平面六杆机构设计

机械原理大作业

姓名：

班级：材料124

小组数据: 3 B

一、题目：计算平面连杆机构的运动学分析

1，图a 所示的为一平面六杆机构。设已知各构件的尺寸如表1所示，原动件1以等角速度ω1=1rad/s 沿着逆时针方向回转，试求各从动杆件的角位移、角速度和角加速度以及E 点的位移、速度和加速度的变化情况。

表1 平面六杆机构的尺寸参数(单位:mm)

mm l 0.652='，mm x G 5.153= mm y G 7.41=

L1

L2

L3 L4 L5

L6

α A B C

26.5 105.6 95

87.5

48.4 39

60°

L3=95

A

1

B 2

C 3

4

D

A

2'

G

6

5

E

F

y

x

θ1

ω1α

%crank_rocker222_main

clear;

l1=26.5;

l2=105.6;

l3=95;

l4=87.5;

l5=48.4;

l6=39.0;

l9=65.0;

lag=159.1;

xg=153.5;

yg=41.7;

omega1=1;

theta7=60;

alpha1=0;

hd=pi/180;du=180/pi;

m=-1;

for n1=1:360

theta1=(n1-1)*hd;

aa=2*l1*l3*sin(theta1);

bb=2*l3*(l1*cos(theta1)-l4);

cc=l2*l2-l1*l1-l3*l3-l4*l4+2*l1*l4*cos(theta1);

theta3(n1)=2*atan((aa+m*sqrt(aa*aa+bb*bb-cc*cc))/(bb-cc));

s1=l3*sin(theta3)-l1*sin(theta1);

theta2(n1)=atan(s1/(l4+l3*cos(theta3)-l1*cos(theta1)));

xe=l1*cos(theta1)+l2*cos(theta2)+l9*cos(theta2-theta7);

ye=l1*sin(theta1)+l2*sin(theta2)+l9*sin(theta2-theta7);

s2=yg-ye;

theta8(n1)=atan(s2/(xg-xe));

s3=(xe-xg).*(xe-xg)+(ye-yg).*(ye-yg)+l5*l5-l6*l6;

theta9(n1)=acos(s3/(2*l5*sqrt((xe-xg).*(xe-xg)+(ye-yg).*(ye-yg)))); theta5(n1)=theta8(n1)-theta9(n1)+pi;

s4=ye+l5*sin(theta8-theta9)-yg;

theta6(n1)=atan(s4/(xe+l5*cos(theta8-theta9)-xg));

theta9(n1)=2*pi-(theta7-theta2(n1));

omega3(n1)=omega1*l1*sin(theta1-theta2)/l3/sin(theta3-theta2);

omega2(n1)=-omega1*l1*sin(theta1-theta3)/l2/sin(theta2-theta3);

omega5(n1)=omega2(n1)*(l2*sin(theta2(n1)-theta6(n1))+l9*sin(theta2(n1 )-theta7-theta6(n1)))+omega1*l1*sin(theta1-theta6(n1))/l5/sin(theta5( n1)-theta6(n1));

omega6(n1)=-omega2(n1)*(l2*sin(theta2(n1)-theta5(n1))+l9*sin(theta2(n 1)-theta7-theta5(n1)))+omega1*l1*sin(theta1-theta5(n1))/l6/sin(theta5 (n1)-theta6(n1));

s4=l2*omega2(n1)*omega2(n1)+l1*omega1*omega1*cos(theta1-theta2)-l3*om ega3(n1)*omega3(n1)*cos(theta3-theta2);

s5=l3*omega3(n1)*omega3(n1)-l1*omega1*omega1*cos(theta1-theta3)-l2*om ega2(n1)*omega2(n1)*cos(theta2-theta3);

s6=omega1*omega1*l1*cos(theta1-theta6(n1))+omega2(n1)*omega2(n1)*(l2* cos(theta2(n1)-theta6(n1))+l9*cos(theta2(n1)-theta7-theta6(n1)))-l5*o mega5(n1)*omega5(n1)*cos(theta5(n1)-theta6(n1))-l6*omega6(n1)*omega6( n1);

s7=omega1*omega1*l1*cos(theta1-theta5(n1))+omega2(n1)*omega2(n1)*(l2* cos(theta2(n1)-theta5(n1))+l9*cos(theta2(n1)-theta7-theta5(n1)))-l5*o mega5(n1)*omega5(n1)-l6*omega6(n1)*omega6(n1)*cos(theta6(n1)-theta5(n 1));

alpha3(n1)=s4/(l3*sin(theta3-theta2));

alpha2(n1)=s5/(l2*sin(theta2-theta3));

alpha5(n1)=(s6+alpha2(n1)*(l2*sin(theta2(n1)-theta6(n1))+l9*sin(theta 2(n1)-theta7-theta6(n1))))/l5/sin(theta5(n1)-theta6(n1));

alpha6(n1)=-(s7+alpha2(n1)*(l2*sin(theta2(n1)-theta5(n1))+l9*sin(thet a2(n1)-theta7-theta5(n1))))/l6/sin(theta5(n1)-theta6(n1));

vex=-l1*omega1.*sin(theta1)-l2*omega2.*sin(theta2)-l9*omega2.*sin(the ta2-theta7);

vey=l1*omega1.*cos(theta1)+l2*omega2.*cos(theta2)+l9*omega2.*cos(thet a2-theta7);

ve=sqrt(vex.*vex+vey.*vey);

aex=-l1*alpha1.*sin(theta1)-l1*omega1.*omega1.*cos(theta1)-l2*omega2. *omega2.*cos(theta2)-l2*alpha2.*sin(theta2)-l9*alpha2.*sin(theta2-the ta7)-l9*omega2.*omega2.*cos(theta2-theta7);

aey=l1*alpha1.*cos(theta1)-l1*omega1.*omega1.*sin(theta1)+l2*alpha2.* cos(theta2)-l2*omega2.*omega2.*sin(theta2)+l9*alpha2.*cos(theta2-thet a7)-l9*omega2.*omega2.*sin(theta2-theta7);

ae=sqrt(aex.*aex+aey.*aey);

end

figure(1);

n1=1:360;

subplot(2,3,1);

plot(n1,real(theta2*du),n1,real(theta3*du),n1,real(theta5*du),n1,real (theta6*du),'k');

title('角位移线图');