1、哈工大机械原理大作业课程：机械原理班别：072103学号：20101002183姓名：段诚诚课本P67题4-23 ：在图示的正弦机构中,已知lAB =100 mm,h1=120 mm,h2 =80 mm,W1 =10 rad/s(常数)，滑块2和构件3的重量分别为 G2 =40 N和 G3 =100 N,质心S2 和S3 的位置如图所示，加于构件3上的生产阻力Fr=400 N，构件1的重力和惯性力略去不计。试用解析法求机构在1=60、150、220位置时各运动副反力和需加于构件1上的平衡力偶Mb 。解：分别对三个构件进行受力分析如图：构件3受力图构件2受力图构件1受力图(1)滑块2：VS2 =
2、LAB W1 as2 = LAB W12 构件3： S=LAB sin1 V3 =LABW1 COS1 a3 =-LABW12 sin1 (2)确定惯性力：F12=m2as2=(G2/g)LABW12 F13=m3a3=(G3/g)LABW12sin1 (3)各构件的平衡方程：构件3：Fy=0,FR23 =Fr-F13 Fx=0,FR4=FR4 MS3 =0,FR4=FR23LA cos1/h2构件2：Fx=0,FR12x=F12cos1 Fy=0,FR12y=FR32-F12sin1构件1： Fx=0,FR41x=FR12x Fy=0,FR41y=FR12y MA =0,Mb =FR32LA
3、Bcos1总共有八个方程，八个未知数。归纳出一元八次方程矩阵：1 0 0 0 0 0 0 0 FR23 Fr-F130 1 -1 0 0 0 0 0 FR4 0-LABCOS1/h2 0 1 0 0 0 0 0 FR4 0 0 0 0 1 0 0 0 0 FR12x = F12cos1 -1 0 0 0 1 0 0 0 FR12y -F12 sin1 0 0 0 -1 0 1 0 0 FR41x 0 0 0 0 0 -1 0 1 0 FR41y 0 -LABCOS1 0 0 0 0 0 0 1 Mb 0 AX=B进而可得：X=AB。接下来运用Matlab软件进行分析:(1)编写函数F用于实现上
4、述运算功能：function y=F(x)%input parameters%x(1)=lAB%x(2)=h1%x(3)=h2%x(4)=W1%x(5)=G2%x(6)=G3%x(7)=Fr%x(8)=theta1%output parameters%y(1)=FR23%y(2)=FR4%y(3)=FR4%y(4)=FR12x%y(5)=FR12y%y(6)=FR41x%y(7)=FR41y%y(8)=Mb%A=1 0 0 0 0 0 0 0; 0 1 -1 0 0 0 0 0; -x(1)*cos(x(8)/x(3) 0 1 0 0 0 0 0; 0 0 0 1 0 0 0 0; -1 0
5、0 0 1 0 0 0; 0 0 0 -1 0 1 0 0; 0 0 0 0 -1 0 1 0; -x(1)*cos(x(8) 0 0 0 0 0 0 1;B=x(7)-(x(6)/10)*x(1)*x(4)2*sin(x(8);0;0;(x(5)/10)*x(1)*x(4)2*cos(x(8);-(x(5)/10)*x(1)*x(4)2*sin(x(8);0;0;0;y=AB;（2）运行程序计算1=60的各未知量值：lAB=0.1; h1=0.120; h2=0.08; W1=10; G2=40; G3=100; Fr=400; th1=60*pi/180; x=lAB h1 h2 W1 G
6、2 G3 Fr th1; y=F(x)y = 313.3975 195.8734 195.8734 20.0000 278.7564 20.0000 278.7564 15.6699得到： 1=60时FR23=FR32=313.3975N FR4=FR4=195.8734NFR12x=20.0000 N FR12y=278.7564 NFR41x=20.0000 N FR41y=278.7564 NMb=15.6699 N*m（3）运行程序计算1=150的各未知量值： th1=150*pi/180; x=lAB h1 h2 W1 G2 G3 Fr th1; y=F(x)y = 350.0000
7、 -378.8861 -378.8861 -34.6410 330.0000 -34.6410 330.0000 -30.3109得到：1=150时FR23=FR32=350.0000 N FR4=FR4=-378.8861 N FR12x=-34.6410 N FR12y=330.0000 N FR41x=-34.6410 N FR41y=330.0000 N Mb=-30.3109 N*m（4）运行程序计算1=220的各未知量值： th1=220*pi/180; x=lAB h1 h2 W1 G2 G3 Fr th1; y=F(x)y = 464.2788 -444.5727 -444.5
8、727 -30.6418 489.9903 -30.6418 489.9903 -35.5658得到：1=220时FR23=FR32=464.2788 N FR4=FR4=-444.5727 N FR12x=-30.6418 NFR12y=489.9903 N FR41x=-30.6418 N FR41y=489.9903 NMb=-35.5658 N*m。（5）取1=0360范围分析其受力：h1=0.120; h2=0.08; W1=10; G2=40; G3=100; Fr=400; th1=linspace(0,2*pi,36);x=zeros(length(th1),8);for n=
9、1:36x(n,:)=lAB h1 h2 W1 G2 G3 Fr th1(n);endp=zeros(8,length(th1);for k=1:36p(:,k)=F(x(k,:);end pp =Columns 1 through 8400.0000 382.1443 364.8625 348.7101 334.2061 321.8169 311.9404 304.8943500.0000 470.0039 426.9963 374.1872 314.6014 250.8119 184.7735 117.7719500.0000 470.0039 426.9963 374.1872 314.
10、6014 250.8119 184.7735 117.771940.0000 39.3572 37.4494 34.3380 30.1229 24.9396 18.9547 12.3607400.0000 375.0020 350.8075 328.1941 307.8886 290.5436 276.7166 266.852140.0000 39.3572 37.4494 34.3380 30.1229 24.9396 18.9547 12.3607400.0000 375.0020 350.8075 328.1941 307.8886 290.5436 276.7166 266.85214
11、0.0000 37.6003 34.1597 29.9350 25.1681 20.0650 14.7819 9.4218Columns 9 through 16300.9050 300.1007 302.5072 308.0472 316.5427 327.7205 341.2215 356.611650.4893 -16.8300 -84.1427 -151.3378 -217.9780 -283.0943 -345.0675 -401.620050.4893 -16.8300 -84.1427 -151.3378 -217.9780 -283.0943 -345.0675 -401.62
12、005.3693 -1.7946 -8.9008 -15.7210 -22.0359 -27.6425 -32.3607 -36.0388261.2670 260.1410 263.5101 271.2661 283.1597 298.8087 317.7101 339.25635.3693 -1.7946 -8.9008 -15.7210 -22.0359 -27.6425 -32.3607 -36.0388261.2670 260.1410 263.5101 271.2661 283.1597 298.8087 317.7101 339.25634.0391 -1.3464 -6.7314
13、 -12.1070 -17.4382 -22.6475 -27.6054 -32.1296Columns 17 through 24373.3963 391.0361 408.9639 426.6037 443.3884 458.7785 472.2795 483.4573-449.9252 -486.8273 -509.1470 -514.0376 -499.3489 -463.9495 -407.9684 -332.9190-449.9252 -486.8273 -509.1470 -514.0376 -499.3489 -463.9495 -407.9684 -332.9190-38.5
14、585 -39.8390 -39.8390 -38.5585 -36.0388 -32.3607 -27.6425 -22.0359362.7548 387.4505 412.5495 437.2452 460.7437 482.2899 501.1913 516.8403-38.5585 -39.8390 -39.8390 -38.5585 -36.0388 -32.3607 -27.6425 -22.0359362.7548 387.4505 412.5495 437.2452 460.7437 482.2899 501.1913 516.8403-35.9940 -38.9462 -40
15、.7318 -41.1230 -39.9479 -37.1160 -32.6375 -26.6335Columns 25 through 32491.9528 497.4928 499.8993 499.0950 495.1057 488.0596 478.1831 465.7939-241.6872 -138.3782 -28.0349 83.7439 191.2451 289.0952 372.6779 438.4701-241.6872 -138.3782 -28.0349 83.7439 191.2451 289.0952 372.6779 438.4701-15.7210 -8.90
16、08 -1.7946 5.3693 12.3607 18.9547 24.9396 30.1229528.7339 536.4899 539.8590 538.7330 533.1479 523.2834 509.4564 492.1114-15.7210 -8.9008 -1.7946 5.3693 12.3607 18.9547 24.9396 30.1229528.7339 536.4899 539.8590 538.7330 533.1479 523.2834 509.4564 492.1114-19.3350 -11.0703 -2.2428 6.6995 15.2996 23.12
17、76 29.8142 35.0776Columns 33 through 36451.2899 435.1375 417.8557 400.0000484.2616 509.2386 513.9257 500.0000484.2616 509.2386 513.9257 500.000034.3380 37.4494 39.3572 40.0000471.8059 449.1925 424.9980 400.000034.3380 37.4494 39.3572 40.0000471.8059 449.1925 424.9980 400.000038.7409 40.7391 41.1141
18、40.0000P矩阵的每一行分别是八个未知量在1等于36个分量下的值。整理表格如下：表一1FR23/FR32FR4FR4FR12XFR12YFR41XFR41YMbradNNNNNNNN*m00.17950.35900.53860.71810.89761.07711.25661.43621.61571.79521.97472.15422.33382.51332.69282.87233.05183.23143.41093.59043.76993.94944.12904.30854.48804.66754.84705.02655.20615.38565.56515.74465.92416.1037
19、6.2832400.0000382.1443364.8625348.7101334.2061321.8169311.9404304.8943300.9050300.1007302.5072308.0472316.5427327.7205341.2215356.6116373.3963391.0361408.9639426.6037443.3884458.7785472.2795483.4573491.9528497.4928499.8993499.0950495.1057488.0596478.1831465.7939451.2899435.1375417.8557400.0000500.00
20、00470.0039426.9963374.1872314.6014250.8119184.7735117.771950.4893-16.8300-84.1427-151.3378-217.9780-283.0943-345.0675-401.6200-449.9252-486.8273-509.1470-514.0376-499.3489-463.9495-407.9684-332.9190-241.6872-138.3782-28.034983.7439191.2451289.0952372.6779438.4701484.2616509.2386513.9257500.0000500.0
21、000470.0039426.9963374.1872314.6014250.8119184.7735117.771950.4893-16.8300-84.1427-151.3378-217.9780-283.0943-345.0675-401.6200-449.9252-486.8273-509.1470-514.0376-499.3489-463.9495-407.9684-332.9190-241.6872-138.3782-28.034983.7439191.2451289.0952372.6779438.4701484.2616509.2386513.9257500.000040.0
22、00039.357237.449434.338030.122924.939618.954712.36075.3693-1.7946-8.9008-15.7210-22.0359-27.6425-32.3607-36.0388-38.5585-39.8390-39.8390-38.5585-36.0388-32.3607-27.6425-22.0359-15.7210-8.9008-1.79465.369312.360718.954724.939630.122934.338037.449439.357240.0000400.0000375.0020350.8075328.1941307.8886
23、290.5436276.7166266.8521261.2670260.1410263.5101271.2661283.1597298.8087317.7101339.2563362.7548387.4505412.5495437.2452460.7437482.2899501.1913516.8403528.7339536.4899539.8590538.7330533.1479523.2834509.4564492.1114471.8059449.1925424.9980400.000040.000039.357237.449434.338030.122924.939618.954712.
24、36075.3693-1.7946-8.9008-15.7210-22.0359-27.6425-32.3607-36.0388-38.5585-39.8390-39.8390-38.5585-36.0388-32.3607-27.6425-22.0359-15.7210-8.9008-1.79465.369312.360718.954724.939630.122934.338037.449439.357240.0000400.0000375.0020350.8075328.1941307.8886290.5436276.7166266.8521261.2670260.1410263.5101
25、271.2661283.1597298.8087317.7101339.2563362.7548387.4505412.5495437.2452460.7437482.2899501.1913516.8403528.7339536.4899539.8590538.7330533.1479523.2834509.4564492.1114471.8059449.1925424.9980400.000040.000037.600334.159729.935025.168120.065014.78199.42184.0391-1.3464-6.7314-12.1070-17.4382-22.6475-
26、27.6054-32.1296-35.9940-38.9462-40.7318-41.1230-39.9479-37.1160-32.6375-26.6335-19.3350-11.0703-2.24286.699515.299623.127629.814235.077638.740940.739141.114140.0000按照上述分析结果输出图像：输出FR23和FR32的图像，程序如下：plot(th1,p(1,:),-)ylabel(FR23,FR32/N);xlabel(theta1/rad);输出FR4和FR4的图像，程序如下：plot(th1,p(3,:),-)xlabel(the
27、ta1/rad);ylabel(FR4,FR4/N);输出FR12 x的图像，程序如下：plot(th1,p(4,:),-)ylabel(FR12x/N);xlabel(theta1/rad);输出FR12 y的图像，程序如下：plot(th1,p(5,:),-)ylabel(FR12y/N);xlabel(theta1/rad);输出FR41X的图像，程序如下：plot(th1,p(6,:),-)xlabel(theta1/rad);ylabel(FR41x/N);输出FR41Y的图像，程序如下：plot(th1,p(7,:),-)xlabel(theta1/rad);ylabel(FR41y/N);输出Mb的图像，程序如下：plot(th1,p(8,:),-)xlabel(theta1/rad);ylabel(Mb/N*m);
