INSTITUTO POLITÉCNICO NACIONAL

ESCUELA SUPERIOR DE INGENIERIA MECÁNICA Y ELÉCTRICA

UNIDAD PROFESIONAL “AZCAPOTZALCO”

ANALISIS DINAMICO DE UN ROBOT DE 4 GRADOS DE LIBERTAD

EXAMEN

INTERFACES Y PERIFÉRICOS II

ALUMNOS:

DE JESUS PEREZ SAÚL DIANA ELIZABETH FAUSTINO DOMÍNGUEZ MARCOS CÉSAR FERNÁNDEZ CALVILLO DANIEL MIGUEL FLEMATE ROJAS FRANCISCO JAVIER OLVERA ARGUETA

PROFESORES:

ING. ISRAEL VÁZQUEZ CIANCA DR. EMMANUEL MERCHÁN CRUZ

MÉXICO, D.F 2012

PUNTO DISTANCIA

1 0

2 0.3571

3 0.3285

4 0.2

5 0.08571

6 0.02857

7 0.2

8 0.2

9 0.2

10 0.2

11 0.2

12 0.2

13 0.2

14 0.2

15 0.2

16 0.2

17 0.2

18 0.2

19 0.2

20 0.02857

21 0.08571

22 0.2

23 0.3285

24 0.3571

25 0

TRAYECTORIA REALIZADA

TI=

0 1 0 -0.7

0 0 -1 0

-1 0 0 1

0 0 0 1

TF=

0 1 0 -0.7

0 0 -1 0

-1 0 0 0.125

0 0 0 1

ACOTACIÓN

Desplazamiento [ ]

PERFIL DE VELOCIDAD DEL EFECTOR FINAL

PERFIL DE ACELERACIÓN DEL EFECTOR FINAL

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

VELOCIDAD

VELOCIDAD

-250

-200

-150

-100

-50

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ACELERACIÓN

ACELERACIÓN

TETA1 VEL1 ACEL1

-1.86E-16 0.00E+00 0.00E+00

6.66E-17 -4.08E-16 -1.59E-15

-7.92E-17 1.59E-16 2.09E-16

-2.69E-17 9.04E-17 -4.97E-16

-8.85E-18 1.90E-16 3.09E-15

7.41E-18 -7.54E-17 -4.27E-15

5.25E-18 4.65E-17 2.29E-16

1.46E-17 7.80E-19 1.46E-15

1.47E-17 -2.90E-16 -1.68E-15

-4.34E-17 4.59E-17 -1.08E-17

-3.42E-17 4.80E-17 1.34E-15

-2.46E-17 -2.20E-16 -3.38E-16

-6.87E-17 -1.53E-16 -1.29E-17

-9.93E-17 -1.50E-16 -8.72E-16

-1.29E-16 2.41E-17 -6.28E-16

-1.25E-16 1.50E-16 1.25E-15

-9.46E-17 -1.01E-16 -1.50E-15

-1.15E-16 2.00E-16 3.57E-16

-7.47E-17 1.29E-16 -4.78E-15

-4.90E-17 1.09E-15 -4.00E-14

1.68E-16 9.09E-15 3.58E-13

4.28E-16 -1.14E-15 -2.27E-14

3.30E-16 8.08E-16 8.94E-15

4.92E-16 -9.81E-16 -2.99E-15

1.69E-16 0.00E+00 0.00E+00

-1.00E-13

-5.00E-14

0.00E+00

5.00E-14

1.00E-13

1.50E-13

2.00E-13

2.50E-13

3.00E-13

3.50E-13

4.00E-13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ACEL1

VEL1

TETA1

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]

TETA2 VEL2 ACEL2

2.21696771 0 0

2.23756594 0.09557977 0.03751292

2.27169748 0.08218391 -16.7406369

2.29869489 5.58148312 92.0146853

3.41499152 -12.8214539 -626.591739

2.3160647 40.883724 1420.74378

3.48411269 0.29307415 0.04610929

3.54272753 0.28385229 0.04990455

3.59949798 0.27387138 0.05472936

3.65427226 0.26292551 0.06034608

3.70685736 0.2508563 0.06653913

3.75702862 0.23754847 0.07312144

3.80453832 0.22292418 0.07994753

3.84912315 0.20693468 0.08693144

3.89051009 0.18954839 0.09406879

3.92841977 0.17073463 0.1014651

3.96256669 0.15044161 0.10937624

3.99265501 0.12856636 0.11827502

4.01836829 0.10491136 0.08374619

4.03935056 0.08816212 -0.38351657

4.05698298 0.16486544 3.11195166

4.06169319 0.07595698 409.442342

4.06820346 -35.0173462 -280.989216

-2.93526577 21.180497 64.4763989

4.02252751 0 0

-1000

-500

0

500

1000

1500

2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ACEL2

VEL2

TETA2

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]

TETA3 VEL3 ACEL3

-5.28550166 0 0

-5.16397223 0.24455826 0.31656393

-5.07664048 0.13151328 -56.9411269

-5.03343836 18.8366735 312.699657

-1.26610367 -43.7032579 -2024.26284

-5.01190991 129.79631 4547.60741

-1.30362933 -0.12883376 -0.1609317

-1.32939608 -0.09664742 -0.15853147

-1.34872557 -0.06494112 -0.15710853

-1.36171379 -0.03351942 -0.15643223

-1.36841768 -0.00223297 -0.15638857

-1.36886427 0.02904474 -0.15697005

-1.36305532 0.06043875 -0.15827511

-1.35096757 0.09209377 -0.16051666

-1.33254882 0.12419711 -0.16404306

-1.3077094 0.15700572 -0.16937927

-1.27630825 0.19088157 -0.17730393

-1.23813194 0.22634236 -0.18899426

-1.19286347 0.26414121 -0.44266694

-1.14003522 0.3526746 -3.40547426

-1.06950031 1.03376945 5.00036795

-1.03996551 0.89090894 -93.0696641

-0.96360571 8.86790985 65.4653672

0.80997626 -4.22516359 -12.8619896

-0.57798998 0 0

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

6000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ACEL3

VEL3

TETA3

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]

TETA4 VEL4 ACEL4

1.49773762 0 0

1.35560997 -0.34013804 -0.35407685

1.23414667 -0.21369719 -21.9527158

1.16394714 6.99776996 118.90276

2.56350114 -16.7827821 -770.332865

1.12504888 49.2424478 1729.32055

2.53190562 -0.16424039 0.11482241

2.49905754 -0.18720488 0.10862692

2.46161656 -0.20893026 0.10237917

2.41983051 -0.22940609 0.09608615

2.37394929 -0.24862332 0.08984943

2.32422463 -0.26659321 0.08384861

2.27090599 -0.28336293 0.07832758

2.2142334 -0.29902845 0.07358522

2.15442771 -0.3137455 0.06997427

2.09167861 -0.32774035 0.06791416

2.02613054 -0.34132318 0.0679277

1.9578659 -0.35490872 0.07071925

1.88688416 -0.36905257 0.35892075

1.81307365 -0.44083672 3.78899083

1.7249063 -1.19863489 -8.11231961

1.6906613 -0.96686592 50.1647919

1.60779122 -5.26649023 -37.1902635

0.55449318 2.17156247 6.61054025

1.26785145 0 0

-1000

-500

0

500

1000

1500

2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ACEL4

VEL4

TETA4

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]

TORQUE1A TORQUE2A TORQUE3A TORQUE4A

-12.0835717 1.87E-15 -9.43E-17 0

-12.2156262 0.08424872 0.05115289 0.00066715

-12.4297409 -26.07868 -10.8967413 -0.08171135

-12.5948073 21.8643468 64.1495096 2.9771923

-15.0030066 -332.012015 -397.092073 14.9234531

-12.6989418 -3681.45566 1143.4625 125.446361

-14.8334734 -0.0018086 -0.02857218 0.00096628

-14.6611454 0.00475228 -0.02688324 0.00094518

-14.4698371 0.01203644 -0.02500767 0.00092987

-14.2630772 0.01988133 -0.02294911 0.00092064

-14.0446694 0.02812731 -0.02071955 0.00091792

-13.8186653 0.03662307 -0.01834008 0.00092216

-13.5893102 0.04523428 -0.01584099 0.00093382

-13.3609713 0.05385417 -0.01326088 0.00095337

-13.1380596 0.06241586 -0.01064519 0.00098134

-12.9249585 0.0709067 -0.0080441 0.00101852

-12.7259705 0.07938736 -0.00551013 0.00106612

-12.5452961 0.08802098 -0.00309568 0.00112615

-12.3870596 0.00880507 -0.04021337 0.00138722

-12.2553963 -1.04231925 -0.51704244 0.00306136

-12.1430335 4.31163677 1.36119585 0.01377224

-12.1127566 366.574559 85.574374 1.73496264

-12.0707301 -352.029282 -271.368728 5.46616684

-15.1319423 87.4144085 86.7974959 3.22317075

-12.3611398 1.97E-15 2.43E-16 0

TORQUES INCISO A

-4000

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

1000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

TORQUE4A

TORQUE3A

TORQUE2A

TORQUE1A

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]

TORQUE1B TORQUE2B TORQUE3B TORQUE4B

-31.3111717 3.24E-15 -7.71E-16 0

-31.4432262 0.32032074 0.232731 0.00984843

-31.6573409 -86.8323613 -50.4893028 -1.50268203

-31.8224073 -18.4204682 280.457898 45.5722423

-34.2306065 -1139.76417 -1587.10744 209.692913

-31.9265418 -16844.1068 4366.06803 1875.69001

-34.0610734 -0.04965648 -0.10629125 0.01426418

-33.8887454 -0.02858898 -0.09967176 0.01395263

-33.6974371 -0.00572617 -0.09229813 0.0137266

-33.4906772 0.01855233 -0.08418118 0.01359045

-33.2722694 0.0438489 -0.07537103 0.01355031

-33.0462653 0.06976309 -0.0659592 0.0136129

-32.8169102 0.09591227 -0.0560776 0.01378498

-32.5885713 0.12195574 -0.04589451 0.01407349

-32.3656597 0.14762055 -0.03560805 0.01448651

-32.1525586 0.17272924 -0.02543843 0.01503536

-31.9535705 0.19723156 -0.0156206 0.01573792

-31.7728961 0.22124765 -0.00639927 0.01662418

-31.6146596 -0.06597965 -0.17034237 0.02047802

-31.4829964 -3.84686483 -2.26601479 0.04519151

-31.3706335 14.0266987 6.00917187 0.20330454

-31.3403566 1044.68668 365.862741 26.7476194

-31.2983301 -1092.82943 -1003.66819 79.9076206

-34.3595423 277.106088 353.036095 47.760637

-31.5887398 4.80E-15 1.28E-15 0

TORQUES INCISO B

-20000

-15000

-10000

-5000

0

5000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

TORQUE4B

TORQUE3B

TORQUE2B

TORQUE1B

ACOTACIÓN

Desplazamiento [ ]

Velocidad [

]

Aceleración [

]

Torque [ ]