哈尔滨工业大学机械原理大作业连杆26题.pdf

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1、1.运动分析题目如图所示机构，已知机构各构件的尺寸为AB=108mm，EF=320mm，BC=CE=CD=200mm，FG=162mm，AD=258mm，AG=514mm，DG=384mm，=80，构件 1 的角速度为1=10rad/s，试求构件 2 上点 E 的轨迹及构件 5 的角位移、角速度和角加速度，并对计算结果进行分析。2.机构的结构分析，组成机构的基本杆组划分3.各基本杆组的运动分析数学模型1（1）RR 基本杆组：delt=0 xB=xA+AB*Cos(f+delt)yB=yA+AB*Sin(f+delt)vxB=vxA-w*AB*Sin(f+delt)vyB=vyA+w*AB*Co

2、s(f+delt)axB=axA-w 2*AB*Cos(f+delt):ayB=ayA-w 2*AB*Sin(f+delt)(2)RRR 基本杆组Ci=lbc*Cos(fbc)Si=lbc*Sin(fbc)Cj=lcd*Cos(fcd)Sj=lcd*Sin(fcd)G1=Ci*Sj-Cj*Siwbc=(Cj*(vxD-vxB)+Sj*(vyD-vyB)/G1wcd=(Ci*(vxD-vxB)+Si*(vyD-vyB)/G1vxC=vxB-wbc*lbc*Sin(fbc)vyC=vyB+wbc*lbc*Cos(fbc)G2=axD-axB+wbc 2*Ci-wcd 2*CjG3=ayD-ayB+

3、wbc 2*Si-wcd 2*Sjebc=(G2*Cj+G3*Sj)/G1ecd=(G2*Ci+G3*Si)/G1axC=axB-ebc*lbc*Sin(fbc)-wbc 2*lbc*Cos(fbc)ayC=ayB+ebc*lbc*Cos(fbc)-wbc 2*lbc*Sin(fbc)EB=2*BC*Cos(febc)xE=xB+EB*Cos(fbc+febc)yE=yB+EB*Sin(fbc+febc)vxE=vxB wbc*EB*Sin(fbc+febc)vyE=vyB+wbc*EB*Cos(fbc+febc)axE=axB-wbc 2*EB*Cos(fbc+delt)-ebc*EB*Si

4、n(fbc+febc)2ayE=ayB-wbc 2*leb*Sin(fbc+delt)+ebc*leb*Sin(fbc+febc)Ci=lef*Cos(fef)Si=lef*Sin(fef)Cj=lfg*Cos(ffg)Sj=lfg*Sin(ffg)G1=Ci*Sj-Cj*Siwef=(Cj*(vxG-vxE)+Sj*(vyG-vyE)/G1wfg=(Ci*(vxG-vxE)+Si*(vyG-vyE)/G1vxF=vxE-wef*lef*Sin(fef)vyF=vyE+wef*lef*Cos(fef)G2=axG-axE+wef 2*Ci-wfg 2*CjG3=ayG-ayE+wef 2*Si

5、-wfg 2*Sjeef=(G2*Cj+G3*Sj)/G1efg=(G2*Ci+G3*Si)/G1axF=axE-eef*lef*Sin(fef)-wef 2*lef*Cos(fef)ayF=ayE+eef*lef*Cos(fef)-wef 2*lef*Sin(fef)4.计算编程Dim xA As DoubleDim yA As DoubleDim vxA As DoubleDim vyA As DoubleDim axA As Double A 点加速度 x 轴分量Dim ayA As Double A 点加速度 y 轴分量Dim xB As Double B点 x 轴坐标Dim yB A

6、s Double B点 y 轴坐标Dim vxB As Double B点速度 x 轴分量Dim vyB As Double B点速度 y 轴分量Dim axB As Double B点加速度 x 轴分量Dim ayB As Double B点加速度 y 轴分量Dim xC As Double C点 x 轴坐标Dim yC As Double C点 y 轴坐标Dim vxC As Double C点速度 x 轴分量Dim vyC As Double C点速度 y 轴分量Dim axC As Double C点加速度 x 轴分量Dim ayC As Double C点加速度 y 轴分量Dim x

7、D As Double D点 x 轴坐标Dim yD As Double D点 y 轴坐标Dim vxD As Double D点速度 x 轴分量Dim vyD As Double D点速度 y 轴分量Dim axD As Double D点加速度 x 轴分量Dim ayD As Double D点加速度 y 轴分量Dim xE As Double E点 x 轴坐标3Dim yE As Double E点 y 轴坐标Dim vxE As Double E点速度 x 轴分量Dim vyE As Double E点速度 y 轴分量Dim axE As Double E点加速度 x 轴分量Dim a

8、yE As Double E点加速度 y 轴分量Dim xF As Double F点 x 轴坐标Dim yF As Double F点 y 轴坐标Dim vxF As Double F点速度 x 轴分量Dim vyF As Double F点速度 y 轴分量Dim axF As Double F点加速度 x 轴分量Dim ayF As Double F点加速度 y 轴分量Dim xG As Double G点 x 轴坐标Dim yG As Double G点 y 轴坐标Dim vxG As Double G点速度 x 轴分量Dim vyG As Double G点速度 y 轴分量Dim ax

9、G As Double G点加速度 x 轴分量Dim ayG As Double G点加速度 y 轴分量Dim delt As Double AB杆初始转角Dim lab As Double AB杆长Dim lbc As Double BC杆长Dim lcd As Double CD杆长Dim lce As Double CE杆长Dim lef As Double EF杆长Dim lfg As Double FG杆长Dim leb As Double ED杆长Dim f As Double AB杆转角Dim fbc As Double BC杆转角Dim fcd As Double CD杆转角D

10、im fce As Double CE杆转角Dim fef As Double EF杆转角Dim ffg As Double FG杆转角Dim fge As Double ge杆转角Dim w As Double AB杆角速度Dim wbc As Double BC角速度Dim wcd As Double CD角速度Dim wce As Double CE角速度Dim wef As Double EF角速度Dim wfg As Double FG角速度Dim e As Double AB杆角加速度Dim ebc As Double BC杆角加速度Dim ecd As Double CD杆角加速

11、度Dim ece As Double CE杆角加速度Dim eef As Double EF杆角加速度Dim efg As Double FG杆角加速度4Dim LBD As Double BD距离Dim leg As Double EG距离Dim JCBD As Double 角 CBDDim jfeg As Double 角 FEGDim fBD As Double BD转角Dim feg As Double EG转角Dim Ci As DoubleDim Cj As DoubleDim Si As DoubleDim Sj As DoubleDim G1 As DoubleDim G2

12、As DoubleDim G3 As DoubleDim val As DoubleDim pi As DoubleDim pa As DoubleDim febc As Double 角 EBCDim i As DoubleDim fj1 As DoublePrivate Sub Command1_Click()求点 E 的轨迹Picture1.Scale(-300,400)-(10,-15)Picture1.Line(-300,0)-(10,0)XPicture1.Line(0,400)-(0,-15)YFor i=-300 To 0 Step 50X 轴坐标Picture1.DrawSt

13、yle=2Picture1.Line(i,400)-(i,0)Picture1.CurrentX=i-10:Picture1.CurrentY=0Picture1.Print iNext iFor i=0 To 350 Step 50Y 轴坐标Picture1.DrawStyle=2Picture1.Line(0,i)-(-400,i)Picture1.CurrentX=-20:Picture1.CurrentY=i+7Picture1.Print iNext iFor fj1=0 To 360 Step 0.01f=fj1*paCall RR1Call RRR1Call RR2Picture

14、1.PSet(xE,yE)Next fj1End Sub5Private Sub Command2_Click()求构件 5 的角位移Picture2.Scale(-20,5)-(380,-0.5)Picture2.Line(-20,0)-(380,0)XPicture2.Line(0,3)-(0,-0.5)YFor i=0 To 360 Step 30X 轴坐标Picture2.DrawStyle=2Picture2.Line(i,3)-(i,0)Picture2.CurrentX=i-10:Picture2.CurrentY=0Picture2.Print iNext iFor i=-0.

15、5 To 3 Step 0.5Y 轴坐标Picture2.Line(0,i)-(380,i)Picture2.CurrentX=-25:Picture2.CurrentY=iPicture2.Print iNext iFor fj1=0 To 360 Step 0.01f=fj1*paCall RR1Call RRR1Call RR2Call RRR2Picture2.PSet(fj1,ffg)Next fj1End SubPrivate Sub Command3_Click()求构件 5 的角速度Picture3.Scale(-20,10)-(380,-10)Picture3.Line(-2

16、0,0)-(380,0)XPicture3.Line(0,10)-(0,-10)YFor i=0 To 360 Step 30X 轴坐标Picture3.DrawStyle=2Picture3.Line(i,10)-(i,-10)Picture3.CurrentX=i-10:Picture3.CurrentY=0Picture3.Print iNext iFor i=-8 To 8 Step 2Y 轴坐标Picture3.Line(0,i)-(380,i)Picture3.CurrentX=-20:Picture3.CurrentY=iPicture3.Print iNext iFor fj1

17、=0 To 360 Step 0.01f=fj1*paCall RR16Call RRR1Call RR2Call RRR2Picture3.PSet(fj1,wfg)Next fj1End SubPrivate Sub Command4_Click()求构件 5 的角加速度Picture4.Scale(-20,300)-(380,-200)Picture4.Line(-20,0)-(380,0)XPicture4.Line(0,300)-(0,-200)YFor i=0 To 360 Step 30X 轴坐标Picture4.DrawStyle=2Picture4.Line(i,300)-(

18、i,-200)Picture4.CurrentX=i-10:Picture4.CurrentY=0Picture4.Print iNext iFor i=-200 To 300 Step 50Y 轴坐标Picture4.Line(0,i)-(380,i)Picture4.CurrentX=-25:Picture4.CurrentY=i+5Picture4.Print iNext iFor fj1=0 To 360 Step 0.01f=fj1*paCall RR1Call RRR1Call RR2Call RRR2Picture4.PSet(fj1,efgNext fj1End SubPriv

19、ate Sub Form_Load()赋初值lab=108lce=200lbc=200lcd=200lef=320lfg=162w=10e=0delt=0 xA=0yA=07vxA=0vyA=0axA=0ayA=0 xD=-178.311284yD=186.464704vxD=0vyD=0axD=0ayD=0 xG=-514yG=0vxG=0vyG=0axG=0ayG=0pi=3.1415926pa=pi/180febc=pa*50End SubPrivate Sub RR1()RR 基本杆组xB=xA+lab*Cos(f+delt)yB=yA+lab*Sin(f+delt)vxB=vxA-w

20、*lab*Sin(f+delt)vyB=vyA+w*lab*Cos(f+delt)axB=axA-w 2*lab*Cos(f+delt)-e*lab*Sin(f+delt)ayB=ayA-w 2*lab*Sin(f+delt)+e*lab*Sin(f+delt)End SubPrivate Sub RR2()RR 基本杆组leb=2*lbc*Cos(febc)xE=xB+leb*Cos(fbc+febc)yE=yB+leb*Sin(fbc+febc)vxE=vxB-wbc*leb*Sin(fbc+febc)vyE=vyB+wbc*leb*Cos(fbc+febc)axE=axB-wbc 2*l

21、eb*Cos(fbc+delt)-ebc*leb*Sin(fbc+febc)ayE=ayB-wbc 2*leb*Sin(fbc+delt)+ebc*leb*Sin(fbc+febc)End SubPrivate Sub RRR1()RRR 基本杆组LBD=Sqr(xD-xB)2+(yD-yB)2)If LBD lbc+lcd And LBD Abs(lbc-lcd)ThenIf MsgBox(RRR 杆组杆长不符合要求,vbOKOnly,提示)=1 ThenEnd8ElseEnd IfElseEnd IfIf LBD Abs(lbc-lcd)Thenval=(lbc 2+LBD 2-lcd 2

22、)/(2*lbc*LBD)JCBD=Atn(-val/Sqr(-val*val+1)+2*Atn(1)ElseEnd IfIf LBD=lbc+lcd ThenJCBD=0ElseEnd IfIf LBD=Abs(lbc-lcd)ThenIf lbc lcd ThenJCBD=0ElseEnd IfIf lbc xB And yD=yB Then 第一象限fBD=Atn(yD-yB)/(xD-xB)ElseEnd IfIf xD=xB And yD yB ThenfBD=pi/2ElseEnd IfIf xD=yB Then 第二象限fBD=pi+Atn(yD-yB)/(xD-xB)ElseE

23、nd IfIf xD xB And yD yB Then 第三象限fBD=pi+Atn(yD-yB)/(xD-xB)ElseEnd IfIf xD=xB And yD xB And yD xD And yC=yD Then 第一象限fcd=Atn(yC-yD)/(xC-xD)ElseEnd IfIf xC=xD And yC=yD Thenfcd=pi/2ElseEnd IfIf xC=yD Then 第二象限fcd=pi+Atn(yC-yD)/(xC-xD)ElseEnd IfIf xC xD And yC yD Then 第三象限fcd=pi+Atn(yC-yD)/(xC-xD)ElseE

24、nd IfIf xC=xD And yC xD And yC lef+lfg And leg Abs(lef-lfg)ThenIf MsgBox(RRR 杆组杆长不符合要求,vbOKOnly,提示)=1 ThenEndElseEnd IfElseEnd IfIf leg Abs(lef-lfg)Thenval=(lef 2+leg 2-lfg 2)/(2*lef*leg)jfeg=Atn(-val/Sqr(-val*val+1)+2*Atn(1)ElseEnd IfIf leg=lef+lfg Thenjfeg=0ElseEnd IfIf leg=Abs(lef-lfg)ThenIf lef

25、lfg Thenjfeg=0ElseEnd IfIf lef xE And yG=yE Then 第一象限feg=Atn(yG-yE)/(xG-xE)ElseEnd IfIf xG=xE And yG yE Thenfeg=pi/2ElseEnd IfIf xG=yE Then 第二象限feg=pi+Atn(yG-yE)/(xG-xE)Else11End IfIf xG xE And yG yE Then 第三象限feg=pi+Atn(yG-yE)/(xG-xE)ElseEnd IfIf xG=xE And yG xE And yG xG And yF=yG Then 第一象限ffg=Atn(

26、yF-yG)/(xF-xG)ElseEnd IfIf xF=xG And yF=yG Thenffg=pi/2ElseEnd IfIf xF=yG Then 第二象限ffg=pi+Atn(yF-yG)/(xF-xG)ElseEnd IfIf xF xG And yF yG Then 第三象限ffg=pi+Atn(yF-yG)/(xF-xG)ElseEnd IfIf xF=xG And yF xG And yF=yG Then 第四象限ffg=2*pi+Atn(yF-yG)/(xF-xG)ElseEnd IfCi=lef*Cos(fef)Si=lef*Sin(fef)Cj=lfg*Cos(ffg

27、)Sj=lfg*Sin(ffg)12G1=Ci*Sj-Cj*Siwef=(Cj*(vxG-vxE)+Sj*(vyG-vyE)/G1wfg=(Ci*(vxG-vxE)+Si*(vyG-vyE)/G1vxF=vxE-wef*lef*Sin(fef)vyF=vyE+wef*lef*Cos(fef)G2=axG-axE+wef 2*Ci-wfg 2*CjG3=ayG-ayE+wef 2*Si-wfg 2*Sjeef=(G2*Cj+G3*Sj)/G1efg=(G2*Ci+G3*Si)/G1axF=axE-eef*lef*Sin(fef)-wef 2*lef*Cos(fef)ayF=ayE+eef*lef

28、*Cos(fef)-wef 2*lef*Sin(fef)End Sub5结果及分析图 1E 点的运动轨迹（1）由图1 所示，E 点的运动轨迹呈稍倾斜“8 字形”。若以“8 字”的中心为出发点，运动形式为循环往复运动：E 点先是向左上方移动，绕一圈后回到出发点，再向右下方移动并再次回到出发点，。13图 2构件 5 的角位移曲线由图 2 所示，构件大约在90 度和 240 度处该构件角位移最大，在160 度和 330 度附近该构件角位移最小。出现两次极大值与极小值的原因应该与构件E 的 8 字形运动有关。图 3构件 5 的角速度曲线由图 3 所示，在角位移为极大极小值对应的角度处，其角速度为0，这验证了角位移曲线方程为角速度曲线方程的一阶导数。而在约 130 度和 190 度时，角速度分别达到了反向和正向的最大值。在其中角速度还有两次达到了正向和反向的极大值，这又证明了E 点 8 字形运动的影响。图 4构件 5 的角加速度曲线14由图 4 所示，在角速度达到极大极小值时，角加速度对应为0，验证了角加速度方程为角速度方程的一阶导数，即角位移曲线的二阶导数为角加速度的方程。15