机械原理第二次大作业.docx
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机械原理第二次大作业.docx
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机械原理第二次大作业
机械原理第二次大作业
题目:
在图示的正弦机构中,已知Lab=100mm,h1=120mm,h2=80mm,W1=10rad/s(常数),滑块2和构件3的重量分别为G2=40N和G3=100N,质心S2和S3的位置如图所示,加于构件3上的生产阻力Fr=400N,构件1的重力和惯性力略去不计。
试用解析法求机构在ϕ1=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:
首先分别对三个构件做受力分析如下
对构件一:
对构件二:
对构件三:
做速度、加速度分析:
对于滑块2:
V2=Lab*ω1
a2n=Lab*(ω1)2
对于构件3:
V3=Lab*ω1*cosϕ1
a3=-Lab*(ω1)2sinϕ1
则构件2、3的惯性力:
F12=m2*a2=(G2/g)*Lab*(ω1)2
F13=(G3/g)*Lab*(ω1)2sinϕ1
又对于构件1:
∑Fx=0,FR41X=FR21X
∑Fy=0,FR41Y=FR21Y
∑Ma=0,Mb=FR32*Lab*cosϕ1
对于构件2:
∑Fx=0,FR12x=F12*cosϕ1
∑Fy=0,FR12y=FR32-F12*sinϕ1
对于构件3:
∑Fy=0,FR23=Fr-F13
∑Fx=0,F'R43=FR43
∑MS3=0,FR41*h2=FR23*Lab*cosϕ1
由方程列出方程矩阵如下:
*
=
则有X=A\B
在MATLAB中编写函数如下:
functiony=f(x)
%input
%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
%y
(1)=FR21x
%y
(2)=FR21y
%y(3)=FR41x
%y(4)=FR41y
%y(5)=FR32
%y(6)=FR43
%y(7)=F’R43
%y(8)=Mb
A=[10-100000;
010-10000;
0000-x
(1)*cos(x(8))001;
10000000;
0100-1000;
000001-10;
00001000;
0000-x
(1)*cos(x(8))x(3)00];
B=[0;0;0;(x(5)/9.8)*x
(1)*(x(4))*(x(4))*cos(x(8));-(x(5)/9.8)*x
(1)*(x(4))*(x(4))*sin(x(8));0;x(7)-(x(6)/9.8)*x
(1)*(x(4))*(x(4))*sin(x(8));0];
y=A\B;
将已知各值以及ϕ=60°带入,求出结果:
Lab=0.1;
h1=0.12;
h2=0.08;
W1=10;
G2=40;
G3=100;
Fr=400;
theta1=60*pi/180;
x=[Labh1h2W1G2G3Frtheta1];
y=f(x)
y=
20.4082
276.2821
20.4082
276.2821
311.6301
194.7688
194.7688
15.5815
从上到下一次为FR21x、FR21y、FR41x、FR41y、FR32、FR43、F’R43、Mb
将ϕ=150°带入,求出结果:
theta1=150*pi/180;
x=[Labh1h2W1G2G3Frtheta1];
y=f(x)
y=
-35.3480
328.5714
-35.3480
328.5714
348.9796
-377.7815
-377.7815
-30.2225
从上到下一次为FR21x、FR21y、FR41x、FR41y、FR32、FR43、F’R43、Mb
将ϕ=220°带入,求出结果
theta1=220*pi/180;
x=[Labh1h2W1G2G3Frtheta1];
y=f(x)
y=
-31.2671
491.8268
-31.2671
491.8268
465.5906
-445.8288
-445.8288
-35.6663
从上到下一次为FR21x、FR21y、FR41x、FR41y、FR32、FR43、F’R43、Mb
将0~360°带入,求出结果
>>Lab=0.1;
h1=0.12;
h2=0.08;
W1=10;
G2=40;
G3=100;
Fr=400;
th1=linspace(0,2*pi,36);
x=zeros(length(th1),8);
forn=1:
length(th1)
x(n,:
)=[Labh1h2W1G2G3Frth1(n)];
end
p=zeros(8,length(th1));
fork=1:
length(th1)
p(:
k)=f(x(k,:
));
end
p
q=p'
q=
40.8163400.000040.8163400.0000400.0000500.0000500.000040.0000
40.1604374.491940.1604374.4919381.7799469.5557469.555737.5645
38.2137349.803638.2137349.8036364.1454426.1571426.157134.0926
35.0387326.728735.0387326.7287347.6633373.0640373.064029.8451
30.7376306.008830.7376306.0088332.8634313.3374313.337425.0670
25.4486288.309825.4486288.3098320.2213249.5684249.568419.9655
19.3416274.200619.3416274.2006310.1433183.7090183.709014.6967
12.6129264.134812.6129264.1348302.9534117.0222117.02229.3618
5.4789258.43575.4789258.4357298.882750.150050.15004.0120
-1.8312257.2867-1.8312257.2867298.0619-16.7156-16.7156-1.3372
-9.0825260.7246-9.0825260.7246300.5176-83.5893-83.5893-6.6871
-16.0418268.6389-16.0418268.6389306.1706-150.4159-150.4159-12.0333
-22.4856280.7752-22.4856280.7752314.8395-216.8051-216.8051-17.3444
-28.2066296.7436-28.2066296.7436326.2454-281.8200-281.8200-22.5456
-33.0211316.0307-33.0211316.0307340.0219-343.8544-343.8544-27.5084
-36.7742338.0166-36.7742338.0166355.7261-400.6227-400.6227-32.0498
-39.3454361.9947-39.3454361.9947372.8534-449.2710-449.2710-35.9417
-40.6520387.1944-40.6520387.1944390.8531-486.5996-486.5996-38.9280
-40.6520412.8056-40.6520412.8056409.1469-509.3747-509.3747-40.7500
-39.3454438.0053-39.3454438.0053427.1466-514.6918-514.6918-41.1753
-36.7742461.9834-36.7742461.9834444.2739-500.3461-500.3461-40.0277
-33.0211483.9693-33.0211483.9693459.9781-465.1626-465.1626-37.2130
-28.2066503.2564-28.2066503.2564473.7546-409.2426-409.2426-32.7394
-22.4856519.2248-22.4856519.2248485.1605-334.0918-334.0918-26.7273
-16.0418531.3611-16.0418531.3611493.8294-242.6091-242.6091-19.4087
-9.0825539.2754-9.0825539.2754499.4824-138.9316-138.9316-11.1145
-1.8312542.7133-1.8312542.7133501.9381-28.1492-28.1492-2.2519
5.4789541.56435.4789541.5643501.117384.083384.08336.7267
12.6129535.865212.6129535.8652497.0466191.9948191.994815.3596
19.3416525.799419.3416525.7994489.8567290.1597290.159723.2128
25.4486511.690225.4486511.6902479.7787373.9214373.921429.9137
30.7376493.991230.7376493.9912467.1366439.7341439.734135.1787
35.0387473.271335.0387473.2713452.3367485.3848485.384838.8308
38.2137450.196438.2137450.1964435.8546510.0778510.077840.8062
40.1604425.508140.1604425.5081418.2201514.3739514.373941.1499
40.8163400.000040.8163400.0000400.0000500.0000500.000040.0000
q中从左到右依次为FR21x,FR21y,FR41x,FR41y,FR32,FR43,F’R43,Mb。
输出FR12x的图像,程序如下:
>>plot(th1,p(1,:
),'--')
title('FR12x-theta1')
ylabel('FR12x/N');
xlabel('\theta1/rad');
输出FR12y的图像,程序如下:
>>plot(th1,p(2,:
),'--')
title('FR12y-theta1')
ylabel('FR12y/N');
xlabel('\theta1/ra
输出FR41X的图像,程序如下:
>>plot(th1,p(3,:
),'--')
title('FR41x-theta1')
xlabel('\theta1/rad');
ylabel('FR41x/N');
输出FR41Y的图像,程序如下:
>>plot(th1,p(2,:
),'--')
title('FR41y-theta1')
xlabel('\theta1/rad');
ylabel('FR41y/N');
输出FR23的图像,程序如下:
>>plot(th1,p(5,:
),'--')
title('FR23-theta1')
ylabel('FR23/N');
xlabel('\theta1/rad');
输出FR43的图像,程序如下:
>>plot(th1,p(6,:
),'--')
title('FR43-theta1')
xlabel('\theta1/rad');
ylabel('FR43/N');
输出Mb的图像,程序如下:
>>plot(th1,p(8,:
),'--')
title('Mb-theta1')
xlabel('\theta1/rad');
ylabel('Mb/N*m');
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