平面六杆机构的运动分析

1、平面六杆机构的运动分析2机械原理大作业（一）平面六杆机构的运动分析班 级:学 号:姓 名: 同组者: 完成时间:一.题目1 . 1说明如图所示为一片面六杆机构各构件尺寸如表格 1所示，又知 原动件1以等角速度3=1rad/s沿逆时针方向回转，试求各从动件 的角位移、角加速度以及E点的位移、速度及加速度的变化情况。1. 2数据组号L1L2L 2L3L4L5L6CtXGyG1-A26.5105.665.067.587.534.425.0600153.541.7表格1条件数据1. 3要求三人一组，编程计算出原动件从0360o时（计算点数N=36）所要求各运动变量的大小，并绘制运动线图及点的轨迹曲线。

2、二.解题步骤由封闭图形ABCD可得：11+比 L+L由封闭图形AGFECD可得于是有：11 sin、l2sn2 = l 3sin七111 C0S1 l2cos)2 T4 l 3sin七2I1C0S1 l2cos2 l,2sin2 l5cos5 = l6cos6 153.5 3 l1sin1 l2sin2 Tcos l5sin5 = l6sin6 41.74对以上1到4导可得-12 cos2 2 l 3cos% 3 T1 cos1 1l2sine2®2 T 3si"3®3 = T1sin脂气< l5sin%®5 T6sine6" 6= &q

3、uot;sin%气一缶 2(l2sin2 l,2cos2)< l5cos55 T6cos6" 6= T1cos皆1 一切 2(l2cos2 + lsin%)811cos112sin2l . . I l . i211sm112cos21 11 cos112cos2 1,2sin2/_ "sin%i12sin2 12cos2T3sin30022213co§3003015cos5-16 cos 6520ksin、-16sin62写做矩阵形式:-12cos21Kcosh00112sin2撬宙300T2cos2 12sin20-确死'_ 12sin2 12co

4、s200。25Mos211C0S1l i3 =hsini©Ico 151 11sin111-611 cos1对上述矩阵求导可得:13*3002 1 11gn%00.,0(.30"sin%-16siff6Ila 150，cos516cos61 11*6T2cos2I .12sin212sin2 T2cos2_12cos2 12sin2E点横坐标及对应的速度和加速度rxe 11C0S/1 2 Co2sin林x="sini 11 2Sin/122cos2 222,2 /lqx=-仍 11 cos 仪 1 1 1Si ng 1 2 安os12 & 声i n 22

5、12Si n9 2c(E点纵坐标及对应的速度和加速度：厂 ye=11 sin% + 12sine 2 T,2 cos。2vey = 11 cos 尸 1 +12 cos2 2 + 1 ,2 sin 2切 222.a f 1 11 sin脂 + « 111 cos% 切 2 12 sin 2 + 口 212 cos9 2 +2. /° 2 1 2 cos% 1 四甘 2'§ = Jxe2 + ye2/ Ve = Jvex2 * Vey2电=农2 +如三.计算程序框图四. 源程序1. #include "stdlib.h"#include

6、"math.h"#include "stdio.h" int agaus(a,b,n) int n;double a,b;( int *js,l,k,i,j,is,p,q;double d,t;js=malloc(n*sizeof(int);l=1;for (k=0;k<=n-2;k+)( d=0.0;for (i=k;i<=n-1;i+)for (j=k;j<=n-1;j+)( t=fabs(ai*n+j);if (t>d) ( d=t; jsk=j; is=i;if (d+1.0=1.0) l=0; else( if (jsk

7、!=k)for (i=0;i<=n-1;i+)( p=i*n+k; q=i*n+jsk; t=ap; ap=aq; aq=t;if (is!=k)( for (j=k;j<=n-1;j+)( p=k*n+j; q=is*n+j;t=ap; ap=aq; aq=t;t=bk; bk=bis; bis=t;if (l=0)( free(js); printf("failnH);return(0);d=ak*n+k;for (j=k+1;j<=n-1;j+)( p=k*n+j; ap=ap/d; bk=bk/d;for (i=k+1;i<=n-1;i+)( for

8、(j=k+1;j<=n-1;j+)( p=i*n+j;ap=ap-ai*n+k*ak*n+j;bi=bi-ai*n+k*bk;d=a(n-1)*n+n-1;if (fabs(d)+1.0=1.0)( free(js); printf("failn");return(0);bn-1=bn-1/d;for (i=n-2;i>=0;i-)( t=0.0;for (j=i+1;j<=n-1;j+)t=t+ai*n+j*bj;bi=bi-t;jsn-1=n-1;for (k=n-1;k>=0;k-)if (jsk!=k)( t=bk; bk=bjsk; bjs

9、k=t;free(js);return(1);2.程序二求解各杆的角度和E点坐标（杆四的角度始终为零，程序中不再求解）/* 输出文件 Output.txt*/#include "stdio.h"#include <conio.h>平面六杆机构的运动分析10#include "dnetn.c"#include "agaus.c"#include <math.h>#define PI 3.14159265358979#define ANGLE (PI/180)#define ALPHA (PI*60/180)/*初

10、始杆长：*/static double dLen7=65.0, 26.5, 105.6, 67.5, 87.5, 34.4, 25.0;/*G点的坐标*/static double dGxy2=153.5,41.7;static double x0 = 0 * ANGLE;main()int i,k;double eps,t,h,xe,ye;int nTemp=0;FILE *pf;/*各角位移的初始估计值*/static doublex4=36.80*ANGLE,69.57*ANGLE,119.00*ANGLE,48.92*ANGLE;pf = fopen("Output.txt&

11、quot;,"w");t=0.1; h=0.1; eps=0.00000001; k=100;for (nTemp = 0; nTemp <= 36; nTemp+)x0 = nTemp * 10 * ANGLE;i=dnetn(4,eps,t,h,x,k);printf("ni=%dn",i);printf("x0=%lfn",x0);fprintf(pf,"%dt",10*nTemp);for (i=0; i<=3; i+)printf("x(%d)=%13.7lfn",i,xi

12、/ANGLE);fprintf(pf,"%lft",xi/ANGLE);xe=dLen1 * cos(x0)+ dLen2 * cos(x0)+dLen0 * cos(ALPHA-(x0);ye=dLen1 * sin(x0)+ dLen2 * sin(x0)-dLen0 * sin(ALPHA-(x0);printf("xe=%13.7lfnye=%13.7lfn",xe,ye);fprintf(pf,"n");printf("n");fclose(pf);getch();/*建立牛顿法矩阵*/void dnet

13、nf(x,y,n) int n;double x,y;(y0 = dLen1 * cos(x0) + dLen2 * cos(x0) - dLen3 * cos(x1)-dLen4;y1 = dLen1 * sin(x0) + dLen2 * sin(x0) - dLen3 * sin(x1);y2 = dLen1 * cos(x0) + dLen2 * cos(x0) + dLen5* cos(x2) - dLen6 * cos(x3) - dGxy0 +dLen0 * cos(ALPHA-(x0);y3 = dLen1 * sin(x0) + dLen2 * sin(x0) + dLen5

14、* sin(x2) - dLen6 * sin(x3) - dGxy1-dLen0 * sin(ALPHA-(x0);n = n;return;3. 程序三求解各杆的角速度和E点速度(杆四的角速度始终为零，程序中不再求解)/*输出文件 Output2.txt*/#include "stdio.h"#include "math.h"#include "agaus.c"#include <conio.h>#define PI 3.14159265358979#define ANGLE (PI/180)#define ALPHA

15、 (PI*35/180)/*初始杆长：依次为*/static double dLen7=65.0, 26.5, 105.6, 67.5, 87.5, 34.4, 25.0;/* G点的坐标*/static double dGxy2=153.5,41.7;static double x0 = 0 * ANGLE;static double w1 = 1.0;double Vex,Vey;main()int i,j,nTime;FILE *fInput;i o平面六杆机构的运动分析1 2FILE *fOutput2;int nX0,nCounter;double dTemp4=0;static d

16、ouble a44= 0.;static double b4=0.;/*将agu_01.C的输出文件output.txt作为输入文件，继续计算*/fInput = fopen("output.txt”,"r”);fOutput2 = fopen("output2.txt”,"w”);for(nTime=0;nTime<=36;nTime+)fscanf(fInput,"%d”,&nX0);x0=nX0*ANGLE;printf("x0= %lfn",x0);for (nCounter=0;nCounter<

17、;4;nCounter+)fscanf(fInput,"%lf",&dTempnCounter);for (nCounter=0;nCounter<4;nCounter+)dTempnCounter = dTempnCounter * ANGLE;/*建立高斯方程组矩阵*/a00 = - dLen2 * sin(dTemp0);a01 = dLen3 * sin(dTemp1);a02 = 0.;a03 = 0.;a10 = dLen2 * cos(dTemp0);a11 = - dLen3 * cos(dTemp1);a12 = 0.;a13 = 0.;a2

18、0 = dLen2 * sin(dTemp0)- dLen0 * sin(ALPHA-(dTemp0);a21 =0.;a22 = dLen5 * sin(dTemp2);a23 = -dLen6 * sin(dTemp3);a30 = dLen2 * cos(dTemp0)+dLen0 * cos(ALPHA-(dTemp0);a31 = 0.;a32 = dLen5 * cos(dTemp2);a33 = - dLen6 * cos(dTemp3);b0 = dLen1 * sin(x0) * w1;b1 = - dLen1 * cos(x0) * w1;b2 = -dLen1* sin(

19、dTemp0)* w1 ;b3 =-dLen1* cos(dTemp0)* w1 ;if (agaus(a,b,4)!=0)for (i=0;i<=3;i+)printf("w%d=%lfn”,i,bi);fprintf(fOutput2,"%lf ",bi);Vex=-dLen1 * sin(x0) * w1-dLen2 * sin(dTemp0) * b0+ dLen0 * sin(ALPHA-(dTemp0) *b0;Vey=dLen1 * cos(x0) * w1+dLen2 * cos(dTemp0) * b0+ dLen0 * cos(ALPHA

20、-(dTemp0) * b0; printf("Vex=%lfnVey=%lfn",Vex,Vey);fprintf(fOutput2,"n");printf("n");fclose(flnput);fclose(fOutput2);getch();4. 程序四求解各杆和点E的角加速度(杆四角加速度始终为零，这里不再求解)/*输出文件 Output3.txt*/#include "stdio.h"#include "math.h"#include "agaus.c"#incl

21、ude <conio.h>#define PI 3.14159265358979#define ANGLE (PI/180)#define ALPHA (PI*35/180)/*初始杆长：依次为*/static double dLen7=65.0, 26.5, 105.6, 67.5, 87.5, 47.2, 37.8;/*G点的坐标*/static double dGxy2=153.5,41.7;static double x0 = 0 * ANGLE;static double w1 = 1.0;main()1 2平面六杆机构的运动分析14int i,nTime;FILE *f

22、Input2;FILE *fOutput3;int nX0,nCounter;double Aex,Aey;double dSeta5=0.;double dOmiga4 = 0.;static double a44= 0.;static double b4=0.;/*将agu_02.C的输出文件output2.txt作为输入文件，继续计算*/fInput2 = fopen("output2.txt”,"r”);fOutput3 = fopen("output3.txt”,"w”);for(nTime=0;nTime<=36;nTime+)fsca

23、nf(fInput2,"%d",&nX0);/*读入角度值*/for (nCounter=0;nCounter<5;nCounter+)fscanf(fInput2,"%lf",&dSetanCounter);/*读入角速度值*/for (nCounter=0;nCounter<4;nCounter+)fscanf(fInput2,"%lf",&dOmiganCounter);/*建立高 斯方程 组矩阵，dSeta0=x1 (角度 我们草 稿的)，dSeta1=x2,dSeta2=x3,dSeta3

24、=x5,dSeta4=x6dOmiga0 =w2, dOmiga1=w3, dOmiga2=w5, dOmiga3=w6*/a00 = - dLen2 * sin(dSeta1);a01 = dLen3 * sin(dSeta2);a02 = 0.;a03 = 0.;a10 = dLen2 * cos(dSeta1);a11 = - dLen3 * cos(dSeta2);a12 = 0.;a13 = 0.;a20 = - dLen0 * sin(ALPHA-(dSeta1)+dLen2 * sin(dSeta1);a21 = 0.;a22 = dLen5 * sin(dSeta3);a23

25、= -dLen6 * sin(dSeta4);a30 = dLen0 * cos(ALPHA-(dSeta1)+dLen2 * cos(dSeta1);a31 = 0.;a32 = dLen5 * cos(dSeta3);a33 = - dLen6 * cos(dSeta4);b0 = - ( - dLen2 * cos(dSeta1) * dOmiga0 * dOmiga0+ dLen3 * cos(dSeta2) * dOmiga1 * dOmiga1 ) + dLen1 *cos(dSeta0) * w1 * w1;b1 = - ( - dLen2 * sin(dSeta1) * dOm

26、iga0 * dOmiga0+ dLen3 * sin(dSeta2) * dOmiga1 * dOmiga1 ) + dLen1 *sin(dSeta0) * w1 * w1;b2 = -w1 * w1* dLen1*cos(dSeta0)-dOmiga0 *dOmiga0*(dLen2*cos(dSeta1)+dLen0 * cos(ALPHA-(dSeta1)+dOmiga3 *dOmiga3*dLen6 * cos(dSeta4)-dLen5*cos(dSeta3) * dOmiga2 * dOmiga2;b3 = w1 * w1* dLen1*sin(dSeta0)-dOmiga0

27、*dOmiga0*(dLen2*sin(dSeta1)-dLen0*sin(ALPHA-(dSeta1)-dOmiga3 *dOmiga3*dLen6 * sin(dSeta4)+ dLen5*sin(dSeta3) * dOmiga2 * dOmiga2;if (agaus(a,b,4)!=0) for (i=0;i<=3;i+)printf("a%d=%lfn",i,bi);fprintf(fOutput3,"%lf ",bi);Aex=-dLen2*sin(dSeta1)*b0+dLen0*sin(ALPHA-(dSeta1)*b0-dLen

28、1*cos(dSeta0)*w1*w1-dLen2*cos(dSeta1)*dOmiga0dOmiga0-dLen0*cos(ALPHA-(dSeta1)*dOmiga0 * dOmiga0;Aey=dLen2*cos(dSeta1)*b0+dLen0*cos(ALPHA-(dSeta1)*b0-dLen1*sin(dSeta0)*w1*w1-dLen2*sin(dSeta1)*dOmiga0dOmiga0+dLen0*sin(ALPHA-(dSeta1)*dOmiga0 * dOmiga0;printf("Aex=%lfnAey=%lf",Aex,Aey);fprintf

29、(fOutput3,"%lf %lf ",Aex,Aey);printf("nn");fprintf(fOutput3,"n"); 1 4平面六杆机构的运动分析15fclose(fInput2);fclose(fOutput3);getch();5. #include "stdlib.h"#include "math.h"#include "stdio.h"int dnetn(n,eps,t,h,x,k)int n,k;double eps,t,h,x; extern voi

30、d dnetnf();extern int agaus();int i,j,l;double am,z,beta,d,*y,*a,*b;y=malloc(n*sizeof(double);a=malloc(n*n*sizeof(double);b=malloc(n*sizeof(double);l=k; am=1.0+eps;while (am>=eps) dnetnf(x,b,n);am=0.0;for (i=0; i<=n-1; i+) z=fabs(bi);if (z>am) am=z;if (am>=eps) l=l-1;if (l=0) free(y); fr

31、ee(b); free(a);printf("failn"); return(0);for (j=0; j<=n-1; j+) z=xj; xj=xj+h;dnetnf(x,y,n);for (i=0; i<=n-1; i+) ai*n+j=yi;xj=z;if (agaus(a,b,n)=0) free(y); free(a); free(b); return(-1);beta=1.0;for (i=0; i<=n-1; i+) beta=beta-bi;if (fabs(beta)+1.0=1.0) free(y); free(a); free(b);

32、printf("failn"); return(-2);1 5平面六杆机构的运动分析1 7d=h/beta;for (i=0; i<=n-1; i+) xi=xi-d*bi; h=t*h;free(y); free(a); free(b);return(k-l);五. 计算结果? 1 （单位：度:）?2 （单位：度:）?3 （单位：度、,）? 5 （单位：度）?6 （单位：度036.7990569.57313122.4627792.665441032.7094766.00299106.4997167.798572029.2776164.0731797.1754452.

33、862793026.5973763.7310390.3834344.249194024.6359164.7551184.2478239.672665023.3010866.8646877.8411637.316076022.4901269.7900470.4814435.419577022.1129773.3007761.2722731.876318022.0990377.2093648.8508123.825399022.3963781.3648232.264598.5942310022.9684485.6444213.79708-12.3279311023.7903589.9462-1.8

34、8955-33.31912024.8456494.18335-12.74873-50.8843913026.1233198.28029-19.47863-64.721114027.61533102.17026-23.43679-75.5877215029.31424105.7939-25.76743-84.2467516031.21099109.09881-27.29596-91.2615217033.29288112.03937-28.59909-97.0319318035.54172114.57678-30.07522-101.8606819037.93229116.67878-31.99

35、02-106.0039620040.43114118.31896-34.50611-109.6995121042.99573119.4754-37.70212-113.1728422045.57385120.12878-41.59328-116.625323048.10309120.26007-46.14952-120.2108524050.51035119.84805-51.3162-124.0104525052.71117118.86702-57.03775-128.0136226054.60905117.28503-63.28435-132.1156127056.09499115.063

36、45-70.07877-136.1348628057.0483112.15863-77.51645-139.8518129057.33997108.52777-85.77334-143.0681630056.84147104.14138-95.10476-145.6934431055.4427999.00639-105.86689-147.8969432053.0835193.20271-118.69237-150.5043933049.7968986.93055-135.48887-156.6045834045.7547380.55028-164.06049-178.7216335041.2

37、812574.57477-207.28198-226.9752736036.7990569.57313-237.53723-267.33456? 1 （单位：度w2 （单位：rad/s ）w3 （单位：rad/s ）|w5 （单位：rad/s ）w6（单位：rad/s ）0-0.43443-0.43443-2.42454-2.8371910-0.37901-0.27611-1.50231-1.968520-0.30588-0.11091-0.91878-1.2061430-0.230840.0386-0.56502-0.5861540-0.163070.16142-0.32443-0.0690

38、150-0.105640.25595-0.129070.3848760-0.058060.325270.048060.803970-0.018540.373760.17951.16597800.01490.405460.116711.28627900.043970.4236-0.388620.799141000.070030.43063-1.16737-0.170181100.094080.42829-1.6884-0.946671200.11680.41789-1.86857-1.347151300.138610.40039-1.87297-1.529481400.159680.37661-

39、1.81572-1.626531500.179960.34725-1.74328-1.703731600.199180.31298-1.66885-1.789361700.216890.27449-1.5923-1.894341800.232460.23246-1.50865-2.020151900.24510.18751-1.41155-2.161372000.253960.14017-1.29477-2.306232100.258090.0908-1.15309-2.4372200.256490.03956-0.98329-2.531192300.24814-0.01365-0.78563

40、-2.564012400.23191-0.06918-0.56583-2.512122500.20665-0.12756-0.33625-2.358052600.17111-0.18948-0.11521-2.093781 7平面六杆机构的运动分析1 82700.12406-0.255570.0769-1.721942800.06444-0.326130.22384-1.25397290-0.00827-0.400580.32055-0.70581300-0.09331-0.476650.37885-0.09149310-0.18751-0.54910.43120.58577320-0.283

41、88-0.608370.527281.338330-0.37062-0.640050.622262.05413340-0.43232-0.62729-0.677430.7279350-0.45511-0.55802-3.06708-2.90494360-0.43443-0.43443-2.42454-2.83719? 1 （单位：度)a2a3a5a601.87731-1.41416-9.3572522.276910-0.5276-1.3131412.8394314.4391320-10.21122-16.13634-41.38351-111.46712300.322270.3023-2.243

42、07-1.31208400.710490.38945-2.223782.07264502.165745.80322-21.27313-59.0065460-0.144353.8797415.29502-4.92108702.030953.01559-66.66643-92.75689801.34149-0.79682-5.6969317.35997903.873711.2010994.506115.59534100-16.918128.13118-53.8692720.51404110-0.62813-1.177686.97249-2.444621200.977911.4819-1.98112

43、6.72186130-0.21204-0.7149-1.26222-4.04646140-1.6445-4.057139.66324.02261150-1.02752-1.887111.3850913.485481600.57409-0.7711137.87656-52.568711700.57409-0.7711137.87656-52.568711800.57409-0.7711137.87656-52.568711900.57409-0.7711137.87656-52.568712000.57409-0.7711137.87656-52.568712100.57409-0.771113

44、7.87656-52.568712200.57409-0.7711137.87656-52.568712300.57409-0.7711137.87656-52.568712400.57409-0.7711137.87656-52.568712500.57409-0.7711137.87656-52.568712600.57409-0.7711137.87656-52.568712700.57409-0.7711137.87656-52.568712800.57409-0.7711137.87656-52.568712900.57409-0.7711137.87656-52.568711 8半

45、向六杆机构的运动分析1 93000.57409-0.7711137.87656-52.568713100.57409-0.7711137.87656-52.568713200.57409-0.7711137.87656-52.568713300.57409-0.7711137.87656-52.568713400.57409-0.7711137.87656-52.568713500.57409-0.7711137.87656-52.568713600.57409-0.7711137.87656-52.56871XeYeVexVeyAexAey170.8016537.6482816.3554-3

46、6.18842173.19724187.86733172.7165631.863085.73079-29.47339-114.7416822.41059172.8899827.49921-3.42435-20.36538-715.62505-1365.89613171.63824.74528-10.59649-11.372780.5446125.093169.2948423.43323-15.9903-3.997-57.98263103.71014166.1371723.22697-19.990991.28259510.37845288.62216162.3797923.76584-22.90

47、2284.5912296.42715358.18851158.1954624.73635-24.904926.2981629.47122281.71398153.7335625.89561-26.09446.82301-0.16224192.37618149.1309227.07215-26.525166.55739569.8676129.35796144.516128.15849-26.241755.84156382.529942655.46328140.0093429.10177-25.296984.96127-44.20371-104.35613135.7202429.89438-23.

48、760814.149548.40659122.97291131.7444730.56486-21.722923.58769-47.86092-40.4638128.1604631.16891-19.290913.40551-237.39024-304.20274125.0266431.78027-16.584673.67982-159.52108-83.47344122.3800632.48145-13.728014.4343317.6055169.77782120.2365733.35457-10.8385.6415317.6055169.77782118.5930234.47284-8.013427.2277617.6055169.77782117.4314335.89317-5.323689.0817817.6055169.77782116.7249637.65056-2.79