平面六杆机构设计

1、机械原理大作业 班级： 材料 124 小组数据 : 3 B 、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 1=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） l2 65.0 mm ， xG 153.5mmyG 41.7mm L1 L2 L3 L4 L5 L6 A B C 26.5 105.6 95 87.5 48.4 39 60 L3=95 %crank_rocker222_

2、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

3、(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).*

4、(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/

5、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(thet

6、a2(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-

7、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(n

8、1)-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

9、/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(

10、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.* c

11、os(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 ); xlabel( 曲柄转角 ph

12、i_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); k ); plot(n1,real(omega2),n1,real(omega3), title( 角速度23线图 ); xlabel( 曲柄转角 phi_1/circ ) ylabel( 角速度 /radcdots-1 ) grid on ;hold on; text(100,0.1, omega_2 )

13、 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 /radcdots-1 ) grid on ;holdon; 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

14、( 曲柄转角 phi_1/circ ) ylabel( 角加速度 /radcdots-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 /radcdots-2 grid on; hold on; text(200,-200,alpha_5) text(200,-450,alp

15、ha_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 ;holdon; 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)=l

16、4+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; o ); o ); o ); plot(x(1),y(1), plot(x(2),y(2), plot(x(3),y(3), o ); o ); plot(x(4),y(4), plot(x(5),y(5), plot(real(x(6),real(y(6