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。组号L1L2L2L3L4L5L6a(Xg)L4，(%)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口变化时（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、题目分析1） 建

2、立封闭图形：L2- L3= L4 - L1L2 + L2 + L5-L6+ L7= L4'- Li2）机构运动分析A.角位移分析由图形封闭性得：L2 cosi2 - L3 cos% = L4 - L1cos%L2 sinh2 - L3 sin 93 = -L1 sin91L2cos%L2' cos2- a - 12 1L5 cos15 - L6 cos'= L4'- L1cos155。L2sin %L2' sin 2。一（a - ?2 >L5 sin 5 - L6 sin % -L7 = _ L1sin B.角速度分析上式对时间求一阶导数，可得速度

3、方程：-L2 sin02 2 + L3 sin日3 & 3 = L1 sin3 &1L2 8巩02'8科33=比，。风必-L2 sin%2 L2 sin（a -12） 2 - L5 sin为 5 L6 sin% 6 = L1sin11'L2cos122 L2 cos（12- ：）2L5cos155 -L6cos166 =-L1cos1化为矩阵形式为：- L2 sin 12L3 sin .002L2 cos2- L3cos飞 003- L2 sin %L2' sin a - -20- L5 sin-5 L6 sin -65jL2 cos92 + L2 co

4、s（a -92）0L5 cos95- L6 cos06 产 6_L1 sin 5- L1 cos%1L1 sin 即ILi cos 31C角加谏度分析:13一L2 sin 62L3 sin 6300 FlL2 cos仇-L3 cos030083-L2 sin % + L2' sin (a -4)0-L5 sin/L6 sin06号5,2 cos% +L2' cos (a 一为)0L5 cos85- L6cos 8 6196-L2 cos82L3 cos63001£一L2 sin%L3 sin%0026 3-L2 cos% -L2' cos (a -92 )0-

5、L5 cos 年L6cos9628 5-L2 sin % + L2' sin (a -% )0-L5 sin 65L6sin，:2&6 1角速度矩阵对时间求一阶导数，可得加速度矩阵为:21D. E点的运动状态L1 cosL1 sindL1 cosdLi sin 0Xe= Xg-6cos% -L5cos%位移： yE= yG L6sin6 -L5sin%速度:Vex = -L6 sin%6 L5 sin'5VEy = L6 cos1 66 - L5 cos%5加速度:22八aEx = -6 cos86 "06 - Le sin% 2aEy = -L6 sin 与

6、 6 L6 cos/26L5cos" 55 L5sin "5526L5sin%5 - L5cos"55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.m3、流程图创建fsolve函数入口 文件 functionl.m利用角速度矩阵W=A旧, w2(m)=W(1),w3(m)=W(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funct

7、ion4.m 将以上各参数分L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,funct ion7.m4、源程序(吉束二a.求从动件的角位移9*-第一个 M文件(functionl.m )function t=function1(th,th1,l1,l2,l20,l3,l4,l40,l5,l6,l7,a)t=l2*cos(th(1)-l3*cos(th(2)+l1*cos(th1)-l4;I2*sin(th(1)-I3*sin(th(2)+I1*sin(th1);I2*cos(th(1)

8、+l20*cos(a-th(1)+l5*cos(th(3)-l6*cos(th(4)+l1*cos(th1)-l40;I2*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=39.0;l7=41.7;a=pi/3;th1=0:pi/18:2*pi;th2356=zeros(length(th1),4);options=optimset( '

9、;display' , 'off' );for m=1:length(th1)th2356(m,:尸fsolve('function1' ,0.656 1.267 2.3091.934,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 onplot(th1,th2, 'r:','LineWidth' ,2.5)

10、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)'),'NorthWest' )lege

11、nd( 'theta_2', 'theta_3', 'theta_5', 'theta_6', 'Location'axis(0,2*pi,-2,2*pi)b.求从动件的角速度第三个脚本文件(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=1:37 A=H2*sin(th2(m),l3*sin(th3(m),0,0;.l2*cos(th2(m),-l

12、3*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); 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； disp(W) end for m=1:37W(m,1)=w2(m)

13、;W(m,2)=w3(m);W(m,3)=w5(m);W(m,4)=w6(m); end hold on plot(th1,w2, 'r:', 'LineWidth' ,2.5)plot(th1,w3, 'b' , 'LineWidth' ,2.5) plot(th1,w5,'g-.', 'LineWidth',2.5)plot(th1,w6,'k-', 'LineWidth',2.5)hold off grid on title('从动件的角速度) xlab

14、el( 'theta_1(rad)')ylabel( 'omega_2omega_3omega_5omega_6(rad/s)'),'SouthWest' )legend( 'omega_2', 'omega_3', 'omega_5', 'omega_6', 'Location'axis(0,2*pi,-2,5) 一一一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;l

15、4=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*cos(th6(m); B1=-H2*cos(th2(m)*w2(m),l3*cos(th3(m)*w3(m),

16、0,0;.-l2*sin(th2(m)*w2(m),l3*sin(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;.I1*sin(th1(m)*w1;.I1*co

17、s(th1(m)*w1;.I1*sin(th1(m)*w1;K=A(B1*B2)+A(w1*B3);k2(m尸K(1); k3(m)=K(2); k5(m)=K(3); k6(m)=K(4); disp(K) end for m=1:37 AA(m,1)=k2(m); AA(m,2)=k3(m); AA(m,3)=k5(m); AA(m,4)=k6(m); end hold on plot(th1,k2, 'r:', 'LineWidth' ,2.5)plot(th1,k3, 'b' , 'LineWidth' ,2.5) plo

18、t(th1,k5,'g-.', 'LineWidth',2.5)plot(th1,k6,'k-', 'LineWidth',2.5)hold off grid on title('从动件的角加速度') xlabel( 'theta_1(rad)'),'Location' , 'NorthWest'ylabel('alpha12alpha_3alpha_5alpha_6(rad/sA2)legend( 'alpha_2', 'alpha_

19、3', 'alpha_5', 'alpha_6'axis(0,2*pi,-15,20)d.求E点的轨迹第五个脚本文件(function5.m) I40=153.5;I7=41.7;I5=48.4;I6=39.0; for m=1:37X(m)=l40+l6*cos(th6(m)-l5*cos(th5(m);Y(m)=l7+l6*sin(th6(m)-l5*sin(th5(m); disp(X(m);disp(丫(m); end plot(X,Y, 'b' , 'LineWidth' ,2.5) axis(110,190,-

20、30,40) title( 'E点的轨迹) xlabel( 'Xe(mm)') ylabel( 'Ye(mm)') grid on e.求E点的速度 第六个脚本文件(function6.m) l5=48.4;l6=39.0; for m=1:37A=-l6*sin(th6(m),l5*sin(th5(m);.I6*cos(th6(m),-I5*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); end V=(vx.A2+vy.A2).A(1/2);

21、disp(V); hold on plot(th1,vx,'r', 'LineWidth',2.5)plot(th1,vy,'b' , 'LineWidth',2.5)plot(th1,V, 'g' , 'LineWidth' ,2.5) hold off grid on title( 'E点的速度) xlabel( 'theta_1(rad)')ylabel( 'Vex Vey V (mm/s)')legend( 'Vex' , 'V

22、ey' , '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) I5=48.4;I6=39.0; for m=1:37A1=-l6*sin(th6(m),l5*sin(th5(m);.I6*cos(th6(m),-I5*cos(th5(m);A2=k6(m),k5(m)'B1=-l6*cos(th6(m),l5*cos(th5(m);.-I6*sin(th6(m),l5*sin(th5(m);B2=w6(m)A2,w5(

23、m)A2'J=A1*A2+B1*B2;jx(m)=J(1);jy(m)=J(2);disp(jx(m);disp(jy(m); end J=(jx.A2+jy.A2).A(1/2)'disp(J)； hold on plot(th1,jx,'r', 'LineWidth',2.5)plot(th1,jy,'b' , 'LineWidth',2.5)plot(th1,J, 'g' , 'LineWidth' ,2.5) hold off grid on title('E点的加速

24、度)xlabel( 'theta_1(rad)')ylabel('a_ex7 a_ey a_e (mm/sA2)')legend( 'a_ex ', 'a_ey', 'a_e', 'Location' , 'SouthWest' )axis(0,2*pi,-1O0,170)一一5、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：9 19 29 39 59 1000.25350.57111.2563-0.4095100.1745330.19280.53151.2624

25、-0.5317200.3490660.15900.55401.2268-0.56230.5235990.14350.61701.1609-0.53910.6981320.13920.70311.0780-0.49760.8726650.14170.80180.9851-0.45951.0471980.14870.90710.8846-0.43711.221730.15921.01560.7778-0.43761.3962630.17231.12480.6660-0.46461.5707960.18791.23300.5524-0.51781.7453290.20591.33880.4416-0

26、.59271.9198620.22621.44090.3393-0.68172.0943950.24901.53830.2501-0.77522.2689280.27441.62971.90592.94692.4434610.30251.71411.83492.89632.6179940.33361.79031.77682.85692.7925270.36751.85741.73132.82292.967060.40421.91441.69742.78883.1415930.44361.96061.67312.75033.3161260.48521.99541.65642.70383.4906

27、590.52842.01831.64462.64703.6651910.57232.02911.63502.57833.8397240.61602.02751.62482.49684.0142570.65802.01331.61162.40234.188790.69691.98621.59382.29494.3633230.73101.94571.57102.17554.5378560.75811.89101.54502.04684.7123890.77601.82111.52241.91524.8869220.78231.73481.52241.80135.0614550.77401.630

28、41.61981.79585.2359880.74831.50672.09502.26565.4105210.70271.36282.71493.30365.5850540.63571.19961.11710.58285.7595870.54841.02191.14220.34075.9341190.44650.84161.17570.07126.1086520.34240.68111.2188-0.19436.2831850.25350.57111.2563-0.40953040506070809010011012013014015016017018019020021022023024025

29、0260270280290300310320330340350360从动件用由位移O 3 2 1 fl>Q>步b.各从动件角速度与。1的关系曲线和计算结果:9 123560-0. 4344-0.43440.1474-0.992410-0.2639-0.0297-0.0883-0.411020-0.13270.2665-0.30690.019130-0.05130.4400-0.43690.212540-0.00230.5366-0.50770.2433500.02900.5888-0.55540.1821600.05900.6152-0.59480.0677700.06800.62

30、54-0.6283-0.0771800.08260.6242-0.6495-0.2318900.09620.6143-0.6481-0.37321000.10960.5969-0.6157-0.47821100.12340.5727-0.5521-0.53161200.13790.5419-0.4678-0.53171300.15330.5047-0.4428-0.33251400.16940.4611-0.3701-0.25231500.18600.4115-0.2958-0.20511600.20260.3564-0.2260-0.19051700.21840.2964-0.1648-0.

31、20431800.23250.2325-0.1151-0.24081900.24360.1656-0.0792-0.29392000.25060.0968-0.0587-0.35832100.25200.0266-0.0543-0.24952200.2468-0.0449-0.0649-0.50412300.2335-0.1179-0.0876-0.57912400.2108-0.1932-0.1170-0.65112500.1773-0.2719-0.1432-0.71422600.1316-0.3557-0.1488-0.75532700.0719-0.4462-0.0950-0.7362

32、280-0.0033-0.54490.1470-0.5051290-0.0948-0.65221.25940.8061300-0.2023-0.76664.01924.4993310-0.3221-0.88192.53983.6258320-0.4446-0.98350.1479-1.2540330-0.5501-1.04140.1588-1.4916340-0.6055-1.00370.2257-1.5689350-0.5702-0.80440.2542-1.4272360-0.4344-0.43440.1474-0.2644从罚件的前速度5«!« 0Ma c.各从动件角

33、加速度与。1的关系曲线和计算结果9 1a 2a 3a 5a 600.96992.4050-1.08353.20214100.90422.0767-1.43933.1194200.59561.3094-0.99181.7454300.35610.7360-0.53730.5580400.21960.4026-0.3188-0.1367500.14700.2130-0.2422-0.5294600.10870.0984-0.2133-0.7617700.08890.0224-0.1655-0.8785800.0797-0.0335-0.0674-0.8716900.0767-0.07910.091

34、8-0.72521000.0776-0.11950.2804-0.46201100.0809-0.15770.4378-0.14861200.0855-0.19490.51230.13841300.0903-0.23160.39570.54741400.0942-0.26720.42850.36711500.0958-0.30070.41710.17441600.0937-0.33070.3783-0.00271700.0866-0.35590.3204-0.14991800.0733-0.37550.2473-0.26241900.0531-0.38940.1626-34152000.025

35、5-0.39890.0713-0.3922210-0.0095-0.4060-0.0193-0.4206220-0.0519-0.4133-0.0995-0.4313230-0.1018-0.4237-0.1562-0.4250240-0.1595-0.4399-0.1710-0.3946250-0.2255-0.4641-0.1136-0.3172260-0.3006-0.49770.0823-0.1225270-0.3849-0.54070.63150.4530280-0.4770-0.59022.60682.7801290-0.5718-0.638312.782015.7278300-0

36、.6569-0.66725.534011.0206310-0.7073-0.6413-13.6792-11.4941320-0.6779-0.4949-0.3316-1.9177330-0.4991-0.11920.3174-0.9030340-0.09350.62030.36690.08433500.51461.6871-0.14501.63973600.96992.4050-1.08533.2021从动件的角加速度ZU14105 6 o-5W"j|£%-ii 一-一%1-一J!： a 1巴:iJr 3 ! 'j一 RJ.1 1jt4油 *i； ;p 1 W H

37、l» *-. .， " " B L . ，J JIl iI3I iiv<：J节¥-IIE> Q卜12三wBrad)56d. E点运动分析结果:9 1XeYeVexVeyVeaexaeyae00174.3046-19.8534-8.6248-37.710238.6839-35.1393147.0985151.2374100.174533172.4238-24.1896-12.1997-12.518217.4796-10.2559129.7075130.1123200.349066170.1713-24.6581-13.53865.623914.

38、6602-7.374778.056578.4041300.523599167.6807-22.7124-15.096515.518521.6501-10.526638.377239.7947400.698132164.8738-19.5563-17.119219.962926.2980-12.267114.709519.1533500.872665161.6988-15.9271-19.962921.226628.6555-11.83150.989911.8728601.047198158.1675-12.2539-21.156620.631429.5509-9.7997-7.107312.1

39、057701.22173154.3402-8.7887-220611418.940329.4959-6.7383-11.824213.6094801.396263150.3092-5.6779-23.473216.635128.7701-3.0636-14.270514.5957901.570796146.1857-2.9976-23.663514.057327.52400.9102-15.017315.04481001.745329142.0899-0.7713-23.153111.472725.83974.9251-14.392315.21171101.919862138.14381.01

40、95-21.95519.099923.76628.7551-12.625815.36431202.094395134.46332.4281-20.11977.119821.342312.1961-9.925815.72471302.268928131.15293.5361-17.73105.676218.617415.0678-6.520116.41801402.443461128.29974.4466-14.90194.869415.677317.2225-2.677517.42941502.617994125.96905.2758-11.76684.748812.688918.56151.

41、286918.60601602.792527124.20166.1437-8.47205.30559.996219.05565.025219.70701702.96706123.01267.1632-5.16116.46928.275818.76288.186420.47101803.141593122.39638.4299-1.95968.11128.344617.836510.458920.67681903.316126122.316910.01221.041910.054610.108516.515711.609920.18812003.490659122.743011.94503.799812.090612.673715.098211.506118.98272103.665191123.629614.22506.324913.995615.358413.8996