平面六杆机构的运动分析

1、平面六杆机构的运动分析（题号 3-c）指导老师 陈永琴班 级 041011学 号 04101042姓 名 师汉同组人 戴峰 杨彤 王建雄1、 题目说明下图为一平面六杆机构。一直各构件的尺寸如下表一，又知原动件1以角速度为1rad/s沿逆时针方向回转，要求个从动件的角位移、角速度、及角加速度以及e点的位移、速度及加速度变化情况。表一组号l1l2l2l3l4l5l6（xg）l4（yg） l73-c26.5105.665.049.087.548.439.0600153.541.7题目要求：三人一组计算出原动件从0到2变化时（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e点的轨迹曲线。2

2、、题目分析1） 建立封闭图形： l2- l3= l4 - l1 l2 + l2+ l5 -l6+ l7= l4- l12） 机构运动分析a角位移分析由图形封闭性得： b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：c角加速度分析：角速度矩阵对时间求一阶导数，可得加速度矩阵为：de点的运动状态位移：速度：加速度：创建fsolve函数入口文件function1.m3、 流程图 调用matlab系统函数fsolve求解各从动件的角位移分别存至th2,th3,th5,th6。绘制角位移随th1的变化曲线function2.m利用角速度矩阵w=ab，w2(m)=w(1),w3(m)=w(

3、2),w5(m)=w(3),w6(m)=w(4) 绘制角速度随th1的变化曲线function2.m利用角加速度矩阵求出从动件角加速度k=a(c-b) 绘制角速度随th1的变化曲线function4.m将以上各参数分别带入e点的位移、速度、加速度解析方程式，进行求解。绘制e点的位移、速度、加速度随th1变化的曲线function5.m,function6.m,function7.m结束4、 源程序a. 求从动件的角位移9*-第一个m文件（function1.m）function t=function1(th,th1,l1,l2,l20,l3,l4,l40,l5,l6,l7,a)t=l2*cos

4、(th(1)-l3*cos(th(2)+l1*cos(th1)-l4;l2*sin(th(1)-l3*sin(th(2)+l1*sin(th1);l2*cos(th(1)+l20*cos(a-th(1)+l5*cos(th(3)-l6*cos(th(4)+l1*cos(th1)-l40;l2*sin(th(1)-l20*sin(a-th(1)+l5*sin(th(3)-l6*sin(th(4)+l1*sin(th1)-l7;第二个脚本文件（function2.m）l1=26.5;l2=105.6;l20=65.0;l3=49.0;l4=87.5;l40=153.5;l5=48.4;l6=39.

5、0;l7=41.7;a=pi/3;th1=0:pi/18:2*pi;th2356=zeros(length(th1),4);options=optimset(display,off);for m=1:length(th1) th2356(m,:)=fsolve(function1,0.656 1.267 2.309 1.934,options,th1(m),l1,l2,l20,l3,l4,l40,l5,l6,l7,a);enddisp(th2356);th2=th2356(:,1);th3=th2356(:,2);th5=th2356(:,3);th6=th2356(:,4);hold onp

6、lot(th1,th2,r:,linewidth,2.5)plot(th1,th3,b,linewidth,2.5)plot(th1,th5,g-.,linewidth,2.5)plot(th1,th6,k-,linewidth,2.5)hold offgrid ontitle(从动件的角位移)xlabel(theta_1(rad)ylabel(theta_2theta_3theta_5theta_6,(rad)legend(theta_2,theta_3,theta_5,theta_6,location,northwest)axis(0,2*pi,-2,2*pi)b求从动件的角速度第三个脚本

7、文件（function3.m）w1=1;l1=26.5;l2=105.6;l20=65.0;l3=49.0;l4=87.5;l40=153.5;l5=48.4;l6=39.0;l7=41.7;a=pi/3;for m=1:37a=-l2*sin(th2(m),l3*sin(th3(m),0,0;. l2*cos(th2(m),-l3*cos(th3(m),0,0;. -l2*sin(th2(m)+l20*sin(a-th2(m),0,-l5*sin(th5(m),l6*sin(th6(m);. l2*cos(th2(m)+l20*cos(a-th2(m),0,l5*cos(th5(m),-l6

8、*cos(th6(m);b=l1*sin(th1(m),-l1*cos(th1(m),l1*sin(th1(m),-l1*cos(th1(m);w=a(w1*b);w2(m)=w(1);w3(m)=w(2);w5(m)=w(3);w6(m)=w(4);disp(w)endfor m=1:37 w(m,1)=w2(m); w(m,2)=w3(m); w(m,3)=w5(m); w(m,4)=w6(m);endhold onplot(th1,w2,r:,linewidth,2.5)plot(th1,w3,b,linewidth,2.5)plot(th1,w5,g-.,linewidth,2.5)p

9、lot(th1,w6,k-,linewidth,2.5)hold offgrid ontitle(从动件的角速度)xlabel(theta_1(rad)ylabel(omega_2omega_3omega_5omega_6(rad/s)legend(omega_2,omega_3,omega_5,omega_6,location,southwest)axis(0,2*pi,-2,5) c求从动件的角加速度第四个脚本文件（function4.m）w1=1;l1=26.5;l2=105.6;l20=65.0;l3=49.0;l4=87.5;l40=153.5;l5=48.4;l6=39.0;l7=

10、41.7;a=pi/3;for m=1:37 a=-l2*sin(th2(m),l3*sin(th3(m),0,0;. l2*cos(th2(m),-l3*cos(th3(m),0,0;. -l2*sin(th2(m)+l20*sin(a-th2(m),0,-l5*sin(th5(m),l6*sin(th6(m);. l2*cos(th2(m)+l20*cos(a-th2(m),0,l5*cos(th5(m),-l6*cos(th6(m); b1=-l2*cos(th2(m)*w2(m),l3*cos(th3(m)*w3(m),0,0;. -l2*sin(th2(m)*w2(m),l3*sin

11、(th3(m)*w3(m),0,0;. -l2*cos(th2(m)*w2(m)-l20*cos(a-th2(m)*w2(m),0,-l5*cos(th5(m)*w5(m),l6*cos(th6(m)*w6(m);. -l2*sin(th2(m)*w2(m)+l20*sin(a-th2(m)*w2(m),0,-l5*sin(th5(m)*w5(m),l6*sin(th6(m)*w6(m); b2=w2(m),w3(m),w5(m),w6(m); b3=l1*cos(th1(m)*w1;. l1*sin(th1(m)*w1;. l1*cos(th1(m)*w1;. l1*sin(th1(m)*w

12、1; k=a(b1*b2)+a(w1*b3); k2(m)=k(1); k3(m)=k(2); k5(m)=k(3); k6(m)=k(4);disp(k)endfor m=1:37 aa(m,1)=k2(m); aa(m,2)=k3(m); aa(m,3)=k5(m); aa(m,4)=k6(m);endhold onplot(th1,k2,r:,linewidth,2.5)plot(th1,k3,b,linewidth,2.5)plot(th1,k5,g-.,linewidth,2.5)plot(th1,k6,k-,linewidth,2.5)hold offgrid ontitle(从动

13、件的角加速度)xlabel(theta_1(rad)ylabel(alpha_2alpha_3alpha_5alpha_6(rad/s2)legend(alpha_2,alpha_3,alpha_5,alpha_6,location,northwest)axis(0,2*pi,-15,20)d求e点的轨迹第五个脚本文件(function5.m)l40=153.5;l7=41.7;l5=48.4;l6=39.0;for m=1:37 x(m)=l40+l6*cos(th6(m)-l5*cos(th5(m);y(m)=l7+l6*sin(th6(m)-l5*sin(th5(m);disp(x(m)

14、;disp(y(m);endplot(x,y,b,linewidth,2.5)axis(110,190,-30,40)title(e点的轨迹)xlabel(xe(mm)ylabel(ye(mm)grid one求e点的速度第六个脚本文件(function6.m)l5=48.4;l6=39.0;for m=1:37 a=-l6*sin(th6(m),l5*sin(th5(m);. l6*cos(th6(m),-l5*cos(th5(m); b=w6(m),w5(m); v=a*b; vx(m)=v(1);vy(m)=v(2);disp(vx(m);disp(vy(m);endv=(vx.2+vy

15、.2).(1/2);disp(v); hold onplot(th1,vx,r,linewidth,2.5)plot(th1,vy,b,linewidth,2.5)plot(th1,v,g,linewidth,2.5)hold offgrid ontitle(e点的速度)xlabel(theta_1(rad)ylabel(vex vey v (mm/s)legend(vex,vey,v,location,northwest)axis(0,2*pi,-70,75)f求e点的加速度第七个脚本文件(function7.m)l5=48.4;l6=39.0;for m=1:37 a1=-l6*sin(t

16、h6(m),l5*sin(th5(m);. l6*cos(th6(m),-l5*cos(th5(m); a2=k6(m),k5(m); b1=-l6*cos(th6(m),l5*cos(th5(m);. -l6*sin(th6(m),l5*sin(th5(m); b2=w6(m)2,w5(m)2; j=a1*a2+b1*b2; jx(m)=j(1);jy(m)=j(2);disp(jx(m);disp(jy(m);end j=(jx.2+jy.2).(1/2);disp(j); hold onplot(th1,jx,r,linewidth,2.5)plot(th1,jy,b,linewidth

17、,2.5)plot(th1,j,g,linewidth,2.5)hold offgrid ontitle(e点的加速度)xlabel(theta_1(rad)ylabel(a_ex a_ey a_e (mm/s2)legend(a_ex ,a_ey,a_e,location,southwest)axis(0,2*pi,-100,170) 5、 计算结果和曲线图：a.各从动件的角位移与1的关系曲线和计算数据：12356000.25350.57111.2563-0.4095100.1745330.19280.53151.2624-0.5317200.3490660.15900.55401.2268

18、-0.5623300.5235990.14350.61701.1609-0.5391400.6981320.13920.70311.0780-0.4976500.8726650.14170.80180.9851-0.4595601.0471980.14870.90710.8846-0.4371701.221730.15921.01560.7778-0.4376801.3962630.17231.12480.6660-0.4646901.5707960.18791.23300.5524-0.51781001.7453290.20591.33880.4416-0.59271101.9198620.

19、22621.44090.3393-0.68171202.0943950.24901.53830.2501-0.77521302.2689280.27441.62971.90592.94691402.4434610.30251.71411.83492.89631502.6179940.33361.79031.77682.85691602.7925270.36751.85741.73132.82291702.967060.40421.91441.69742.78881803.1415930.44361.96061.67312.75031903.3161260.48521.99541.65642.7

20、0382003.4906590.52842.01831.64462.64702103.6651910.57232.02911.63502.57832203.8397240.61602.02751.62482.49682304.0142570.65802.01331.61162.40232404.188790.69691.98621.59382.29492504.3633230.73101.94571.57102.17552604.5378560.75811.89101.54502.04682704.7123890.77601.82111.52241.91522804.8869220.78231

21、.73481.52241.80132905.0614550.77401.63041.61981.79583005.2359880.74831.50672.09502.26563105.4105210.70271.36282.71493.30363205.5850540.63571.19961.11710.58283305.7595870.54841.02191.14220.34073405.9341190.44650.84161.17570.07123506.1086520.34240.68111.2188-0.19433606.2831850.25350.57111.2563 -0.4095

22、 b.各从动件角速度与1的关系曲线和计算结果：123560-0. 4344-0.43440.1474-0.992410-0.2639-0.0297-0.0883-0.411020-0.13270.2665-0.30690.019130-0.05130.4400-0.43690.212540-0.00230.5366-0.50770.2433500.02900.5888-0.55540.1821600.05900.6152-0.59480.0677700.06800.6254-0.6283-0.0771800.08260.6242-0.6495-0.2318900.09620.6143-0.64

23、81-0.37321000.10960.5969-0.6157-0.47821100.12340.5727-0.5521-0.53161200.13790.5419-0.4678-0.53171300.15330.5047-0.4428-0.33251400.16940.4611-0.3701-0.25231500.18600.4115-0.2958-0.20511600.20260.3564-0.2260-0.19051700.21840.2964-0.1648-0.20431800.23250.2325-0.1151-0.24081900.24360.1656-0.0792-0.29392

24、000.25060.0968-0.0587-0.35832100.25200.0266-0.0543-0.24952200.2468-0.0449-0.0649-0.50412300.2335-0.1179-0.0876-0.57912400.2108-0.1932-0.1170-0.65112500.1773-0.2719-0.1432-0.71422600.1316-0.3557-0.1488-0.75532700.0719-0.4462-0.0950-0.7362280-0.0033-0.54490.1470-0.5051290-0.0948-0.65221.25940.8061300-

25、0.2023-0.76664.01924.4993310-0.3221-0.88192.53983.6258320-0.4446-0.98350.1479-1.2540330-0.5501-1.04140.1588-1.4916340-0.6055-1.00370.2257-1.5689350-0.5702-0.80440.2542-1.4272360-0.4344-0.43440.1474-0.2644c.各从动件角加速度与1的关系曲线和计算结果1235600.96992.4050-1.08353.20214100.90422.0767-1.43933.1194200.59561.3094-

26、0.99181.7454300.35610.7360-0.53730.5580400.21960.4026-0.3188-0.1367500.14700.2130-0.2422-0.5294600.10870.0984-0.2133-0.7617700.08890.0224-0.1655-0.8785800.0797-0.0335-0.0674-0.8716900.0767-0.07910.0918-0.72521000.0776-0.11950.2804-0.46201100.0809-0.15770.4378-0.14861200.0855-0.19490.51230.13841300.0

27、903-0.23160.39570.54741400.0942-0.26720.42850.36711500.0958-0.30070.41710.17441600.0937-0.33070.3783-0.00271700.0866-0.35590.3204-0.14991800.0733-0.37550.2473-0.26241900.0531-0.38940.1626-34152000.0255-0.39890.0713-0.3922210-0.0095-0.4060-0.0193-0.4206220-0.0519-0.4133-0.0995-0.4313230-0.1018-0.4237

28、-0.1562-0.4250240-0.1595-0.4399-0.1710-0.3946250-0.2255-0.4641-0.1136-0.3172260-0.3006-0.49770.0823-0.1225270-0.3849-0.54070.63150.4530280-0.4770-0.59022.60682.7801290-0.5718-0.638312.782015.7278300-0.6569-0.66725.534011.0206310-0.7073-0.6413-13.6792-11.4941320-0.6779-0.4949-0.3316-1.9177330-0.4991-

29、0.11920.3174-0.9030340-0.09350.62030.36690.08433500.51461.6871-0.14501.63973600.96992.4050-1.08533.2021d.e点运动分析结果：1xeyevexveyveaexaeyae00174.3046-19.8534-8.6248-37.710238.6839-35.1393147.0985151.2374100.174533172.4238-24.1896-12.1997-12.518217.4796-10.2559129.7075130.1123200.349066170.1713-24.6581-1

30、3.53865.623914.6602-7.374778.056578.4041300.523599167.6807-22.7124-15.096515.518521.6501-10.526638.377239.7947400.698132164.8738-19.5563-17.119219.962926.2980-12.267114.709519.1533500.872665161.6988-15.9271-19.962921.226628.6555-11.83150.989911.8728601.047198158.1675-12.2539-21.156620.631429.5509-9.

31、7997-7.107312.1057701.22173154.3402-8.7887-220611418.940329.4959-6.7383-11.824213.6094801.396263150.3092-5.6779-23.473216.635128.7701-3.0636-14.270514.5957901.570796146.1857-2.9976-23.663514.057327.52400.9102-15.017315.04481001.745329142.0899-0.7713-23.153111.472725.83974.9251-14.392315.21171101.919

32、862138.14381.0195-21.95519.099923.76628.7551-12.625815.36431202.094395134.46332.4281-20.11977.119821.342312.1961-9.925815.72471302.268928131.15293.5361-17.73105.676218.617415.0678-6.520116.41801402.443461128.29974.4466-14.90194.869415.677317.2225-2.677517.42941502.617994125.96905.2758-11.76684.74881

33、2.688918.56151.286918.60601602.792527124.20166.1437-8.47205.30559.996219.05565.025219.70701702.96706123.01267.1632-5.16116.46928.275818.76288.186420.47101803.141593122.39638.4299-1.95968.11128.344617.836510.458920.67681903.316126122.316910.01221.041910.054610.108516.515711.609920.18812003.490659122.

34、743011.94503.799812.090612.673715.098211.506118.98272103.665191123.629614.22506.324913.995615.358413.899610.107117.18582203.839724124.940916.80968.681515.544319.804313.21167.430015.15752304.014257126.656619.617410.979916.516219.832813.26373.497313.71702404.18879128.778522.528513.362516.690721.380714.1899-1.718114.29352504.