六杆受力分析

1、六杆机构受力分析（MATLAB ）当初始角位移为30度时，求算PRP杆组的受力情况: clear;clc;xa=0;ya=0;v=0.2;ff=100;g=9.8;m4=5;m5=10;l1=50;fil1=30/180*pi;xd=215;yd=0;l2=200;13=160;1=120;omig1=2;xb=xa+11*cos(fi11);yb=ya+11*sin(fi11);vbx=-omig1*11*sin(fi11);vby=omig1*11*cos(fi11);abx=-omig1*omig1*11*cos(fi11);aby=-omig1*omig1*11*sin(fi11);h

2、=sqrt(xd-xb).*(xd-xb)+ (yd-yb).*(yd-yb);de1ta=atan(yd-yb)/(xd-xb);gama=acos(h.*h+12*12-13*13)/(2.*h.*12);fi12=gama-de1ta;xc=xb+12*cos(fi12);yc=yb+12*sin(fi12);omig13=(-vbx).*(xc-xb)+(-vby).*(yc-yb)/(yc-yd).*(xc-xb)-(yc-yb).*(xc-xd);omig12=(-vbx).*(xc-xd)+(-vby).*(yc-yd)/(yc-yd).*(xc-xb)-(yc-yb).*(xc

3、-xd);e=-abx+omig12*omig12.*(xc-xb)-omig13*omig13.*(xc-xd);f=-aby+omig12*omig12.*(yc-yb)-omig13*omig13.*(yc-yd);vcx=vbx-12*omig12*sin(fi12);vcy=vby+12*omig12*cos(fi12);e12=(e.*(xc-xd)+f.*(yc-yd)/(xc-xb).*(yc-yd)-(xc-xd).*(yc-yb);acx=abx-e12.*(yc-yb)-omig12*omig12.*(xc-xb);acy=aby+e12.*(xc-xb)-omig12*

4、omig12.*(yc-yb);xe=1+0*cos(fi11);ye=11*sin(fi11)+(1-11*cos(fi11)*tan(fi12);vex=0+0*cos(fi11);vey=omig1*11*cos(fi11)+1*omig12/(cos(fi12)*(cos(fi12)+omig1*11*sin(fi11)*tan(fi12)-omig12*11 *cos(fi11)/(cos(fi12)*(cos(fi12);aex=0+0*cos(fi11);aey=-omig1*omig1*11*sin(fi11)+e12*1/(cos(fi12)*(cos(fi12)+2*1*o

5、mig12*omig12*sin(fi12)/(cos(fi12)*(cos(fi12)*(cos(fi12)+omig1*omig1*11*cos(fi11)*tan(fi12)+omig1*omig12*11*sin(fi11)/(co s(fi12)*(cos(fi12)-e12*11*cos(fi11)/(cos(fi12)*(cos(fi12)+omig1*omig12*11*sin(fi11)/(cos(fi12) )*(cos(fi12)-2*omig12*omig12*11*cos(fi11)*sin(fi12)/(cos(fi12)*(cos(fi12)*(cos(fi12)

6、;A=1 0 -1 0 0 0;0 1 0 -1 0 0;cos(fi12) sin(fi12) 0 0 0 0;0 0 1 0 -1 0;0 0 0 1 0 -1;0 0 0 0 v -1;B=0;m4*aey+m4*g;0;0;m5*aey+m5*g;0;C=inv(A)*BC =R24x=-8.3957*1.0e+003R24y=5.1653*1.0e+003R45x=-8.3957*1.0e+003R45y=2.8838*1.0e+003R56x=-8.3957*1.0e+003R56y=-1.6791*1.0e+003当初始角位移为30度时，求算RRR杆组的受力情况：clear;cl

7、c;R24x=-8.3957*1.0e+003;R24y=5.1653*1.0e+003;xa=0;ya=0;v=0.2;ff=100;g=9.8;m2=10;js2=0.2;js3=0.2;m3=10;m4=5;m5=10;l1=50;fil1=30/180*pi;xd=215;yd=0;l2=200;l3=160;l=120;omigl=2;xb=xa+l1*cos(fil1);yb=ya+l1*sin(fil1);vbx=-omigl*l1*sin(fil1);vby=omigl*l1*cos(fil1);abx=-omigl*omigl*l1*cos(fil1);aby=-omigl*

8、omigl*l1*sin(fil1);h=sqrt(xd-xb).*(xd-xb)+ (yd-yb).*(yd-yb);delta=atan(yd-yb)/(xd-xb);gama=acos(h.*h+l2*l2-l3*l3)/(2.*h.*l2);fil2=gama-delta;xc=xb+l2*cos(fil2);yc=yb+l2*sin(fil2);omigl3=(-vbx).*(xc-xb)+(-vby).*(yc-yb)/(yc-yd).*(xc-xb)-(yc-yb).*(xc-xd);omigl2=(-vbx).*(xc-xd)+(-vby).*(yc-yd)/(yc-yd).*

9、(xc-xb)-(yc-yb).*(xc-xd);e=-abx+omigl2*omigl2.*(xc-xb)-omigl3*omigl3.*(xc-xd);f=-aby+omigl2*omigl2.*(yc-yb)-omigl3*omigl3.*(yc-yd);vcx=vbx-l2*omigl2*sin(fil2);vcy=vby+l2*omigl2*cos(fil2);el2=(e.*(xc-xd)+f.*(yc-yd)/(xc-xb).*(yc-yd)-(xc-xd).*(yc-yb);el3=(e.*(xc-xb)+f.*(yc-yb)/(xc-xb).*(yc-yd)-(xc-xd).

10、*(yc-yb); acx=abx-el2.*(yc-yb)-omigl2*omigl2.*(xc-xb);acy=aby+el2.*(xc-xb)-omigl2*omigl2.*(yc-yb);as2x=abx-el2.*(yc-yb)/2-omigl2*omigl2.*(xc-xb)/2;as2y=aby+el2.*(xc-xb)/2-omigl2*omigl2.*(yc-yb)/2;xe=l+0*cos(fil1);ye=l1*sin(fil1)+(l-l1*cos(fil1)*tan(fil2);vex=0+0*cos(fil1);Vey=omigl*l1*cos(fil1)+l*om

11、igl2/(cos(fil2)*(cos(fil2)+omigl*l1*sin(fil1)*tan(fil2)-omigl2*l1 *cos(fil1)/(cos(fil2)*(cos(fil2);aex=0+0*cos(fil1);aey=-omigl*omigl*l1*sin(fil1)+el2*l/(cos(fil2)*(cos(fil2)+2*l*omigl2*omigl2*sin(fil2)/(cos( fil2)*(cos(fil2)*(cos(fil2)+omigl*omigl*l1*cos(fil1)*tan(fil2)+omigl*omigl2*l1*sin(fil1)/(c

12、o s(fil2)*(cos(fil2)-el2*l1*cos(fil1)/(cos(fil2)*(cos(fil2)+omigl*omigl2*l1*sin(fil1)/(cos(fil2) )*(cos(fil2)-2*omigl2*omigl2*l1*cos(fil1)*sin(fil2)/(cos(fil2)*(cos(fil2)*(cos(fil2);fil3=atan(yc-yd)/(xc-xd);as3x=l3/2*el3*cos(fil3)+omigl3*omigl3*l3/2*sin(fil3);as3y=omigl3*omigl3*l3/2*cos(fil3)+l3/2*e

13、l3*sin(fil3);A=1 0 -1 0 0 0;0 1 0 -1 0 0;(yc-yb)/2 (xb-xc)/2 (yc-yb)/2 (xb-xc)/2 0 0;0 0 1 0 -1 0;0 0 0 1 0 -1;00 (yd-yc)/2 (xc-xd)/2 (yd-yc)/2 (xc-xd)/2;B=m2*as2x+R24x;m2*as2y+R24y+m2*g;js2*el2+R24y*(xe-(xb+xc)/2)-R24x*(ye-(yb+yc)/2);m3*as3x;m3*as3y+m3*g;js3*el3;C=inv(A)*BC =R12x=-7.4060*1.0e+003R1

14、2y=-5.5947*1.0e+003R23x=3.3282*1.0e+003R23y=-9.7564*1.0e+003R36x=2.9970*1.0e+003R36y=-8.7134*1.0e+003当初始角位移为30度时，求算原动件的受力以及平衡力矩：clear;clc;R12x=-7.4060*1.0e+003;R12y=-5.5947*1.0e+003;xa=0;ya=0;v=0.2;ff=100;g=9.8;m1=5;M=200;m2=10;js2=0.2;js3=0.2;m3=10;m4=5;m5=10;11=50;omig1=2;fi11=30/180*pi;as1x=11*om

15、ig1*omig1/2*cos(fi11);as1y=11*omig1*omig1/2*sin(fi11);xd=215;yd=0;12=200;13=160;1=120;xb=xa+11*cos(fi11);yb=ya+11*sin(fi11);vbx=-omig1*11*sin(fi11);vby=omig1*11*cos(fi11);abx=-omig1*omig1*11*cos(fi11);aby=-omig1*omig1*11*sin(fi11);h=sqrt(xd-xb).*(xd-xb)+ (yd-yb).*(yd-yb);de1ta=atan(yd-yb)/(xd-xb);ga

16、ma=acos(h.*h+12*12-13*13)/(2.*h.*12);fi12=gama-de1ta;xc=xb+12*cos(fi12);yc=yb+12*sin(fi12);omig13=(-vbx).*(xc-xb)+(-vby).*(yc-yb)/(yc-yd).*(xc-xb)-(yc-yb).*(xc-xd);omig12=(-vbx).*(xc-xd)+(-vby).*(yc-yd)/(yc-yd).*(xc-xb)-(yc-yb).*(xc-xd);e=-abx+omig12*omig12.*(xc-xb)-omig13*omig13.*(xc-xd);f=-aby+omi

17、g12*omig12.*(yc-yb)-omig13*omig13.*(yc-yd);vcx=vbx-12*omig12*sin(fi12);vcy=vby+12*omig12*cos(fi12);e12=(e.*(xc-xd)+f.*(yc-yd)/(xc-xb).*(yc-yd)-(xc-xd).*(yc-yb);e13=(e.*(xc-xb)+f.*(yc-yb)/(xc-xb).*(yc-yd)-(xc-xd).*(yc-yb);acx=abx-e12.*(yc-yb)-omig12*omig12.*(xc-xb);acy=aby+e12.*(xc-xb)-omig12*omig12.

18、*(yc-yb);as2x=abx-e12.*(yc-yb)/2-omig12*omig12.*(xc-xb)/2;as2y=aby+e12.*(xc-xb)/2-omig12*omig12.*(yc-yb)/2;xe=1+0*cos(fi11);ye=11*sin(fi11)+(1-11*cos(fi11)*tan(fi12);vex=0+0*cos(fi11);vey=omig1*11*cos(fi11)+1*omig12/(cos(fi12)*(cos(fi12)+omig1*11*sin(fi11)*tan(fi12)-omig12*11*cos(fi11)/(cos(fi12)*(c

19、os(fi12);aex=0+0*cos(fi11);aey=-omig1*omig1*11*sin(fi11)+e12*1/(cos(fi12)*(cos(fi12)+2*1*omig12*omig12*sin(fi12)/(cos( fil2)*(cos(fil2)*(cos(fil2)+omigl*omigl*l1*cos(fil1)*tan(fil2)+omigl*omigl2*l1*sin(fil1)/(co s(fil2)*(cos(fil2)-el2*l1*cos(fil1)/(cos(fil2)*(cos(fil2)+omigl*omigl2*l1*sin(fil1)/(cos

20、(fil2) )*(cos(fil2)-2*omigl2*omigl2*l1*cos(fil1)*sin(fil2)/(cos(fil2)*(cos(fil2)*(cos(fil2);fil3=atan(yc-yd)/(xc-xd);as3x=l3/2*el3*cos(fil3)+omigl3*omigl3*l3/2*sin(fil3);as3y=omigl3*omigl3*l3/2*cos(fil3)+l3/2*el3*sin(fil3);A=-1 0 0;0 -1 0;-yb/2 xb/2 1;B=m1*as1x+R12x;m1*as1y+R12y;-M-yb/2*R12x+xb/2*R1

21、2y;C=inv(A)*BC =R16x= 0.6973*1.0e+004R16y=0.5345*1.0e+004Mb=-5.6908*1.0e+004每次求算时，需给定初始角位移fil1,对于PRP杆组，只给定初始角位移fil1,就可得出R24x, R24y, R45x，R45y，R56x，R56y；而对于RRR杆组，给定初始角位移fil1后，需将上一 步得出的R24x，R24y代入，然后就可以求算出R12x，R12y，R23x，R23y，R36x，R36y； 对于原动件，给定初始角位移fil1后，需将上一步得出的R12x，R12y代入，然后就可以求 算出 R16x，R16y，Mb。具体的求

22、算结果如下：当初始角位移fil1=30R24x=-8.3957*1.0e+003R24y=5.1653*1.0e+003R12x=-7.4060*1.0e+003R12y=-5.5947*1.0e+003R23x=3.3282*1.0e+003R23y=-9.7564*1.0e+003R36x=2.9970*1.0e+003R36y=-8.7134*1.0e+003R45x=-8.3957*1.0e+003R45y=2.8838*1.0e+003R56x=-8.3957*1.0e+003R56y=-1.6791*1.0e+003R16x= 0.6973*1.0e+004R16y=0.5345*

23、1.0e+004Mb=-5.6908*1.0e+004时当初始角位移fil1=90时R24x=-2.3401 *1.0e+003R24y=1.4934*1.0e+003R45x=-2.3401*1.0e+003 R45y=0.8396*1.0e+003 R56x=-2.3401*1.0e+003 R56y=-0.4680*1.0e+003 R12x=-1.6212*1.0e+003 R12y=-3.1610*1.0e+003 R23x=1.5939*1.0e+003 R23y=-3.2319*1.0e+003 R36x=1.3478*1.0e+003 R36y=-2.7551*1.0e+003

24、 R16x= 0.1621*1.0e+004 R16x=0.2661*1.0e+004 Mb=8.1260*1.0e+004当初始角位移fil1=150时 R24x=-309.2120 R24y=324.9744 R45x=-309.2120 R45y=196.0355 R56x=-309.2120 R56y=-61.8424 R12x=870.5160 R12y=-54.1100 R23x=-48.1341 R23y=60.0668 R36x=235.8573 R36y=-329.6487R16x= -0.0438*1.0e+004 R16y=-0.0196*1.0e+004 Mb=-1.9220*1.0e+004当初始角位移fil1=210时 R24x=-485.3828 R24y= 761.3179 R45x=-485.3828 R45y=475.1864 R56x=-485.3828 R56y=-97.0766 R12x=1.6980*1.0e+003 R12y=1.2577*1.0e+003 R23x=