Análisis De Mecanismos Asistidos Por ComputadoraTeoría De Maquinas

En los problemas 8-7 y 8-8 desarrolle una hoja de cálculo que determine la posición y velocidad del seguidor en los ángulos de la manivela que se encuentran entre 0 y 360 grados. Hagala flexible, de modo que se modifique rápidamente la longitud de cualquier eslabón. Use los valores listados para elaborar una gráfica de la velocidad del seguidor contra el ángulo de la manivela.

8-7 Bancada = 9 in; Manivela = 1 in; Acoplador = 10 in; Seguidor = 3.5 in; Velocidad de la manivela = 200 rad/s; Aceleración de la manivela = 0 rad/s^2.

θ BD γ θ4 θ3 ω3 ω4 α3 α4 L1 90 8.0 43.7 59.8 16.1 -25.0 -25.0 795.7 17476.4 L2 1

10 8.0 44.1 59.0 14.9 -21.7 -7.6 1671.5 18000.5 L3 1020 8.1 45.1 59.0 13.9 -17.8 9.4 2320.9 17638.4 L4 3.2

30 8.1 46.8 59.9 13.1 -13.7 24.9 2750.8 16511.4ω2 200

40 8.3 49.0 61.5 12.5 -9.7 38.2 2994.0 14801.2 α2 050 8.4 51.5 63.7 12.1 -6.0 49.0 3092.5 12696.460 8.5 54.4 66.3 11.9 -2.7 57.2 3085.2 10359.270 8.7 57.5 69.3 11.9 0.3 62.9 3002.4 7913.080 8.9 60.7 72.6 11.9 3.0 66.5 2865.1 5446.090 9.1 63.8 76.0 12.1 5.4 68.1 2685.6 3018.8

100 9.2 66.9 79.4 12.5 7.7 67.9 2469.6 673.9110 9.4 69.8 82.7 12.9 9.8 66.1 2218.2 -1556.8120 9.5 72.5 86.0 13.5 11.7 62.8 1928.9 -3646.8130 9.7 74.9 89.0 14.1 13.6 58.2 1597.5 -5571.8140 9.8 77.0 91.8 14.8 15.3 52.4 1218.5 -7308.1150 9.9 78.6 94.2 15.6 16.9 45.6 786.8 -8832.6160 9.9 79.8 96.3 16.5 18.2 37.8 298.6 -10123.0170 10.0 80.5 98.0 17.4 19.3 29.2 -247.6 -11159.8180 10.0 80.8 99.2 18.4 20.0 20.0 -849.7 -11927.0190 10.0 80.5 100.0 19.4 20.3 10.4 -1501.3 -12413.5200 9.9 79.8 100.2 20.4 20.0 0.5 -2191.0 -12612.6210 9.9 78.6 100.0 21.4 19.2 -9.5 -2902.1 -12521.5220 9.8 77.0 99.3 22.3 17.7 -19.5 -3613.0 -12139.7230 9.7 74.9 98.1 23.2 15.4 -29.2 -4297.0 -11466.3240 9.5 72.5 96.4 23.9 12.4 -38.6 -4923.1 -10498.9250 9.4 69.8 94.2 24.4 8.7 -47.6 -5456.6 -9231.6260 9.2 66.9 91.6 24.7 4.4 -55.8 -5860.0 -7655.7270 9.1 63.8 88.6 24.8 -0.5 -63.2 -6094.9 -5761.7280 8.9 60.7 85.3 24.7 -5.8 -69.4 -6124.6 -3543.8290 8.7 57.5 81.7 24.2 -11.2 -73.9 -5918.3 -1007.7300 8.5 54.4 78.0 23.6 -16.5 -76.4 -5456.4 1817.5310 8.4 51.5 74.1 22.6 -21.1 -76.2 -4738.7 4865.2

320 8.3 49.0 70.4 21.5 -24.9 -72.8 -3790.9 8016.3330 8.1 46.8 66.9 20.1 -27.2 -65.8 -2670.0 11090.7340 8.1 45.1 63.9 18.8 -28.1 -55.2 -1462.7 13854.8350 8.0 44.1 61.5 17.4 -27.3 -41.3 -273.7 16055.3360 8.0 43.7 59.8 16.1 -25.0 -25.0 795.7 17476.4

0 30 60 90120

150180

210240

270300

330360

-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5

Velocidad

Velocidad

posicion

velo

cidad

8-8 Bancada = 360 mm; Manivela = 40 mm; Acoplador = 400 mm; Seguidor = 140 mm; Velocidad de la manivela = 6 rad/s; Aceleración de la manivela = 20 rad/s^2.

θ BD γ θ4 θ3 ω3 ω4 α3 α4 L1 3600 320.0 46.4 64.9 18.5 -0.8 -0.8 -2.0 11.0 L2 40

10 320.7 46.7 64.0 17.3 -0.7 -0.3 -0.9 13.1 L3 40020 322.7 47.6 63.9 16.3 -0.6 0.2 0.0 14.4 L4 140

30 326.0 49.1 64.5 15.4 -0.4 0.6 0.9 15.1ω2 6

40 330.4 51.0 65.8 14.8 -0.3 0.9 1.5 15.2 α2 2050 335.7 53.3 67.6 14.3 -0.2 1.2 2.1 14.660 341.8 55.9 69.9 14.0 -0.1 1.5 2.4 13.670 348.4 58.7 72.5 13.9 0.0 1.7 2.7 12.380 355.2 61.5 75.4 13.9 0.1 1.8 2.9 10.790 362.2 64.4 78.5 14.1 0.1 1.8 3.0 9.0

100 369.1 67.2 81.5 14.3 0.2 1.9 3.1 7.1110 375.6 69.9 84.6 14.7 0.3 1.8 3.1 5.1120 381.6 72.3 87.6 15.3 0.3 1.7 3.1 3.1

130 386.9 74.5 90.4 15.9 0.4 1.6 3.0 1.1140 391.5 76.4 93.0 16.6 0.5 1.5 2.8 -0.9150 395.1 77.9 95.3 17.4 0.5 1.3 2.6 -2.8160 397.8 79.0 97.3 18.2 0.5 1.1 2.3 -4.6170 399.5 79.7 98.9 19.2 0.6 0.8 1.9 -6.2180 400.0 79.9 100.1 20.2 0.6 0.6 1.4 -7.8190 399.5 79.7 100.9 21.2 0.6 0.3 0.9 -9.1200 397.8 79.0 101.2 22.2 0.6 0.1 0.2 -10.2210 395.1 77.9 101.1 23.2 0.6 -0.2 -0.5 -11.1220 391.5 76.4 100.5 24.1 0.5 -0.5 -1.3 -11.7230 386.9 74.5 99.5 25.0 0.5 -0.8 -2.1 -12.1240 381.6 72.3 98.0 25.7 0.4 -1.0 -2.9 -12.2250 375.6 69.9 96.1 26.2 0.3 -1.3 -3.8 -12.1260 369.1 67.2 93.8 26.6 0.2 -1.5 -4.6 -11.6270 362.2 64.4 91.1 26.7 0.0 -1.7 -5.3 -10.7280 355.2 61.5 88.2 26.6 -0.1 -1.9 -5.8 -9.5290 348.4 58.7 84.9 26.3 -0.3 -2.0 -6.2 -7.9300 341.8 55.9 81.5 25.6 -0.5 -2.1 -6.3 -5.9310 335.7 53.3 78.1 24.8 -0.6 -2.1 -6.2 -3.5320 330.4 51.0 74.7 23.7 -0.7 -2.0 -5.8 -0.7330 326.0 49.1 71.6 22.5 -0.8 -1.8 -5.1 2.3340 322.7 47.6 68.8 21.1 -0.8 -1.5 -4.2 5.5350 320.7 46.7 66.5 19.8 -0.8 -1.2 -3.1 8.4360 320.0 46.4 64.9 18.5 -0.8 -0.8 -2.0 11.0

0 30 60 90120

150180

210240

270300

330360

-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5

Velocidad

Velocidad

posicion

velo

cidad

BD=

RAIZ ($ L$12+$ L$22−2∗$ L$1∗$ L$2∗cos (RADIANES (A 2 ) ) )

Γ =

GRADOS (ACOS ( $ L $32+$ L $42−B222∗$ L$3∗$ L$ 4 ))θ4 =

GRADOS (2∗ATAN ( $ L$2∗SENO (RADIANES (A 2 ) )−$ L$3∗SENO (RADIANES (C2 ) )$ L$ 2∗cos (RADIANES ( A2 ) )+$ L$4−$ L$1−$ L $3∗cos (RADIANES (C 2 ) ) ))

θ3 =

GRADOS (2∗ATAN ( −$ L$2∗SENO (RADIANES (A2 ) )+$ L$ 4∗SENO (RADIANES (C 2 ) )$ L$ 1+$ L$ 3−$ L$2∗cos (RADIANES (A2 ) )−$ L$4∗cos (RADIANES (C 2 ) ) ))

ω3 =

−$ L$5∗( $ L$2∗SENO (RADIANES (D2−A 2 ) )$ L$3∗SENO (RADIANES (C 2 ) ) )

ω4 =

−$ L$5∗( $ L$2∗SENO (RADIANES (E2−A2 ) )$ L$4∗SENO (RADIANES (C2 ) ) )

α3 =

( ($ L$6∗$ L$2∗SENO (RADIANES (A 2−D 2 ) ) )+($ L$52∗$ L$2∗cos (RADIANES (A2−D2 )) )−($G$ 22∗$ L$4 )+($ F $22∗$ L$3∗cos (RADIANES (D 2−E2 ) ) )$ L$ 3∗SENO (RADIANES (D 2−E2 ) ) )

α4 =

( ($ L$6∗$ L$2∗SE NO (RADIANES (A 2−E2 ) ) )+($ L $52∗$ L$2∗cos (RADIANES (A 2−E2 ) ) )+($ H $ 22∗$ L$3 )−($ F $22∗$ L$ 4∗cos (RADIANES (D 2−E2 ) ) )$ L$4∗SENO (RADIANES (D2−E2 ) ) )

8.9descentrado= 3in; manivela 7.5in; acoplador=52.5in; velocidad de la manivela= 4 rad/s; aceleración de la manivela =0 rad/sclear allclc %Teoria de maquinas %Mecanismo de manivela-corredera descentrado L1=3;L2=7.5;L3=52.5;w2=4;a=0; A=[];B=[];C=[];D=[];E=[];F=[];G=[];H=[];for i=0:10:360 A=[A i]; pi=4*atand(1.0);a=i*(pi/180);b=L2*(sind(a));c=L2*(cosd(a));d=asind((L1+b)/L3);ta3=d(180/pi);e=L2*(sind(d));f=L2*(cosd(d));g=L3*(sind(d));h=L3*(cosd(d));L4=(c+h);w3=-w2*(c/f);v4=-w2*(b)-w3*(g);a3=(b*((w2)^2)+g*((w3)^2))/h;a4=-(g*(a3)+c*((w2)^2)+h*((w3)^2)); B=[B ta3];C=[C w3];D=[D a3];E=[E L4];F=[F v4];G=[G a4]; end

fprintf ' theta 3 w3 a3 L4 v4 a4'H=[B' C' D' E' F' G']

theta 3 w3 a3 L4 v4 a4

H =

3.2758 -4.0065 0.9188 59.9142 12.0196 -964.1311

4.7006 -3.9525 1.6828 59.7095 11.7957 -942.8374

6.0849 -3.7801 2.3094 59.2519 10.7760 -871.5569

7.3870 -3.4931 2.7343 58.5595 8.5784 -757.6525

8.5672 -3.0988 2.9324 57.6595 4.9514 -613.3539

9.5889 -2.6076 2.9245 56.5874 -0.1772 -454.6955

10.4199 -2.0335 2.7731 55.3842 -6.6720 -299.8526

11.0336 -1.3938 2.5671 54.0947 -14.1858 -166.9482

11.4101 -0.7086 2.3977 52.7648 -22.1847 -71.5803

11.5370 0 2.3328 51.4393 -30.0000 -24.4949

11.4101 0.7086 2.3977 50.1601 -36.9038 -29.9047

11.0336 1.3938 2.5671 48.9644 -42.1957 -84.8634

10.4199 2.0335 2.7731 47.8842 -45.2896 -179.8526

9.5889 2.6076 2.9245 46.9456 -45.7855 -300.4265

8.5672 3.0988 2.9324 46.1689 -43.5187 -429.5032

7.3870 3.4931 2.7343 45.5691 -38.5784 -549.8064

6.0849 3.7801 2.3094 45.1565 -31.2973 -646.0307

4.7006 3.9525 1.6828 44.9374 -22.2146 -706.4835

3.2758 4.0065 0.9188 44.9142 -12.0196 -724.1311

1.8530 3.9413 0.1054 45.0865 -1.4814 -697.0992

0.4746 3.7589 -0.6648 45.4505 8.6261 -628.7119

-0.8185 3.4645 -1.3145 45.9995 17.5983 -527.1271

-1.9876 3.0660 -1.7964 46.7231 24.8666 -404.5747

-2.9975 2.5747 -2.1005 47.6073 30.0497 -276.1752

-3.8173 2.0044 -2.2520 48.6335 32.9867 -158.3380

-4.4218 1.3722 -2.2999 49.7786 33.7449 -66.8215

-4.7923 0.6970 -2.2996 51.0141 32.6014 -14.6664

-4.9171 0 -2.2942 52.3068 30.0000 -10.3237

-4.7923 -0.6970 -2.2996 53.6188 26.4870 -56.3420

-4.4218 -1.3722 -2.2999 54.9089 22.6367 -148.9063

-3.8173 -2.0044 -2.2520 56.1335 18.9748 -278.3380

-2.9975 -2.5747 -2.1005 57.2491 15.9130 -430.4443

-1.9876 -3.0660 -1.7964 58.2137 13.7007 -588.4253

-0.8185 -3.4645 -1.3145 58.9898 12.4017 -734.9732

0.4746 -3.7589 -0.6648 59.5459 11.8952 -854.2382

1.8530 -3.9413 0.1054 59.8586 11.9003 -933.4531

3.2758 -4.0065 0.9188 59.9142 12.0196 -964.1311