哈工大机械原理大作业一连杆23题

机械原理大作业（一）作业名称： 连杆机构运动分析 设计题目： 23题 院 系： 能源学院 班 级： 1102102 设 计 者： 韩青松 学 号： 1110200218 指导教师： 唐德威 设计时间： 2013年6月 运动分析题目：如图所示机构，已知机构各构件的尺寸为AB=180mm，=130，BC=290mm，CD=300mm，e=65mm，AD=150mm，DE=180mm，EF=500mm，构件1的角速度为1=10rad/s,试求构件5上点F的位移、速度和加速度，并对计算结果进行分析。1. 建立以点A为原点的固定平面直角坐标系A-x,y,如图所示。 2. 对机构进行结构分析该机构由原动件AB（级组），BCDE（RRR级杆组）和EF（RRP级杆组）组成。3. 本杆组的运动分析数学模型（1） 原动件AB（级组）已知原动件AB的转角1=02 原动件AB的角速度 1=10rad/s原动件AB的角加速度 1=0运动副A的位置坐标 xA=0 yA=0 A点与机架相连，即该点速度和加速度均为0。运动副A的速度 vxA=0 vyA=0运动副A的加速度 axA=0 ayA=0原动件AB长度 lAB=180mm可求出运动副B的位置坐标 xB=xA+lABcos1 yB=xA+lABsin1运动副B的速度 vxB= vxA -1 lAB sin1 vyB= vyA+1 lAB cos1运动副B的加速度 axB= axA-12 lAB cos1-1lAB sin1 ayB=ayA-12 lAB sin1+1lAB cos1（2） BCD（RRR级杆组）由（1）知B点位置坐标、速度、加速度运动副D点位置坐标 xD=150mm yD=0 D点与机架相连，即该点速度和加速度均为0。运动副D的速度 vxD=0 vyD=0运动副D的加速度 axD=0 ayD=0 杆BC长 lBC=290mm 杆CD长 lC=300mm 可求得BC杆相对于X轴正方向转角 2=2arctanB0+A02+B02-C02A0+B0CD杆相对于x轴正方向转角 3=arctanyC-yDxC-xD其中A0=2lBC（xD-xB）,B0=2 lBC（yD-yB）,C0=lBC2+lBD2-lCD2,lBD2=(xD-xB)2+(yD-yB）2求导可得BC杆2、2和CD杆3、3 。则运动副C的位置坐标 xC=xB+lBCcos2 yC=xB+lBCsin2最后求导得vXc、vyC 以及axC 、ayC 。（3）构件2上E点的运动 CE为同一构件上的两点由（2）知C点位置坐标、速度、加速度以及构件2的转角、角速度和角加速度。可求出点E的位置坐标 xE=xD+lDEcos2 yE=xD+lDEsin2点E的速度 vxE= vxD 2 lDE sin2 vyE= vyD+2 lBD cos2点E的加速度 axE= axD-22 lDE cos2-2lDE sin2 ayE=ayD-22 lDE sin2+2lDE cos2（4）构件4上f点的运动（RRP级杆组）由（3）知E点置坐标、速度、加速度杆EF lEF=500mm杆EF与x轴夹角4=arcsin(yF-yE)/lEF)得运动副F点位置坐标 xF=xE+lEFcos(4) yG=e=65mm运动副F点速度 vxF=(vxEcos(4)-vyEsin(4)cos(4) vyF = 0最后vxF求导得axg ， ayF = 0 4. 编程程序段以下程序段采用MATLAB编写f1=0:pi/720:2*pi;%开始%w1=10;xA=0;yA=0;vxA=0;vyA=0;axA=0;ayA=0;lab=180;xB=xA+cos(f1)*lab;%运动副B位置%yB=yA+sin(f1)*lab;vxB=vxA-w1*lab*sin(f1);%运动副B速度%vyB=vyA+w1*lab*cos(f1);axB=axA-w12*lab*cos(f1)-w1*lab*sin(f1); %运动副B加速度%ayB=ayA-w12*lab*sin(f1)+w1*lab*cos(f1);lbc=290; %杆BC长%lcd=300; %杆CD长%xD=150; %运动副D位置、速度、加速度% yD=0;vxD=0;vyD=0;axD=0;ayD=0;lbd=realsqrt(xD-xB).2+(yD-yB).2); %BD间距离%A0=2*lbc*(xD-xB);B0=2*lbc*(yD-yB);C0=lbc.2+lbd.2-lcd.2;fbc=2*atan(B0+1*realsqrt(A0.2+B0.2-C0.2)./(A0+C0);%BC杆转角%xC=xB+lbc*cos(fbc); %运动副C位置%yC=yB+lbc*sin(fbc);fcd=atan(yC-yD)./(xC-xD);%CD杆转角%C2=lbc*cos(fbc);S2=lbc*sin(fbc);C3=lcd*cos(fcd);C32=C3.*(f12.149).*(f16.220);S3=lcd*sin(fcd);S32=S3.*(f12.149).*(f16.220);G1=C2.*S32-C32.*S2;wbc=(C32.*(vxD-vxB)+S32.*(vyD-vyB)./G1; %杆BC角速度%wcd=(C2.*(vxD-vxB)+S2.*(vyD-vyB)./G1; %杆CD角速度%vxC=vxB-lbc*wbc.*sin(fbc); %运动副C速度%vyC=vxB+lbc*wbc.*cos(fbc);G2=axD-axB+wbc.2.*C2-wcd.2.*C32;G3=ayD-ayB+wbc.2.*S2-wcd.2.*S32;ebc=(G2.*C3+G3.*S3)./G1; %杆BC角加速度%ecd=(G2.*C2+G3.*S2)./G1; %杆CD角加速度%axC=axB-lbc*ebc.*sin(fbc)-lbc*wbc.2.*cos(fbc); %运动副C加速度%ayC=ayB+lbc*ebc.*cos(fbc)-lbc*wbc.2.*sin(fbc);fde=fcd-130/180.*pi;wde=wcd;ede=ecd;lde=180;xE=xD+lde.*cos(fde);%运动副E位置%xE2=xE.*(f12.149).*(f16.220);yE=yD+lde.*sin(fde); yE2=yE.*(f12.149).*(f16.220);vxE=vxD-wde.*lde.*sin(fde);%运动副E速度%vxE2=vxE.*(f12.149).*(f16.220);vyE=vyD+wde.*lde.*cos(fde); vyE2=vyE.*(f12.149).*(f16.220);axE=axD-wde.2.*lde.*cos(fde)-ede.*lde.*sin(fde); %运动副E加速度%ayE=ayD-wde.2.*lde.*sin(fde)+ede.*lde.*cos(fde);axE2=axE.*(f12.149).*(f16.220);ayE2=ayE.*(f12.149).*(f16.220);lef=500;%杆EF长%yF=65;fef=asin(yF-yE)./lef);%EF杆转角%fef2=fef.*(f12.149).*(f16.220);xF=xE2+lef*cos(fef2);subplot(3,1,1);plot(xF,yF);%输出F点的位移%title(F点位移图 );xlabel(xF（mm）);ylabel(yF（mm）);vF=(vxE2.*cos(fef2)-vyE2.*sin(fef2)./cos(fef2);subplot(3,1,2);plot(f1,vF);% 输出F点的速度图%title(F点速度图);xlabel(（rad）);ylabel(vF（mm/s）);aF=diff(vF)/(pi/720*4.25);% 求F点的加速度%aF(1441)=aF(1);subplot(3,1,3);plot(f1,aF);%输出F点的加速度图%title(F点加速度图 );xlabel(（rad）);ylabel( vF（mm/s）);5. 计算结果F点轨迹F点位移图像F点速度图像F点加速度图像6、 计算结果分析角度位移（mm）速度（m/s）加速度（m/s2）角度位移（mm）速度（mm/s）加速度（m/s2）111.87742410.809411602.318447191-16.405044-7.929395403.164163123.77319610.912622580.393892192-17.782844-7.858408410.290064135.68664811.011891557.140416193-19.148146-7.786195417.208490147.61707111.106984532.545785194-20.500739-7.712793423.920098159.56371711.197667506.601231195-21.840418-7.638237430.4255381611.52579411.283703479.301640196-23.166986-7.562564436.7254741713.50247211.364856450.645736197-24.480251-7.485809442.8205931815.49287811.440890420.636249198-25.780027-7.408008448.7116221917.49609611.511568389.280068199-27.066134-7.329197454.3993382019.51117311.576658356.588380200-28.338399-7.249411459.8845822121.53711211.635926322.576787201-29.596655-7.168684465.1682722223.57287711.689145287.265408202-30.840742-7.087054470.2514142325.61739311.736089250.678956203-32.070504-7.004553475.1351122427.66954511.776540212.846797204-33.285792-6.921218479.8205822529.72818111.810281173.802977205-34.486464-6.837081484.3091572631.79211111.837106133.586249206-35.672384-6.752179488.6022992733.86011111.85681392.240035207-36.843419-6.666544492.7016062835.93092011.86920949.812407208-37.999447-6.580210496.6088192938.00324611.8741116.356010209-39.140346-6.493211500.3258303040.07576611.871343-38.072020210-40.266005-6.405580503.8546873142.14712711.860742-83.410179211-41.376315-6.317349507.1975973244.21594611.842154-129.592730212-42.471176-6.228551510.3569303346.28081811.815438-176.549873213-43.550490-6.139217513.3352253448.34031211.780465-224.207929214-44.614167-6.049378516.1351883550.39297611.737120-272.489558215-45.662121-5.959067518.7596943652.43734011.685301-321.313991216-46.694273-5.868312521.2117893754.47191611.624920-370.597287217-47.710549-5.777144523.4946853856.49520311.555906-420.252609218-48.710877-5.685593525.6117643958.50568811.478200-470.190519219-49.695195-5.593685527.5665724060.50185011.391762-520.319292220-50.663442-5.501451529.3628144162.48216311.296566-570.545237221-51.615563-5.408916531.0043554264.44509611.192604-620.773045222-52.551510-5.316109532.4952124366.38911911.079883-670.906136223-53.471235-5.223053533.8395464468.31270510.958430-720.847025224-54.374699-5.129776535.0416654570.21433210.828286-770.497687225-55.261865-5.036301536.1060074672.09248910.689509-819.759939226-56.132700-4.942651537.0371414773.94567510.542178-868.535814227-56.987176-4.848850537.8397534875.77240410.386384-916.727944228-57.825268-4.754920538.5186464977.57120710.222239-964.239938229-58.646956-4.660882539.0787225079.34063810.049869-1010.976760230-59.452223-4.566756539.5249855181.0792739.869417-1056.845101231-60.241055-4.472562539.8625215282.7857159.681044-1101.753739232-61.013442-4.378318540.0964975384.4585959.484924-1145.613897233-61.769376-4.284041540.2321505486.0965789.281248-1188.339584234-62.508854-4.189749540.2747775587.6983629.070221-1229.847925235-63.231875-4.095458540.2297275689.2626828.852063-1270.059471236-63.938439-4.001181540.1023925790.7883158.627007-1308.898498237-64.628550-3.906933539.8981965892.2740768.395298-1346.293281238-65.302216-3.812727539.6225905993.7188268.157194-1382.176350239-65.959443-3.718575539.2810436095.1214737.912964-1416.484723240-66.600243-3.624488538.8790296196.4809727.662890-1449.160115241-67.224628-3.530476538.4220246297.7963277.407259-1480.149125242-67.832612-3.436547537.9154966399.0665937.146372-1509.403390243-68.424209-3.342711537.36489964100.2908816.880533-1536.879723244-68.999438-3.248975536.77566265101.4683526.610058-1562.540214245-69.558315-3.155344536.15318566102.5982266.335265-1586.352312246-70.100861-3.061825535.50283567103.6797776.056480-1608.288872247-70.627094-2.968420534.82993268104.7123375.774032-1628.328181248-71.137035-2.875135534.13975169105.6952955.488253-1646.453955249-71.630705-2.781972533.43751270106.6280995.199479-1662.655303250-72.108126-2.688931532.72837771107.5102554.908046-1676.926679251-72.569319-2.596014532.01744472108.3413304.614290-1689.267794252-73.014306-2.503222531.30974273109.1209464.318548-1699.683511253-73.443109-2.410552530.61023074109.8487874.021155-1708.183720254-73.855748-2.318003529.92378975110.5245943.722445-1714.783185255-74.252244-2.225572529.25522376111.1481663.422747-1719.501377256-74.632619-2.133256528.60925277111.7193583.122388-1722.362281257-74.996891-2.041050527.99051578112.2380852.821689-1723.394192258-75.345080-1.948949527.40356079112.7043142.520967-1722.629500259-75.677203-1.856948526.85284880113.1180682.220532-1720.104447260-75.993277-1.765040526.34275181113.4794251.920687-1715.858892261-76.293318-1.673216525.87754582113.7885151.621730-1709.936047262-76.577339-1.581469525.46141583114.0455161.323949-1702.382225263-76.845355-1.489791525.09845284114.2506601.027625-1693.246562264-77.097375-1.398171524.79265185114.4042250.733028-1682.580756265-77.333408-1.306598524.54791086114.5065350.440422-1670.438785266-77.553463-1.215063524.36803487114.5579610.150059-1656.876637267-77.757545-1.123553524.25672688114.558916-0.137818-1641.952039268-77.945657-1.032057524.21759889114.509854-0.422977-1625.7241822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