机械原理大作业平面连杆机构报告.pdf

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1、平面连杆机构的运动分析（题号：平面六杆机构）（题号：平面六杆机构）一、题目说明一、题目说明1、题目简介：如图所示平面六杆机构，试用计算机完成其运动分析。已知其尺寸参数如下表所示：组号l1l2l3l4l5l6600ABCl2-A2-B26.53-C67.587.552.443l2=116.6l2=111.62=126.62、题目要求与成员组成及分工：（1）题目要求：三人一组计算出原动件从 0 到 360 时（计算点数 37）所要求的各运动变量的大小，并绘出运动曲线图及轨迹曲线,本组选取题号为：2A，2B 组。(2)分工比例：杨帆 40%10分曾琪 40%10 分彭杰：20%8 分二、题目分析1、

2、建立封闭图形：L1+L2=L3+L4L1+L2=L5+L6+AG2、机构运动分析：a、角位移分析由图形封闭性得：L1 cos1 L2 cos2 L3 cos3 L4L1sin1 L2sin2 L3sin3L cos L cos L cos(2)xG L6 cos6 L5 cos512221L1sin1 L2sin2 L2sin(2)yG L6sin6 L5sin5将上式化简可得：L2 cos2 L3 cos3 L4 L1 cos1L2sin2 L3sin3 L1sin1L cos L cos(2)L5 cos5 L6 cos6 xG L4323L sin L sin(2)L5sin5 L6si

3、n6 yG332b、角速度分析上式对时间求一阶导数，可得速度方程：化为矩阵形式为：L2 sin22 L3 sin33 L1 sin11L2 cos22 L3 cos33 L1 cos11 L sin L sin(2)2 L5 sin55 L6 sin66 03332L3 cos33 L2 cos(2)2 L5 cos55 L6 cos66 0 L2 sin2L2 cos2 L2 sin(2)L2 cos(2)L1 sin1 L1 cos1100L3sin3 L3 cos3 L3 sin3L3 cos300 L5sin5L5 cos5 2 03L6sin6 5 L6 cos6 60c、角加速度分

4、析：矩阵对时间求一阶导数，可得加速度矩阵为：L sinL2cos2L2sin(2)L2cos(2)L2cos2L2sin2L2cos(2)L2sin(2)L sinL3cos3L3sin3L3cos3L3cos3L3sin3L3cos3L3sin300L5sin5L5cos500L5cos5L5sin5 03L6sin6 5 L6cos6 600L1cos1L1sin1002 2 20321L6cos6 52 2L6sin66d、E 点的运动状态xE xG L6 cos6 L5 cos5位移：y y L sin L sinG6655EvEx L6 sin66 L5 sin55速度：v L co

5、s L cos666555Ey加速度：22a L cos L sin L cos L5 sin55Ex66666655522aEy L6 sin66 L6 cos66 L5 sin55 L5 cos55三、流程图三、流程图开始开始输入输入 l1,l2,l3,l4,l5,l6,l2l1,l2,l3,l4,l5,l6,l2,xg,yg,xg,yg,I=0I=0 1=I*101=I*10用矢量法求解角位移函数，用矢量法求解角位移函数，并计算并计算 2 2，3 3，5 5，6 6，并计算，并计算 Xe,YeXe,Ye调用系数矩阵调用系数矩阵 A A 子函数，计算子函数，计算 A A调用原动件位置参数矩

6、阵调用原动件位置参数矩阵 B B 子程序，创建矩阵子程序，创建矩阵 B B调用求解角速度子程序，调用高斯消去法求解调用求解角速度子程序，调用高斯消去法求解A*A*=B*=B*1 1，得到，得到2 2，3 3，5 5，6 6，再求解，再求解 VexVex，VeyVey调用系数矩阵调用系数矩阵 DADA，计算计算 DADA调用系数矩阵调用系数矩阵 DBDB，计算计算 DBDB调用求解角加速度子程序，计算调用求解角加速度子程序，计算 B B（K K）=-DA*=-DA*+DB*+DB*1,1,然后调用高斯消去法程序结然后调用高斯消去法程序结 A*a=BA*a=B（K K）求的求的 a2a2，a3a3

7、，a5a5，a6a6，再求出，再求出 aexaex，aeyaeyI=I+1I=I+1I36I36N N输出结果输出结果结束结束四、源程序四、源程序#include#include#include#define PI 3.1415926#define N 4void Solutionangle(double 18,double);/*矢量法求角位移*/void Solutionspeed(double NN,double N,double 18,double);/*角速度求解*/void Solutionacceleration(double NN,double NN,double N,doub

8、le 18);/*角加速度求解*/void GaussianE(double NN,double N,double N);/*高斯消去*/void FoundmatrixA(double 18,double NN);/创建系数矩阵 Avoid FoundmatrixB(double 18,double,double N);/创建系数矩阵 Bvoid FoundmatrixDA(double 18,double NN);/创建矩阵 DAvoid FoundmatrixDB(double 18,double,double N);/创建矩阵 DB/定义全局变量double l1=26.5,l2=11

9、1.6,l3=67.5,l4=87.5,l5=52.4,l6=43.0;double l2g=65.0,xg=153.5,yg=41.7,inang=60*PI/180,as1=1.0;/主函数void main()int i,j;FILE*fp;double shuju3618;double psvalue18,aNN,daNN,bN,dbN,ang1;/建立文件，并制表头 if(fp=fopen(filel,w)=NULL)printf(Cannt open this file.n);exit(0);fprintf(fp,n The Kinematic Parameters of Poin

10、t 5n);fprintf(fp,ang2 ang3 ang5 ang6);fprintf(fp,as2 as3 as5 as6);fprintf(fp,aas2 aas3 aas5 aas6);fprintf(fp,xe ye vex vey aexaeyn);/计算数据并写入文件 for(i=0;i36;i+)ang1=i*PI/18;Solutionangle(psvalue,ang1);FoundmatrixB(psvalue,ang1,b);FoundmatrixA(psvalue,a);Solutionspeed(a,b,psvalue,ang1);FoundmatrixDA(ps

11、value,da);FoundmatrixDB(psvalue,ang1,db);Solutionacceleration(a,da,db,psvalue);for(j=0;j4;j+)shujuij=psvaluej*180/PI;for(j=4;j18;j+)shujuij=psvaluej;fprintf(fp,n);for(j=0;j18;j+)fprintf(fp,%12.3f,shujuij);fclose(fp);/输出数据 for(i=0;i36;i+)ang1=i*PI/18;printf(n 输出 ang1=%d 时的求解n,i*10);printf(angle angsp

12、eed angacceleration E:n);for(j=0;j4;j+)printf(%lft,shujuij);printf(n);for(j=4;j8;j+)printf(%lft,shujuij);printf(n);for(j=8;j12;j+)printf(%lft,shujuij);printf(n);for(j=12;j18;j+)printf(%lft,shujuij);printf(n);/*矢量法求角位移*/void Solutionangle(double value18,double ang1)double xe,ye,A,B,C,phi,alpha,csn,an

13、g5g,d2,d,ang2,ang3,ang5,ang6;A=2*l1*l3*sin(ang1);B=2*l3*(l1*cos(ang1)-l4);C=l2*l2-l1*l1-l3*l3-l4*l4+2*l1*l4*cos(ang1);ang3=2*atan(A+sqrt(A*A+B*B-C*C)/(B-C);if(ang30)/限定 ang3 大小 ang3=2*atan(A-sqrt(A*A+B*B-C*C)/(B-C);ang2=asin(l3*sin(ang3)-l1*sin(ang1)/l2);xe=l4+l3*cos(ang3)+l2g*cos(ang2-inang);ye=l3*

14、sin(ang3)+l2g*sin(ang2-inang);phi=atan2(yg-ye),(xg-xe);d2=(yg-ye)*(yg-ye)+(xg-xe)*(xg-xe);d=sqrt(d2);csn=(l5*l5+d2-l6*l6)/(2.0*l5*d);alpha=atan2(sqrt(1.0-csn*csn),csn);ang5g=phi-alpha;ang5=ang5g-PI;ang6=atan2(ye+l5*sin(ang5g)-yg,xe+l5*cos(ang5g)-xg);value0=ang2;value1=ang3;value2=ang5;value3=ang6;va

15、lue12=xe;value13=ye;/限定角度大小 for(int i=0;i2*PI)valuei-=2*PI;while(valuei0)valuei+=2*PI;/*角速度求解*/void Solutionspeed(double a2NN,double b2N,double value18,double ang1)double ang2,ang3;ang2=value0;ang3=value1;double p2N;GaussianE(a2,b2,p2);value4=p20;value5=p21;value6=p22;value7=p23;value14=-l3*value5*s

16、in(ang3)-l2g*value4*sin(ang2-inang);value15=l3*value5*cos(ang3)+l2g*value4*cos(ang2-inang);/*角加速度求解*/void Solutionacceleration(double a3NN,double da3NN,double db3N,doublevalue18)int i,j;double ang2,ang3;ang2=value0;ang3=value1;double bkN=0;double p3N;for(i=0;iN;i+)for(j=0;jN;j+)bki+=-da3ij*value4+j;

17、bki+=db3i*as1;GaussianE(a3,bk,p3);value8=p30;value9=p31;value10=p32;value11=p33;value16=-l3*value9*sin(ang3)-l3*value5*value5*cos(ang3)-l2g*value8*sin(ang2-inang)-l2g*value4*value4*cos(ang2-inang);value17=l3*value9*cos(ang3)-l3*value5*value5*sin(ang3)+l2g*value8*cos(ang2-inang)-l2g*value4*value4*sin

18、(ang2-inang);/*高斯消去法解矩阵方程*/void GaussianE(double a4NN,double b4N,double p4N)int i,j,k;double a4gNN,b4gN,t;for(i=0;iN;i+)for(j=0;jN;j+)a4gij=a4ij;for(i=0;iN;i+)b4gi=b4i;/使主对角线上的值尽可能大 if(a4g00a4g11)for(j=0;jN;j+)t=a4g0j;a4g0j=a4g1j;a4g1j=t;t=b4g0;b4g0=b4g1;b4g1=t;if(a4g22a4g33)for(j=0;jN;j+)t=a4g2j;a4

19、g2j=a4g3j;a4g3j=t;t=b4g2;b4g2=b4g1;b4g3=t;/初等行变换 for(j=0;jN;j+)for(i=0;iN;i+)if(i!=j)for(k=0;kN;k+)if(k!=j)a4gik-=a4gij/a4gjj*a4gjk;b4gi-=b4gj*a4gij/a4gjj;a4gij=0;for(i=0;iN;i+)b4gi/=a4gii;p40=b4g0;p41=b4g1;p42=b4g2;p43=b4g3;/创建系数矩阵 Avoid FoundmatrixA(double value518,double a5NN)double ang2,ang3,ang

20、5,ang6;ang2=value50;ang3=value51;ang5=value52;ang6=value53;a500=-l2*sin(ang2);a501=l3*sin(ang3);a510=l2*cos(ang2);a511=-l3*cos(ang3);a520=-l2*sin(ang2)-l2g*sin(ang2-inang);a522=l5*sin(ang5);a523=l6*sin(ang6);a530=l2*cos(ang2)+l2g*cos(ang2-inang);a532=-l5*cos(ang5);a533=-l6*cos(ang6);a502=a503=a512=a

21、513=a521=a531=0;/创建系数矩阵 Bvoid FoundmatrixB(double value618,double ang1,double b6N)b60=b62=l1*sin(ang1)*as1;b61=b63=-l1*cos(ang1)*as1;/创建矩阵 DAvoid FoundmatrixDA(double value718,double da7NN)double ang2,ang3,ang5,ang6,as2,as3,as5,as6;ang2=value70;ang3=value71;ang5=value72;ang6=value73;as2=value74;as3=

22、value75;as5=value76;as6=value77;da700=-l2*as2*cos(ang2);da701=l3*as3*cos(ang3);da710=-l2*as2*sin(ang2);da711=l3*as3*sin(ang3);da720=as2*(-l2*cos(ang2)-l2g*cos(ang2-inang);da722=as5*l5*cos(ang5);da723=as6*l6*cos(ang6);da730=as2*(-l2*sin(ang2)-l2g*sin(ang2-inang);da732=as5*l5*sin(ang5);da733=as6*l6*si

23、n(ang6);da702=da703=da712=da713=da721=da731=0;/创建矩阵 DBvoid FoundmatrixDB(double value818,double ang1,double db8N)db80=db82=l1*as1*cos(ang1);db81=db83=l1*as1*sin(ang1);五、计算结果及相关曲线图：五、计算结果及相关曲线图：A A 组：组：数据数据ang231.41627.44124.31922.07120.58719.72519.35619.3819.72420.33821.18822.25323.51824.97326.6128.

24、42330.40232.53334.79937.17339.62242.10544.56946.95249.18251.17452.82954.03654.67354.60753.70851.86749.03545.2740.797ang359.51856.10754.60354.83956.48259.17862.62166.5770.8475.28779.79984.28288.65992.85996.825100.501103.84106.8109.344111.44113.061114.183114.784114.839114.323113.203111.44108.986105.78

25、9101.79796.97291.3284.9378.03871.08ang5274.846267.104261.96257.865254.057250.122245.733240.472233.659224.179210.788193.987177.339164.018154.479147.803142.952139.123135.751132.448128.955125.1120.784115.961110.623104.77998.43491.54783.99675.5265.57352.83733.036355.866313.857ang660.93347.45939.40435.15

26、333.43333.16833.433.14531.15825.65614.566357.785339.158322.764309.822299.87292.122285.905280.708276.145271.914267.78263.564259.15254.486249.588244.523239.386234.241229.036223.378215.831200.978164.371116.27636.012as2-0.434-0.357-0.267-0.184-0.115-0.06-0.0160.0190.0490.0740.0960.1170.1360.1550.1730.19

27、0.2060.220.2320.2420.2470.2480.2440.2320.2130.1840.1450.0940.031-0.046-0.136-0.234-0.332-0.417-0.471-0.47764.679as3-0.434-0.245-0.0590.10.2230.3110.3730.4140.4380.450.4510.4440.430.4090.3830.3520.3160.2760.2320.1860.1380.0870.033-0.023-0.081-0.143-0.21-0.282-0.359-0.44-0.524-0.605-0.67-0.702-0.68-0.

28、589as5288.382as6-1.783-1.285-1.053-0.973-0.984-1.059-1.185-1.361-1.584-1.817-1.916-1.703-1.316-1.029-0.792-0.561-0.423-0.352-0.328-0.336-0.365-0.407-0.457-0.508-0.559-0.609-0.66-0.719-0.795-0.908-1.1-1.507-2.666-4.566-4.309-2.74582.34-2.79-2.163-1.748-1.493-1.365-1.344-1.418-1.585-1.842-2.151-2.343-

29、2.175-1.762-1.409-1.132-0.872-0.689-0.563-0.482-0.435-0.415-0.415-0.43-0.454-0.479-0.5-0.512-0.515-0.515-0.532-0.62-0.964-2.29-4.892-5.087-3.75aas20.3670.50.5060.440.3560.2810.2240.1820.1540.1350.1220.1140.1090.1050.10.0950.0880.0770.0630.0440.019-0.01-0.046-0.087-0.136-0.192-0.256-0.327-0.403-0.478

30、-0.542-0.573-0.542-0.415-0.1830.111aas31.021.1091.0050.8070.60.4250.2870.1820.10.036-0.017-0.062-0.101-0.135-0.166-0.193-0.218-0.239-0.257-0.272-0.286-0.299-0.312-0.327-0.346-0.368-0.395-0.426-0.456-0.479-0.478-0.429-0.297-0.0490.3160.72aas52.3862.4641.9911.5731.3331.2731.3931.7372.4183.5894.8164.19

31、81.8840.1671.6391.0330.5740.2540.034-0.114-0.21-0.267-0.293-0.296-0.289-0.286-0.306-0.374-0.519-0.812-1.491-3.607-10.853-3.427-7.154-0.053aas60.3491.6171.8271.6861.5141.4461.5491.9042.6714.0935.815.5893.1631.1281.7221.2550.8690.5790.3590.1880.053-0.05-0.117-0.146-0.137-0.096-0.0410.001-0.021-0.219-0

32、.937-3.591-13.3-7.758-10.479-3.359xe178.818179.925179.397177.642174.992171.677167.862163.678159.245154.681150.103145.621141.343137.36133.75130.574127.871125.663123.955122.737121.992121.704121.861122.467123.543125.136127.319130.188133.853138.412143.915150.292157.279164.354170.77175.756yevexveyaexaey2

33、7.07211.761-39.671-65.17650.7621.0491.265-28.775-53.89670.23117.111-6.912-16.411-40.0268.52315.229-12.885-5.559-29.07454.70315.007-17.2672.525-21.62237.98715.947-20.567.817-16.36123.15117.601-23.03410.801-12.09311.6119.617-24.812.058-8.1583.29821.74-25.88612.111-4.295-2.27123.8-26.30111.395-0.475-5.

34、60925.693-26.05910.2583.224-7.14827.373-25.198.9836.676-7.24828.834-23.7517.7939.745-6.22430.108-21.8186.85912.31-4.37131.25-19.4896.29914.279-1.97632.333-16.8716.18415.6050.67533.436-14.0796.53316.2963.30234.639-11.2167.3216.4235.64536.013-8.3718.47416.1147.47837.612-5.6069.8915.5558.62239.472-2.94

35、311.43714.9678.95641.603-0.36912.96514.5888.40543.9882.17514.31714.6546.93146.5814.78415.32915.3744.50349.3097.58815.8316.9011.06952.06710.73515.63719.301-3.48354.71514.37214.53922.491-9.3457.07418.61312.28526.139-16.76858.91923.4828.57929.51-26.0359.96528.8213.0931.257-37.15359.87734.175-4.45929.25

36、-49.40558.28638.654-14.08820.76-60.39754.87240.91-25.1833.568-65.13349.50739.43-36.038-21.485-56.41742.47333.327-43.773-47.791-29.08534.5923.312-45.351-64.53912.208图像图像角位移角位移角速度角速度角加速度角加速度E E 点的位移、速度及加速度点的位移、速度及加速度六、六、体会及建议：体会及建议：经过近八周的作业研讨，我组基本掌握了平面六杆机构解析算法的基本原理以及其运动规律及特点。在作业进行过程中，我小组合理分工，加强了团队协作，在互助进步中理论知识逐步完善。本次的作业给了我们一次锻炼机会，从理论到程序实践，每一步都环环相扣，每一个结果都息息相关，最终在我们共同的努力下完成了本次作业。这次的大作业我们走了很多弯路，但总算是顺利的完成了。总之是要感谢的人很多，学习到的东西也很多，它让我们授意匪浅。