平面六杆机构设计

机械原理大作业

姓名：

班级： 小组数据:

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。

%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(n1)-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*omega3(n1)*omega3(n1)*cos(theta3-theta2);

s5=l3*omega3(n1)*omega3(n1)-l1*omega1*omega1*cos(theta1-theta3)-l2*omega2(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*omega5(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*omega5(n1)*omega5(n1)-l6*omega6(n1)*omega6(n1)*cos(theta6(n1)-theta5(n1));

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(theta2(n1)-theta7-theta6(n1))))/l5/sin(theta5(n1)-theta6(n1));

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

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

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

xlabel('曲柄转角 \phi_1/\circ') ylabel('角位移/\circ') grid on; hold on;

text(100,100,'\phi_3') text(100,40,'\phi_2') text(100,175,'\phi_5') text(100,0,'\phi_6')

subplot(2,3,2);

plot(n1,real(omega2),n1,real(omega3),'k'); title('角速度23线图');

xlabel('曲柄转角 \phi_1/\circ') ylabel('角速度 /rad\cdots^{-1}') grid on;hold on; text(100,0.1,'\omega_2') text(100,0.35,'\omega_3')

subplot(2,3,3);

plot(n1,real(omega5),n1,real(omega6),'k'); title('角速度56线图');

xlabel('曲柄转角\phi_1/\circ') ylabel('角速度/rad\cdots^{-1}') grid on;hold on; text(200,14,'\omega_5') text(200,25,'\omega_6')

subplot(2,3,4);

plot(n1,real(alpha2),n1,real(alpha3),'k'); title('角加速度23线图'); xlabel('曲柄转角\phi_1/\circ') ylabel('角加速度/rad\cdots^{-2}') grid on; hold on;

text(200,0,'\alpha_2') text(200,-0.2,'\alpha_3')

subplot(2,3,5);

plot(n1,real(alpha5),n1,real(alpha6),'k'); title('角加速度56线图'); xlabel('曲柄转角\phi_1/\circ') ylabel('角加速度/rad\cdots^{-2}')

grid on; hold on;

text(200,-200,'\alpha_5') text(200,-450,'\alpha_6')

subplot(2,3,6);

plot(n1,real(ve),n1,real(ae),'k'); title('e点的速度和加速度线图 '); xlabel('曲柄转角\phi_1/\circ') ylabel('速度/m*s^{-1}') grid on;hold on; text(80,25,'ve') text(65,45,'ae')

figure(2) m=moviein(20); j=0;

for n1=1:5:360; j=j+1; clf; x(1)=0; y(1)=0;

x(2)=l1*cos((n1-1)*hd); y(2)=l1*sin((n1-1)*hd); x(3)=l4+l3*cos(theta3(n1)); y(3)=l3*sin(theta3(n1)); x(4)=l4; y(4)=0;

x(5)=l4+l3*cos(theta3(n1)); y(5)=l3*sin(theta3(n1));

x(6)=l4+l3*cos(theta3(n1))+l2-cos(theta2(n1)-theta7); y(6)=l3*sin(theta3(n1))+l2*sin(theta2(n1)-theta7); x(7)=xg+l6*cos(theta6(n1)); y(7)=yg+l6*sin(theta6(n1)); x(8)=xg; y(8)=yg;

plot(real(x),real(y)); grid on; hold on;

plot(x(1),y(1),'o'); plot(x(2),y(2),'o'); plot(x(3),y(3),'o');

plot(x(4),y(4),'o'); plot(x(5),y(5),'o');

plot(real(x(6)),real(y(6)),'o'); plot(real(x(7)),real(y(7)),'o'); plot(real(x(8)),real(y(8)),'o'); axis([-150 350 -150 200]); title('平面六连杆机构'); xlabel('mm') ylabel('mm') m(j)=getframe; end movie(m);

杆2 杆3 杆5 杆6的角位移线图

杆2杆3

的角速度

杆5杆6的角速度线图

杆2杆3的角加速度线图

杆5杆6的角加速线图

E点的速度加速度线图

机构动画简图

总体线图

机械原理大作业

姓名：

班级： 小组数据:

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。

%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(n1)-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*omega3(n1)*omega3(n1)*cos(theta3-theta2);

s5=l3*omega3(n1)*omega3(n1)-l1*omega1*omega1*cos(theta1-theta3)-l2*omega2(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*omega5(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*omega5(n1)*omega5(n1)-l6*omega6(n1)*omega6(n1)*cos(theta6(n1)-theta5(n1));

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(theta2(n1)-theta7-theta6(n1))))/l5/sin(theta5(n1)-theta6(n1));

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

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

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

xlabel('曲柄转角 \phi_1/\circ') ylabel('角位移/\circ') grid on; hold on;

text(100,100,'\phi_3') text(100,40,'\phi_2') text(100,175,'\phi_5') text(100,0,'\phi_6')

subplot(2,3,2);

plot(n1,real(omega2),n1,real(omega3),'k'); title('角速度23线图');

xlabel('曲柄转角 \phi_1/\circ') ylabel('角速度 /rad\cdots^{-1}') grid on;hold on; text(100,0.1,'\omega_2') text(100,0.35,'\omega_3')

subplot(2,3,3);

plot(n1,real(omega5),n1,real(omega6),'k'); title('角速度56线图');

xlabel('曲柄转角\phi_1/\circ') ylabel('角速度/rad\cdots^{-1}') grid on;hold on; text(200,14,'\omega_5') text(200,25,'\omega_6')

subplot(2,3,4);

plot(n1,real(alpha2),n1,real(alpha3),'k'); title('角加速度23线图'); xlabel('曲柄转角\phi_1/\circ') ylabel('角加速度/rad\cdots^{-2}') grid on; hold on;

text(200,0,'\alpha_2') text(200,-0.2,'\alpha_3')

subplot(2,3,5);

plot(n1,real(alpha5),n1,real(alpha6),'k'); title('角加速度56线图'); xlabel('曲柄转角\phi_1/\circ') ylabel('角加速度/rad\cdots^{-2}')

grid on; hold on;

text(200,-200,'\alpha_5') text(200,-450,'\alpha_6')

subplot(2,3,6);

plot(n1,real(ve),n1,real(ae),'k'); title('e点的速度和加速度线图 '); xlabel('曲柄转角\phi_1/\circ') ylabel('速度/m*s^{-1}') grid on;hold on; text(80,25,'ve') text(65,45,'ae')

figure(2) m=moviein(20); j=0;

for n1=1:5:360; j=j+1; clf; x(1)=0; y(1)=0;

x(2)=l1*cos((n1-1)*hd); y(2)=l1*sin((n1-1)*hd); x(3)=l4+l3*cos(theta3(n1)); y(3)=l3*sin(theta3(n1)); x(4)=l4; y(4)=0;

x(5)=l4+l3*cos(theta3(n1)); y(5)=l3*sin(theta3(n1));

x(6)=l4+l3*cos(theta3(n1))+l2-cos(theta2(n1)-theta7); y(6)=l3*sin(theta3(n1))+l2*sin(theta2(n1)-theta7); x(7)=xg+l6*cos(theta6(n1)); y(7)=yg+l6*sin(theta6(n1)); x(8)=xg; y(8)=yg;

plot(real(x),real(y)); grid on; hold on;

plot(x(1),y(1),'o'); plot(x(2),y(2),'o'); plot(x(3),y(3),'o');

plot(x(4),y(4),'o'); plot(x(5),y(5),'o');

plot(real(x(6)),real(y(6)),'o'); plot(real(x(7)),real(y(7)),'o'); plot(real(x(8)),real(y(8)),'o'); axis([-150 350 -150 200]); title('平面六连杆机构'); xlabel('mm') ylabel('mm') m(j)=getframe; end movie(m);

杆2 杆3 杆5 杆6的角位移线图

杆2杆3

的角速度

杆5杆6的角速度线图

杆2杆3的角加速度线图

杆5杆6的角加速线图

E点的速度加速度线图

机构动画简图

总体线图