平面连杆机构运动分析报告.docx
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平面连杆机构运动分析报告.docx
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平面连杆机构运动分析报告
大作业
(一)
平面连杆的运动分析
班级:
姓名:
姓名:
姓名:
指导教师:
完成日期:
一、题目及原始数据
1.1、平面连杆的运动分析题目:
如图1.1所示,为一平面六杆。
设已知各构件的尺寸如表1.1所示,又知原动件1以等角速度
=1rad/s沿逆时针方向回转,试求各从动件的角位移、角速度及角加速度以及位移E点的位移、速度及加速度的变化情况。
表1.1平面六杆的尺寸参数
=65mm,
=153.5mm,
=41.7mm
题号
A
B
C
1-A
105.6
67.5
87.5
34.4
25
60°
=26.5
=24
=29.5
要求每组(每三人为一组,每人一题)至少打印一份源程序,每个同学计
算出原动件从0º到360º时(计算点数N=36)所要求各运动变量的大小,并绘出各组应的运动线图以及E点的轨迹曲线。
图1.1
二、平面连杆运动分析方程
2.1、位移方程:
2.2、速度方程:
2.3、加速度方程:
三、计算程序框图
4、计算源程序
4.1主程序
%输入已知数据
clear
l1=0.0240;
l2=0.1056;
l3=0.0675;
l4=0.0875;
l5=0.0344;
l6=0.025;
l22=0.065;
xg=0.1535;
yg=0.0417;
omega1=1;
alph1=0;
hd=pi/180;
du=180/pi;
t1=1:
10:
361;
theta2=1:
10:
361;
theta3=1:
10:
361;
theta5=1:
10:
361;
theta6=1:
10:
361;
omega2=1:
10:
361;
omega3=1:
10:
361;
omega5=1:
10:
361;
omega6=1:
10:
361;
alph2=1:
10:
361;
alph3=1:
10:
361;
alph5=1:
10:
361;
alph6=1:
10:
361;
xe=1:
10:
361;
ye=1:
10:
361;
V=1:
10:
361;
a=1:
10:
361;
theta1=0;
options=gaoptimset('PopulationSize',100,'Generations',10000,'StallGenLimit',500,'TolFun',1e-100);
theta0=ga((thet)weiyi_0(thet,theta1),4,options);
iftheta0
(1)<0
theta0
(1)=theta0
(1)+2*pi;end
iftheta0
(1)>2*pi
theta0
(1)=theta0
(1)-2*pi;end
iftheta0
(2)<0
theta0
(2)=theta0
(2)+2*pi;end
iftheta0
(2)>2*pi
theta0
(2)=theta0
(2)-2*pi;end
iftheta0(3)<0
theta0(3)=theta0(3)+2*pi;end
iftheta0(3)>2*pi
theta0(3)=theta0(3)-2*pi;end
iftheta0(4)<0
theta0(4)=theta0(4)+2*pi;end
iftheta0(4)>2*pi
theta0(4)=theta0(4)-2*pi;
end
%调用子函数Fun_jixie计算该六杆的各杆角位移、角速度、角加速度以及E点的角位移、角速度、角加速度
forn1=1:
10:
361
theta1=(n1-1)*hd;
t1(n1)=theta1*du;
theta=fsolve((thet)weiyi(thet,theta1),theta0);
iftheta
(1)<0
theta
(1)=theta
(1)+2*pi;end
iftheta
(1)>2*pi
theta
(1)=theta
(1)-2*pi;end
iftheta
(2)<0
theta
(2)=theta
(2)+2*pi;end
iftheta
(2)>2*pi
theta
(2)=theta
(2)-2*pi;end
iftheta(3)<0
theta(3)=theta(3)+2*pi;end
iftheta(3)>2*pi
theta(3)=theta(3)-2*pi;end
iftheta(4)<0
theta(4)=theta(4)+2*pi;end
iftheta(4)>2*pi
theta(4)=theta(4)-2*pi;end
[xe(n1),ye(n1)]=weiyi_E(theta1,theta,l1,l2,l22);
[omega,alph]=Fun_jixie(theta1,omega1,l1,l2,l3,l5,l6,l22,theta);
[V(n1),a(n1)]=sudu_jasudu_E(omega
(1),alph
(1),theta,theta1,omega1,l1,l2,l22,alph1);theta2(n1)=theta
(1);theta3(n1)=theta
(2);theta5(n1)=theta(3);theta6(n1)=theta(4);omega2(n1)=omega
(1);omega3(n1)=omega
(2);omega5(n1)=omega(3);omega6(n1)=omega(4);
alph2(n1)=alph
(1);alph3(n1)=alph
(2);alph5(n1)=alph(3);alph6(n1)=alph(4);
theta0=theta;
end
%绘制各杆件的角位移、角速度、角加速度
n2=1:
10:
361;
n1=1:
10:
361;
figure
(1);%%%%%%
subplot(2,2,1)%绘制位移线图
plot((n1-1),theta2(n2)*du,'r-',(n1-1),theta3(n2)*du,'g-',(n1-1),theta5(n2)*du,'y-',(n1-1),theta6(n2)*du,'k-','LineWidth',1.5);
title('各杆角位移线图');
xlabel('原动件1\theta_1/\circ');
ylabel('角位移/\circ');
gridon;holdon;
text(200,60,'θ2');
text(200,150,'θ3');
text(200,350,'θ5');
text(200,260,'θ6');
%%%%%%
subplot(2,2,2)%绘制角速度线图
plot((n1-1),omega2(n2),'r-',(n1-1),omega3(n2),'g-',(n1-1),omega5(n2),'y-',(n1-1),omega6(n2),'k-','LineWidth',1.5);
title('各杆角速度线图');
xlabel('原动件1\theta_1/\circ');
ylabel('角速度/rad\cdots^{-1}');
gridon;holdon;
%%%%%%
subplot(2,2,3)%绘制角加速度线图
plot((n1-1),alph2(n2),'r-',(n1-1),alph3(n2),'g-',(n1-1),alph5(n2),'y-',(n1-1),alph6(n2),'k-','LineWidth',1.5);
title('各杆角加速度线图');
xlabel('原动件1\theta_1/\circ');
ylabel('角加速度/rad\cdots^{-2}');
gridon;holdon;
%%%%%%%
%求E点的位移
figure
(2)
subplot(2,2,1)
plot(xe(n1),ye(n1),'r-','LineWidth',1.5);
title('E的位移线图');
xlabel('E在x方向位移');
ylabel('E在y方向位移');
gridon;holdon;
%求E点角速度与角加速度
subplot(2,2,2)%绘制E点角速度
plot((n1-1),V(n1),'r-','LineWidth',1.5);
title('E点角速度');
xlabel('原动件1\theta_1/\circ');
ylabel('E点角速度/rad\cdots^{-1}');
gridon;holdon;
subplot(2,2,3)%绘制E点角加速度
plot((n1-1),a(n1),'r-','LineWidth',1.5);
title('E点角加速度');
xlabel('原动件1\theta_1/\circ');
ylabel('E点角加速度/rad\cdots^{-2}');
gridon;holdon;
%将数据输出到Exel表shuju1.xls中
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',t1(n1)','sheet1','A1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',theta2(n1)'*du,'sheet1','B1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',theta3(n1)'*du,'sheet1','C1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',theta5(n1)'*du,'sheet1','D1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',theta6(n1)'*du,'sheet1','E1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',omega2(n1)','sheet1','F1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',omega3(n1)','sheet1','G1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',omega5(n1)','sheet1','H1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',omega6(n1)','sheet1','I1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',alph2(n1)','sheet1','J1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',alph3(n1)','sheet1','K1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',alph5(n1)','sheet1','L1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',alph6(n1)','sheet1','M1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',V(n1)','sheet1','N1');
xlswrite('E:
\机械原理大作业\平面六杆\Matlab程序\shuju3.xls',a(n1)','sheet1','O1');
4.2从动件角位移,角速度,角加速度
function[omega,alph]=Fun_jixie(theta1,omega1,l1,l2,l3,l5,l6,l22,theta)
%从动件角位移
theta2=theta
(1);theta3=theta
(2);theta5=theta(3);theta6=theta(4);
%%%%%%
%计算从动件角速度
A=[-l2*sin(theta2),l3*sin(theta3),0,0;
l2*cos(theta2),-l3*cos(theta3),0,0;
-l22*sin(theta2-pi/3),-l3*sin(theta3),-l5*sin(theta5),l6*sin(theta6);
l22*cos(theta2-pi/3),l3*cos(theta3),l5*cos(theta5),-l6*cos(theta6)];
B=[l1*sin(theta1);-l1*cos(theta1);0;0];
omega=A\(omega1*B);
omega2=omega
(1);omega3=omega
(2);omega5=omega(3);omega6=omega(4);
%%%%%
%计算角从动件角加速度
A=[-l2*sin(theta2),l3*sin(theta3),0,0;
l2*cos(theta2),-l3*cos(theta3),0,0;
-l22*sin(theta2-pi/3),-l3*sin(theta3),-l5*sin(theta5),l6*sin(theta6);
l22*cos(theta2-pi/3),l3*cos(theta3),l5*cos(theta5),-l6*cos(theta6)];
At=[-l2*omega2*cos(theta2),l3*omega3*cos(theta3),0,0;
-l2*omega2*sin(theta2),l3*omega3*sin(theta3),0,0;
-l22*omega2*cos(theta2-pi/3),-l3*omega3*cos(theta3),-l5*omega5*cos(theta5),l6*omega6*cos(theta6);
-l22*omega2*sin(theta2-pi/3),-l3*omega3*sin(theta3),-l5*omega5*sin(theta5),l6*omega6*sin(theta6)];
Bt=[omega1*l1*cos(theta1);omega1*l1*sin(theta1);0;0;];
alph=A\(-At*omega+omega1*Bt);
end
4.3E点角速度,角加速度
function[V,a]=sudu_jasudu_E(omega,alph,theta,theta1,omega1,l1,l2,l22,alph1)
%求E点角速度
A=[-l1*sin(theta1),-l2*sin(theta
(2))+l22*sin(pi/3-theta
(1));l1*cos(theta1),l2*cos(theta
(1))-l22*cos(pi/3-theta
(1))];
B=[omega1;omega
(1)];
Vx=-l1*sin(theta1)*omega1-l2*sin(theta
(2))+l22*sin(pi/3-theta
(1))*omega
(1);
Vy=l1*cos(theta1)*omega1+l2*cos(theta
(1))-l22*cos(pi/3-theta
(1))*omega
(1);
V=sqrt(Vx^2+Vy^2);
%求E点角加速度
D1=[alph1;alph
(1)];
D2=[-l1*cos(theta1)*omega1,-l2*cos(theta
(1))*omega
(1)-l22*cos(pi/3-theta
(1))*omega
(1);-l1*sin(theta1)*omega1,-l2*sin(theta
(2))*omega
(1)+l22*sin(pi/3-theta
(1))*omega
(1)];
a1=A*D1+D2*B;
a=sqrt(a1
(1)^2+a1
(2)^2);
end
4.4E点位移
function[xe,ye]=weiyi_E(theta1,theta,l1,l2,l22)
xe=l1*cos(theta1)+l2*cos(theta
(1))+l22*cos(pi/3-theta
(1));
ye=l1*sin(theta1)+l2*sin(theta
(2))+l22*sin(pi/3-theta
(1));
end
5、计算结果
1-C
各杆角位移变化
主动杆1
从动杆2
从动杆3
从动杆5
从动杆6
/(°)
0
35.6084
65.6281
207.9752
248.0929
10
30.8934
61.5375
194.8392
245.6683
20
27.0862
59.5197
185.6508
242.7925
30
24.2472
59.4280
179.3291
237.8174
40
22.2711
60.9068
174.5082
230.1716
50
21.0007
63.5668
169.5566
219.5693
60
20.2899
67.0707
162.6546
205.5980
70
20.0246
71.1528
152.0191
187.9072
80
20.1229
75.6089
136.6623
167.0176
90
20.5287
80.2819
118.6181
146.7459
100
21.2050
85.0474
102.4070
132.5408
110
22.1289
89.8033
90.2305
125.7210
120
23.2870
94.4630
81.3183
123.9271
130
24.6719
98.9507
74.4878
124.7856
140
26.2796
103.1990
68.9103
126.7727
150
28.1066
107.1472
64.1954
129.0116
160
30.1477
110.7413
60.0940
130.9266
170
32.3934
113.9345
56.4453
132.1274
180
34.8277
116.6874
53.1161
132.3493
190
37.4267
118.9678
49.9679
131.4342
200
40.1568
120.7503
46.8439
129.3229
210
42.9741
122.0147
43.5755
126.0459
220
45.8240
122.7435
40.0051
121.7036
230
48.6401
122.9190
36.0147
116.4381
240
51.3440
122.5200
31.5507
110.3952
250
53.8440
121.5184
26.6324
103.6769
260
56.0339
119.8763
21.3373
96.2852
270
57.7910
117.5442
15.7582
88.0633
280
58.9751
114.4610
9.9287
78.6388
290
59.4298
110.5579
3.6988
67.3608
300
58.9895
105.7702
356.5045
53.1802
310
57.4975
100.0632
346.8670
34.3210
320
54.8445
93.4802
331.2049
7.5042
330
51.0310
86.2118
302.1698
327.0469
340
46.2458
78.6793
258.9097
278.6551
350
40.9100
71.5539
227.0232
254.5326
360
35.6084
65.6281
207.9744
248.0919
各杆角加位移变化
主动杆1
从动杆2
从动杆3
从动杆5
从动杆6
/(°)
/(rad/s)
0
-0.5086
-0.5086
-1.5567
-0.3234
10
-0.4292
-0.3058
-1.0981
-0.2238
20
-0.3315
-0.1005
-0.7553
-0.3786
30
-0.2382
0.0760
-0.5319
-0.6263
40
-0.1597
0.2131
-0.4595
-0.9068
50
-0.0969
0.3132
-0.5604
-1.2182
60
-0.0472
0.3832
-0.8498
-1.5798
70
-0.0072
0.4299
-1.3021
-1.9614
80
0.0260
0.4588
-1.7368
-2.1529
90
0.0546
0.4738
-1.7842
-1.7954
100
0.0803
0.4776
-1.4218
-1.0270
110
0.1043
0.4721
-1.0319
-0.3838
120
0.1272
0.4586
-0.7715
-0.0154
130
0.1497
0.4379
-0.6117
0.1604
140
0.1718
0.4108
-0.5087
0.2231
150
0.1935
0.3780
-0.4374
0.2155
160
0.2145
0.3401
-0.3851
0.1612
170
0.2343
0.2979
-0.3466
0.0746
180
0.2521
0.2521
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