r5+⃗r

4

2=⃗ra

Página 19


20/30


r5∗ei θ5+

r4

2∗e i θ4=ra∗e

i θa

(¿θa)

(¿θ4)=ra∗cos¿

(¿θ5)+

r 4

2∗cos¿

r5∗cos¿

(¿θa)

(¿θ4)=r

a∗sin¿

(¿θ5)+

r 4

2∗sin¿

r5∗sin ¿

θ4=sin−1(2(

ra∗sin θa−r 5∗sin θ5r 4

))

θ5=cos−1

r5

2+ra2−( r42 )

2

2∗r5∗ra

+θa

⃗r8+⃗r

6=⃗ra

r8∗ei θ8+r

6∗eiθ6=ra∗e

i θa

(¿θa)

(¿θ6)=

ra∗

cos

¿(¿θ8)+r

6∗cos¿

r8∗cos¿

(¿θa)(¿θ

6)=ra∗sin ¿

(¿θ8)+r

6∗sin ¿

r8∗sin¿

Página 20


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θa=tan−1 r8∗sin θ8+r6∗sin θ6

r8∗cosθ8+r6∗cosθ6

(¿θ8)+

r6∗

sin(¿θ6)

sin θar8∗sin ¿ra=¿

Cn "23&2 ")&)$n"2

P6)-6* 1"

Ángulos θ1 θ3 θ4 θ5 θ6 θ7 θa

radianes1.484861

38

1.446617

98

-

0.591226

07

1.688910

64 4.331

2.119638

61

0.548842

28

sexagesimales 85.07629

82.88510

46

-

33.87475

87

96.76745

16

248.1480

21

121.4463

46

31.44634

65

Posiciones r1 (cm r7 (cm ra (cm θ!

29.41290

06

90.86620

39

41.753239

23

6.336740

931

363.0685

112

P6)-/* 2"

Ángulos θ1 θ3 θ4 θ5 θ6 θ7 θa

radianes

-

1.361566

18

-

1.275708

48

0.491216

3

1.786819

8 2.041

2.709814

37

1.139018

05

sexagesimales

-

78.01199

57

-

73.09271

2

28.14462

06

102.3772

33

116.9406

86

155.2609

27

65.26092

68

Posiciones r1 (cm r7 (cm ra (cm θ!

Página 21


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23.47526

65

60.34349

53

79.741222

53

2.199356

813

126.0138

63

A*5)) & V&56-,&)

P&!& #"%)$,&,"2: H 1!&,2

E)&)$n"2 & 3$%$(&! ,"!$#&,& ," %&2


23/30


raωa (i ei θa )+ ŕa e

i θa=r5ω

5(i e iθ5 )+

r4

2ω

4 (ie i θ4)

raωa

(−sin

(θa

))+ŕa cos

(θa

)=r

5ω

5

(−sin

(θ

5

))+r4

2

ω4

(−sin

(θ

4

))

raωa (cos (θa ))+ŕa sin (θa )=r5ω5 (cos (θ5 ))+r4

2ω

4 (cos (θ4 ))

r6ω

6 (i ei θ6 )=raωa (i e

i θa )+ŕ aei θa

r6ω6 (−sin (θ6 ) )=r aωa (−sin (θa ))+ ŕacos (θa )

r6ω6 (cos (θ6 ))=raωa (cos (θa ) )+ŕa sin (θa )

P2$)$=n 1

"elocidades

#1(rad$s

#3(rad$s

#4(rad$s

#5(rad$s

#6(rad$s

#7(rad$s

-

3.708569

73

-

4.032370

89

-

0.878388

66

-

1.793611

22 2.5

-

1.335999

94

#a(rad$s

r%1(cm$s

r%7(cm$s

r%a(cm$s

-

1.335999

94

56.60351

08

-

19.10675

33 41.5814

P2$)$=n

"elocidades

#1(rad$s

#3(rad$s

#4(rad$s

#5(rad$s

#6(rad$s

#7(rad$s

-

3.294366

92

-

4.916012

-

0.363575

84

1.445586

15 2.5

0.541005

15

#a(rad$s

r%1(cm$s

r%7(cm$s

r%a(cm$s

0.54100515

-16.96980

72.1323946

-54.58557

Página 23


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17 92

A*5)) & ,-&5&(,-6*&)

P&!& #"%)$,&,"2: !&,2E)&)$n"2 & 3$%$(&! ,"!$#&,& ," %&2 #"%)$,&,"2:

r6ω

6

2 (−ei θ6 )+r6α

6 (ie i θ6 )=r aωa

2 (−ei θa )+raα a ( iei θa )+2 ŕaωa (ie

i θa )+ŕaei θa

IR :r6ω62 (−cos (θ6 ))+r6α 6(−sin (θ6 ))=raωa2 (−cos (θa ))+r aα a (−sin (θa ))+2 ŕ aωa (−sin (θa ))+ ŕa cos (θa )

II :r 6ω62 (−sin (θ6 ))+r6α 6 (cos (θ6 ))=raωa2 (−sin (θa ))+raα a (cos (θa ))+2 ŕ aωa (cos (θa ))+ŕ asin (θa )

r5ω

5

2 (−ei θ5 )+r5α

5(i ei θ5 )+

r4

2ω

4

2 (−e i θ4 )+r64

2α 4 (i ei θ4 )=raωa

2 (−e i θa )+raα a (i ei θa )+2 ŕaωa (i e

i θa )+ŕa ei θa

IR :r65ω

5

2 (−cos (θ5 ))+r5α 5 (−sin (θ5 ))+r4

2ω

4

2 (−cos (θ4 ))+r4

2α

4 (−sin (θ4 ))=raωa2 (−cos (θa ))+raα a (−sin (θ

II :r5ω

5

2 (−sin (θ5 ) )+r5α 5 (cos (θ5 ))+r4

2ω

4

2 (−sin (θ4 ))+r4

2α

4 (cos (θ4 ) )=r aωa2(−sin (θa ))+r aα a (cos (θa ))+2 ŕ

r5ω

5

2 (−ei θ5 )+r5α

5(i ei θ5 )=

r4

2ω

4

2 (−ei θ4 )+r64

2α

4 (iei θ4 )+r

7ω

7

2 (−e iθ7)+r7α 7 (ie i θ7)+2 ŕ

7ω

7 (iei θ7)+ŕ

7ei θ

7

IR :r65ω52 (−cos (θ5 ))+r5α 5 (−sin (θ5 ))=r4ω42 (−cos (θ4 ))+r4α 4 (−sin (θ4 ))+r7ω72(−cos (θ7 ))+r7α 7 (−sin (θ7 )

II :r5ω

5

2 (−sin (θ5 ) )+r5α 5 (cos (θ5 ))=r4

2ω

4

2 (−sin (θ4 ))+r4

2α

4 (cos (θ4 ))+r7ω72(−sin (θ7 ) )+r7α 7 (cos (θ7 ))+2 ŕ7

r1ω

1

2 (−e i θ1 )+r1α

1 (ie i θ1 )+2 ŕ

1ω

1(i ei θ1 )+ŕ

1eiθ

1=r7ω

7

2 (−ei θ7 )+r7α

7(i e iθ7 )+2 ŕ

7ω

7(i ei θ7 )+ ŕ

7ei θ

7

IR :r1ω12 (−cos (θ1 ))+r1α 1 (−sin (θ1) )+2 ŕ1ω1 (−sin (θ1) )+ŕ1cos (θ1 )=r7ω72 (−cos (θ7 ))+r7α 7 (−sin (θ7))+2 ŕ7

II :r 1ω12 (−sin (θ1 ))+r1α 1 (cos (θ1 ))+2 ŕ 1ω1 (cos (θ1 ))+ ŕ1sin (θ1)=r7ω72 (−sin (θ7 ))+r7α 7 (cos (θ7 ) )+2 ŕ7ω7 (co

r1ω

1

2 (−e i θ1 )+r1α

1 (ie i θ1 )+2ŕ

1ω

1(i ei θ1 )+ŕ

1eiθ

1=r2ω

2

2 (−e i θ2 )+r2α 2( iei θ2 )+r

3ω

3

2 (−ei θ3 )+r3α 3 (i ei θ3 )

IR :r1ω12 (−cos (θ1 ))+r1α 1 (−sin (θ1) )+2 ŕ1ω1 (−sin (θ1) )+ŕ1 cos (θ1 )=r62ω22 (−cos (θ2))+r 2α 2(−sin (θ2) )+rww

II :r 1ω12 (−sin (θ1 ))+r1α 1 (cos (θ1 ))+2 ŕ 1ω1 (cos (θ1 ))+ ŕ1sin (θ1 )=r2ω22 (−sin (θ2 ))+r2α 2 (cos (θ2 ))+r 3ω32 (−si

Página 24


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P6)-/* 1

&celeraciones

'1(rad$s!

'3(rad$s!

'4(rad$s!

'5(rad$s!

'6(rad$s!

'7(rad$s!

25.14817

89

-

10.67190

19

8.165764

98

3.851087

04 -1.605

6.008426

01

'a(rad$s!

r%%1(cm$s!

r%%7(cm$s!

r%%a(cm$s!

6.008426

01

-

167.9437

53

-

109.1040

08

187.2857

37

P6)-/* 2

&celeraciones

'1(rad$s!

'3(rad$s!

'4(rad$s!

'5(rad$s!

'6(rad$s!

'7(rad$s!

-

1.724196

1

-

10.26605

11

-

1.056456

56

-

1.579518

41 -1.605

-

1.317987

49

'a(rad$s!

r%%1(cm$s!

r%%7(cm$s!

r%%a(cm$s!

-

1.31798

749

306.1449

541

-

70.2318

731

-

49.4679

035

Página 25


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2.4. D,9(,,) -*&+-6)

Página 26


27/30


2.. A*5)) -*&+6)++-6

2..1. P6( &5 8+66 9(:-6

D&32

266

255

244

233

222

mg 042918.0 g9246.0:m

mg 138333.0 g66.1:m

mg 106667.1 g32.3:m

mg 027552.0 g9694.0:m

mg 000257.0 g2042.0:m

==

==

==

==

==

6&%%&02 %&2 &)"%"!&)$n"2 ," %2 )"n3! ," g!",&,

26a6

25a5

24a4

23a3

22a2

!g

m 3351.3 K (26.6811):

!g

m 0913.3 K (24.7302):

!g

m 1825.6 K (49.4603):

!g

m 9413.8 K (71.5303):

!g

m 15.6 K (49.2):

aa

aa

aa

aa

aa

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=⋅=

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E?")32 ,$n0$)2

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m 1684.0:

m 0.8547:

m 6767.3:

m 0.4975:

m 0:

mm 6.1672)( 0836.3 m:

mm 2632.10)( 1316.5 m:mm 0518.41)( 5259.20 m:

mm 3354.17)( 6677.8 m:

mm 5116.2)( 2558.1 m:

mm

0.5K

i6 66i6

i5 55i5

i4 44i4

i3 33i3

i2 22i2

i6i666i6

i5i555i5

i4i444i4

i3i333i3

i2i222i2

aaa

aa

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=

D$23&n)$&2 ," ,"2


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2..2. P6( &5 8+66 ,*,5;+-6

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