機械原理大作業(yè)(一)--連桿(2題)

1、機械原理大作業(yè)（三）作業(yè)名稱： 連桿機構(gòu)運動分析 設(shè)計題目： （32）題 院 系： 機電工程學(xué)院 班 級： 設(shè) 計 者： 學(xué) 號： 哈爾濱工業(yè)大學(xué)一、運動分析題目如圖所示機構(gòu)，已知機構(gòu)各構(gòu)件的尺寸為AB=100mm,BC=1.25AB,CD=1.13AB,CE=0.85AB,BE=0.65AB,EF=0.81AB, FG=1.56AB,AD=0.58AB,AG=1.85AB,DG=1.6AB,構(gòu)件1的角速度為W1=10rad/s，試求構(gòu)件2上點E的軌跡及構(gòu)件5的角位移，角速度，角加速度，并對計算結(jié)果進(jìn)行分析。機構(gòu)結(jié)構(gòu)分析：二、機構(gòu)的結(jié)構(gòu)分析及基本桿組劃分機構(gòu)各構(gòu)件都在同一平面內(nèi)運動，活動構(gòu)件數(shù)

2、 n=5，=7，=0則機構(gòu)的自由度為:F=3×n-2×-1×=3×5-2×7-0=12.基本桿組劃分（1）去除虛約束和局部自由度本機構(gòu)中無虛約束或局部自由度。（2）拆桿組。從遠(yuǎn)離原動件（即桿1）進(jìn)行拆分，就可以得到由桿 4,5 組成的 RRR級桿組GFE, 2,3 組成的 RRR級桿組CDB，最后剩下級機構(gòu)桿1。（3）確定機構(gòu)的級別由（2）知，機構(gòu)為級機構(gòu)三、各基本桿組的運動分析數(shù)學(xué)模型1）級桿組AB（原動件）在級桿組AB中，即已知構(gòu)件上A點的運動參數(shù)，求同一構(gòu)件上B點（回轉(zhuǎn)副）的運動參數(shù)。調(diào)用級機構(gòu)子程序即可求解位置分析 由圖可得B點的矢量方

3、程x,y軸上的投影坐標(biāo)方程為 （1）速度和加速度分析 將式（1）對時間t求導(dǎo)即可得出速度方程： （2） （3）其中因為設(shè)B為原點：=0；=0 ；=0 ；=0 ；=0 ；=0 由上（1）（2）（3）方程可求出F點的位移，速度，加速度2）RRR級桿組DEF分析，求出F點的角位移，角速度，角加速度上面1）中已求得F點的位移，速度，加速度。由點D為固定點，有D點的位移，速度，加速度均為0。 位置方程 內(nèi)運動副E的矢量方程 （4）其在x,y軸上的投影，可得內(nèi)運動副E的位置方程 （5）將（5）式移項后分別平方相加消去得 （5）式中由于F-E-D為逆時針解出 =代入（5）可求得，。=角速度方程, (6) 其

4、中 兩桿的角加速度， (8)式中： 3）H點是DEF桿（同一構(gòu)件）上的點，求其位移，速度，加速度在已知B點的運動參數(shù)的情況下，可求出H點的運動參數(shù)。位置分析 由圖可得H點的矢量方程x,y軸上的投影坐標(biāo)方程為 （10）速度和加速度分析 將式（1）對時間t求導(dǎo)即可得出速度方程： (11） （12）其中4）RRR級桿組GCH分析，求GC桿的角位移，角速度，角加速度求法與RRR級桿組DEF相同。y四、建立坐標(biāo)系x五、計算編程（1）主程序：%主程序w = 10;t =0:0.01:6*pi/10;L = length(t)xf,yf,vxf,vyf,axf,ayf = Igan(w,t);%求F點的位移

5、，速度，加速度for o=1:L %求DEF桿組的F點的角位移，角速度，角加速度 ff1,wf1,aaf1,fd1=IIganDEF2(xf(o),yf(o),vxf(o),vyf(o),axf(o),ayf(o); ff(o)=ff1;wf(o)=wf1;aaf(o)=aaf1;fd(o)=fd1;endxh,yh,vxh,vyh,axh,ayh=IIganH(xf,yf,vxf,vyf,axf,ayf,ff,wf,aaf);for o=1:L %求GCH桿組的構(gòu)件5的角位移，角速度，角加速度 fcg1,wcg1,aacg1=IIganGCH(xh(o),yh(o),vxh(o),vyh(o

6、),axh(o),ayh(o); fcg(o) = fcg1;wcg(o) = wcg1;aacg(o) = aacg1;endfigure(1)%畫圖subplot(3,1,1);plot(t,fcg),grid onxlabel('時間');ylabel('角位移');subplot(3,1,2);plot(t,wcg),grid onxlabel('時間');ylabel('角速度');subplot(3,1,3);plot(t,aacg),grid onxlabel('時間');ylabel('角加

7、速度');figure(2)plot(xh,yh)（2）求點B位移，速度，加速度的函數(shù)%一級桿組 I gan 輸出點B的位移，速度，加速度function xf,yf,vxf,vyf,axf,ayf = Igan(w,t)%xf:x方向位移；yf:y方向位移；%vxf:x方向速度；vyf:y方向速度；%axf:x方向加速度；ayf:y方向加速度；%w:原動件轉(zhuǎn)動角速度；xf = 200.*cos(w.*t);yf = 200.*sin(w.*t);vxf = -w.*200.*sin(w.*t);vyf = w.*200.*cos(w.*t);axf = -w.2.*200.*cos(

8、w.*t);ayf = -w.2.*200.*sin(w.*t);end（3）DCB桿組分析函數(shù)：求點B角位移，角速度，角加速度%2級桿組DCB 輸出點B的角位置，角速度，角加速度function ff,wf,aaf,fd=IIganDEF2(xf,yf,vxf,vyf,axf,ayf)%ff:CB在點B的轉(zhuǎn)角；wB：轉(zhuǎn)角的導(dǎo)數(shù)，即角速度；aaB:角加速度xD= 0;yD = -0.58*200;a = 2*1.25*200*(xD-xB);b = 2*1.25*200*(yD-yB);c = (1.25*200)2+(xD-xB)2+(yD-yB)2-(1.13*200)2;z1 = a2+

9、b2-c2;zz = a+c;z2 = (b-(z1)0.5)/(a+c);ff = 2*atan(b-(z1)0.5)/(a+c);if ff<0 ff = ff+2*pi;endxe = xf+1.25*200*cos(ff);ye = yf+1.25*200*sin(ff);fd = atan(ye-yd)/(xe-xd);if xe<0&&ye>yd fd = fd+pi;elseif xe<0&&ye<yd fd = fd+pi;elseif xe>0&&ye<yd fd = fd+2*pi;e

10、lse fd = fd;endcd = 1.13*200*cos(fd);sd = 1.13*200*sin(fd);cf = 1.25*200*cos(ff);sf = 1.25*200*sin(ff);g1 = cf*sd-cd*sf;wf = (cd*(-vxf)+sd*(-vyf)/g1;wd = (cf*(-vxf)+sf*(-vyf)/g1;g2 = -axf+(wf2)*cf-(wd2)*cd;g3 = -ayf+(wf2)*sf-(wd2)*sd;aaf = (g2*cd+g3*sd)/g1;（4）求E點的位移，速度，加速度的函數(shù)%2級桿組DCB 輸出點E的位置，速度，加速度f

11、unction xh,yh,vxh,vyh,axh,ayh=IIganH(xf,yf,vxf,vyf,axf,ayf,ff,wf,aaf)%xh:x方向位移；yh:y方向位移；%vxh:x方向速度；vyh:y方向速度；,%axh:x方向加速度；ayh:y方向加速度；f = acos(1.252+0.652-0.852)/(2*1.25*0.65);xh = xf+0.65.*200.*cos(f+ff);yh = yf+0.65.*200.*sin(f+ff);vxh = vxf-wf.*0.65.*200.*sin(f+ff);vyh = vyf+wf.*0.65.*200.*cos(f+f

12、f);axh = axf-(wf.2).*0.65.*200.*cos(f+ff)-aaf.*0.65.*200.*sin(f+ff);ayh = ayf-(wf.2).*0.65.*200.*sin(f+ff)+aaf.*0.65.*200.*cos(f+ff);end（5）GFE桿組分析函數(shù)：求F點的角位移，角速度，角加速度%二級桿組GFE 求GF桿角位移，角速度，角加速度function fcg,wcg,aacg,fch=IIganGCH(xh,yh,vxh,vyh,axh,ayh)%fcg:c點的角位移；wcg：c點的角速度；aaf:c點的角加速度fb = acos(1.852+0.5

13、82-1.62)/(2*1.85*0.58);xg = -1.85*200*sin(fb);yg = -1.85*200*cos(fb);a = 2*0.81*200*(xg-xh);b = 2*0.81*200*(yg-yh);c = (0.81*200)2+(xg-xh)2+(yg-yh)2-(1.56*200)2;zzz = (b+(a2+b2-c2)0.5)/(a+c);fch = 2*atan(b+(a2+b2-c2)0.5)/(a+c);if fch<0 fch = fch+2*pi;endxc = xh+0.81*200*cos(fch);yc = yh+0.81*200*

14、sin(fch);fcg = atan(yc-yg)/(xc-xg);cg = 1.56*200*cos(fcg);sg = 1.56*200*sin(fcg);ch = 0.81*200*cos(fch);sh = 0.81*200*sin(fch);g1 = ch*sg-cg*sh;wch = (cg*(-vxh)+sg*(-vyh)/g1;wcg = (ch*(-vxh)+sh*(-vyh)/g1;g2 = -axh+(wch2)*ch-(wcg2)*cg;g3 = -ayh+(wch2)*sh-(wcg2)*sg;aacg = (g2*ch+g3*sh)/g1;end六、計算結(jié)果構(gòu)件5

15、的角位移，角速度，角加速度H點的軌跡圖計算結(jié)果構(gòu)件5角位移(rad)角速度(r/s)角加速度(r/s2)10.0985364623.19783750313.5404248520.1310746283.2978552716.37607889230.1642460813.323635938-1.30222337940.1972837073.270379137-9.40384584850.2293795973.135033835-17.6540793960.2597131692.91854773-25.5205737770.2875042762.628463594-32.2322662880.312

16、088762.280528204-36.9654645190.3329980251.89765293-39.16839751100.3500118521.505688408-38.83237698110.3631592251.127702703-36.49691726120.3726666620.779654872-32.98831402130.3788783210.469171714-29.10110749140.3821781260.196949608-25.41023432150.382932466-0.040799078-22.24292117160.381456937-0.25013

17、3688-19.73954683170.378001635-0.437915336-17.93233785180.372747408-0.611056302-16.80776689190.365806883-0.776280383-16.34674367200.357226177-0.940195635-16.54813923210.346984897-1.10954939-17.44279857220.334992976-1.291599028-19.10336273230.321083336-1.494572912-21.65273825240.304999539-1.728210811-

18、25.27124837250.286377732-2.004354144-30.19822393260.264722847-2.337477278-36.71547854270.239380922-2.744851375-45.08343686280.209514438-3.245602845-55.37086465290.174098512-3.857144647-67.0809784300.131976187-4.586423475-78.48005879310.082039233-5.413247506-85.74196597320.023613798-6.266921877-82.67

19、03728233-0.042934901-7.009372863-62.5505328534-0.115571016-7.451382867-22.7659150535-0.190363115-7.41685402531.1290260136-0.262025098-6.82187831287.1233172337-0.325056788-5.706838429133.598624738-0.374859563-4.201932414164.676040139-0.408323904-2.464824289180.398543440-0.42385133-0.635155735183.7521

20、00341-0.4210822121.178617948177.546140242-0.4006322732.886051523162.306931243-0.3640495974.385375615135.135650444-0.3141028585.52897156490.0345656545-0.2553469166.10901973422.2136747546-0.1945084165.919087475-61.047941147-0.1396748184.928398754-131.993310848-0.0976650573.42748275-159.597753449-0.071

21、2171381.894005413-140.888948850-0.0586602560.689076628-98.2431549451-0.055914543-0.064856044-53.3564547452-0.058574244-0.405518759-16.4444418853-0.062964178-0.42790122110.3175965654-0.066398248-0.2294902328.0038635255-0.0670917720.10823292138.5031825656-0.0639794670.52275927843.647414657-0.056534176

22、0.96845925144.9632964158-0.0446144861.41323531443.6315065359-0.0283464151.83516659240.5138981660-0.0080368072.21956021936.20321949610.0158863962.55653101231.07707651620.0429123332.83910570525.34811992630.072468863.06180029919.10859673640.1039321213.21962518712.37219937650.1366282943.3075225595.12009

23、5121660.1698322033.320323629-2.639556408670.2027688013.253400545-10.79174801680.2346254573.104197164-19.02218785690.2645839552.874594517-26.75320071700.2918779352.573455309-333158708712.217894775-37.52071845720.3361334371.831687915-39.28069983730.3524888471.440615279-38.55871507740.3650

24、040751.066776704-35.96549575750.3739312960.724727996-32.34227282760.3796263850.420783332-28.45496966770.3824736420.154708624-24.83533184780.382832643-0.07780271-21.77372294790.381008608-0.283026004-19.38705081800.377240056-0.467866713-17.69611463810.371696235-0.639211531-16.68418818820.364478491-0.8

25、03753513-16.33389821830.355621828-0.968102601-16.64867941840.345094463-1.139063335-17.66577624850.332794019-1.324021829-19.46570847860.318539403-1.531420835-22302057541-1.771311801-26.00087305880.282964327-2.055946292-31260739954-2.400275169-37.98746125900.234701058-2.82199

26、4579-46.68266765910.203977892-3.340296223-57.26763383920.167517062-3.971632345-69.09312002930.124152519-4.719791527-80.1321699940.072815587-5.557800627-86.1434937950.012960194-6.404286812-80.6321500296-0.054806917-7.110128998-57.1967504797-0.128128582-7.48269576-14.4135736298-0.202785786-7.356418274

27、40.759614599-0.273368565-6.66800382895.84948082100-0.334460745-5.476783215139.9614602101-0.381690412-3.921901756168.33102-0.412212737-2.160318685181.7346159103-0.42465973-0.326504119183.3258891104-0.4188502751.475595656175.6481821105-0.3955516743.155986042158.7060902106-0.3564875184.607511131128.992

28、9174107-0.3046833155.67222790380.24731696108-0.2450496566.135149278.790621108109-0.1846484995.80478722-74.8342556110-0.1315784934.699359303-140.2081974111-0.0921274653.15922524-159.2548319112-0.068228741.66224436-134.6756867113-0.0576367970.530450915-90.43268482114-0.056095747-0.148742988-46.4640933

29、115-0.059276872-0.42875497-11.24230861116-0.063667388-0.40752388813.87765943117-0.066743473-021911167118-0.066854771069680202119-0.0630385340.59654617644.1000013120-0.0548422011.04401823944.89732378121-0.0421766851.48625523643.212981122-0.025203671.90274407239.85983027123-0

30、.0042538862.27975480235.390711441240.0202286232.6080108430.152142461250.0477215592.88087678724.333546311260.0776436813.09301001418.011025381270.1093627563.23943624611.189338091280.1421964323.3150656583.8495221231290.1754108593.314752789-3.988450371300.2082233833.234085551-12.182497881310.2398175383.

31、071070981-20.37673891320.2693791092.828598888-27.949201761330.2961577772.516892039-34.081247531340.3195469152.154389914-38.0018021350.3391578071.765594403-39.321556921360.3548568361.376047771-38.231618871370.3667472451.006769144-35.405179181380.375104490.670893648-31.689351061390.3802939950.37347483

32、1-27.816973771400.3826989360.113420844-24.276604581410.382671253-0.114033588-21.323820621420.380505461-0.315342219-19.054304581430.376428441-0.497437041-17.479086131440.370597886-0.667174659-16.579266091450.363103913-0.831220774-16.33977821460.353970403-0.996195194-16.768977131470.343154077-1.168970

33、649-17.910768871480.330540019-1.357075432-19.853788241490.31593275-1.569182361-22.739585371500.29904202-1.815671547-26.768676411510.279462769-2.109219565-32.198048151520.256649645-2.465256881-39.313150081530.229889194-2.90187306-48.336729291540.198279421-3.438211785-59.202559391550.160740266-4.089491084-71.088284041560.116102322-4.855826729-81.64806021570.063348462-5.702760652-86.22005971580.002078737-6.537792154-78.07542829159-0.066840513-7.201403192-51.2743855516