机械原理大作业连杆19

连杆机构运动分析1.运动分析题目〔19〕如图1所示机构，机构各构件的尺寸为AB=112mm，β=90°，AD=264mm，DG=278mm，EF=116mm，FG=24mm，BC=CE=CD=200mm，构件1的角速度ω1=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。图12.机构的结构分析，组成机构的根本杆组划分该构件由Ι级杆组RR〔机架、原动件1〕、Ⅱ级杆组RRR〔杆2、杆3〕和Ⅱ级杆组RRR〔杆4、杆5〕组成。杆组如图2所示：图23.各根本杆组的运动分析数学模型3.1.原动件1原动件1的转角ψ1=0~360°，初始角度δ=0°，原动件1的角速度ω1=10rad/s，角加速度ε=0.所以运动副A的位置坐标为：XA=264mm,YA=0mm运动副A的速度：vXA=0,vYA=0，运动副A的加速度：aXA=0,aYA=0，原动件杆1长度：lAB=112mm。那么可得B点位置方程：XB=XA+lABcosψ1,YB=XA+lABsinψ1。对上述位移公式求导可得B点速度方程：VXB=VXA-ω1lsinψ1,VYB=VYA+ω1lcosψ1再求导得B点加速度方程：aXB=εXA-ω12lABcosψ1-εlABsinψ1，aYB=εYA-ω12lABsinψ1+εlABcosψ13.2Ⅱ级杆组RRR〔杆2、杆3〕运动副D点位置坐标XD=0，YD=0，该点的速度、加速度均为0，杆BC长lBC=200mm，杆CD长lCD=200mm。可求得BC杆相对于X轴正方向转角：ψ2=2arctanB以及CD杆相对于X轴正方向转角：ψ3=arctany式中，A0=2lBC〔XD-XB〕,B0=2lBC〔YD-YB〕,C0=lBC2求导可得BC杆ω2，ε2和CD杆ω3，ε3。那么运动副C的位置坐标为：XC=XB+lBCcosψ2，YC=YB+lBCsinψ2求导得到vXc、vYC以及aXC、aYC。3.3构件2上点E的运动可以认为BE为1级机构，那么点E的位置方程为：XE=XB+lBEcosψ2，YE=YB+lBEsinψ2点E的速度方程：vxE=vxB–ω2lBEsinψ2,vyE=vyB+ω2lBEcosψ2点E的加速度方程：axE=axB-ω22lBEcosψ2-α2lBEsinψ2,ayE=aYB-ω22lBEsinψ2+α2lBEcosψ23.4Ⅱ级杆组RRR〔杆4、杆5〕运动副E点位置方程、速度、加速度由3.3可知，那么杆EF长LEF=116mm，杆FG长LGF=28mm。可求得EF杆相对于X轴正方向转角Ψ4=2arctanBFG杆相对于X轴正方向转角Ψ5=arctany其中A1=2lEF〔XG-XE〕,B1=2lEF〔YG-YE〕,C1=lEF2求导可得EF杆ω5，ε5和CD杆ω5，ε5，那么运动副F的位置坐标为XF=xE+lEFcosψ4，YF=YE+lEFsinψ4最后求导得到vXF、vYF以及aXF、aYF。题目所要求的，构件5的角位移、角速度和角加速度，即为运动副F的角位移Ψ5，ω5和ε5。4.建立坐标系 建立以点D为原点、AD为x轴的固定平面直角坐标系D-xy，如图2所示。图25.计算编程OptionExplicit'定义自变量DimxA,yA,vxA,vyA,axA,ayAAsDoubleDimxB,yB,vxB,vyB,axB,ayBAsDoubleDimxC,yC,vxC,vyC,axC,ayCAsDoubleDimxD,yD,vxD,vyD,axD,ayDAsDoubleDimxE,yE,vxE,vyE,axE,ayEAsDoubleDimxF,yF,vxF,vyF,axF,ayFAsDoubleDimxG,yG,vxG,vyG,axG,ayGAsDoubleDimlab,lbc,lcd,lce,lef,lfgAsDouble'杆的长度Dimlbd,lde,legAsDouble'距离DimdeltAsDouble'构件1的初始角位移Dimfab,fbc,fcd,fef,ffg,fbd,fegAsDouble'角位移Dimwab,wbc,wcd,wef,wfgAsDouble'杆的角速度Dimeab,ebc,ecd,eef,efgAsDouble'杆的角加速度Dimcos_cdbAsDouble'角CDB的余弦值DimfcdbAsDouble'角CDBDimcos_fgeAsDouble'角FGE的余弦值DimffgeAsDouble'角FGEDimCi,Cj,Si,Sj,G1,G2,G3AsDoubleDimCii,Cjj,Sii,Sjj,G11,G22,G33AsDoubleDimpiAsDouble'圆周率DimpaAsDouble'角度和弧度相互转换的系数DimiAsDouble'循环变量DimfjAsDouble'角度循环变量PrivateSubCommand1_Click()Picture1.ClsPicture1.Scale(-200,500)-(200,-100)Picture1.Line(-190,0)-(190,0)'X轴Picture1.Line(0,500)-(0,-100)'Y轴Fori=-160To160Step40'X轴坐标Picture1.DrawStyle=2Picture1.Line(i,500)-(i,-100)Picture1.CurrentX=i-10:Picture1.CurrentY=0Picture1.PrintiNextiFori=0To500Step50'Y轴坐标Picture1.DrawStyle=2Picture1.Line(-190,i)-(190,i)Picture1.CurrentX=-10:Picture1.CurrentY=iPicture1.PrintiNextiForfj=0To360Step0.01fab=fj*paCallRR1CallRRR1CallRR2Picture1.PSet(xE,yE),vbRedNextfjEndSubPrivateSubCommand2_Click()Picture2.Scale(-10,390)-(380,-70)Picture2.Line(-10,0)-(380,0)'X轴Picture2.Line(0,380)-(0,-80)'Y轴Fori=-30To390Step30'X轴坐标Picture2.DrawStyle=2Picture2.Line(i,1000)-(i,-100)Picture2.CurrentX=i-10:Picture2.CurrentY=0Picture2.PrintiNextiFori=-30To390Step30'Y轴坐标Picture2.DrawStyle=2Picture2.Line(-10,i)-(380,i)Picture2.CurrentX=-10:Picture2.CurrentY=iPicture2.PrintiNextiForfj=0To360Step0.01fab=fj*paCallRR1CallRRR1CallRR2CallRRR2ffg=ffg/(2*pi)*360Picture2.PSet(fj,ffg),vbRedNextfjEndSubPrivateSubCommand3_Click()Picture3.Scale(-10,60)-(380,-80)Picture3.Line(-10,0)-(380,0)'X轴Picture3.Line(0,100)-(0,-100)'Y轴Fori=0To360Step30'X轴坐标Picture3.DrawStyle=2Picture3.Line(i,60)-(i,-80)Picture3.CurrentX=i-10:Picture3.CurrentY=0Picture3.PrintiNextiFori=-80To60Step10'Y轴坐标Picture3.Line(0,i)-(380,i)Picture3.CurrentX=-10:Picture3.CurrentY=iPicture3.PrintiNextiForfj=0To360Step0.01fab=fj*paCallRR1CallRRR1CallRR2CallRRR2Picture3.PSet(fj,wfg),vbRedNextfjEndSubPrivateSubCommand4_Click()Picture4.Scale(-10,200)-(380,-200)Picture4.Line(-10,0)-(380,0)'X轴Picture4.Line(0,200)-(0,-200)'Y轴Fori=0To360Step30'X轴坐标Picture4.DrawStyle=2Picture4.Line(i,200)-(i,-200)Picture4.CurrentX=i-10:Picture4.CurrentY=0Picture4.PrintiNextiFori=-200To200Step40'Y轴坐标Picture4.DrawStyle=2Picture4.Line(-10,i)-(380,i)Picture4.CurrentX=-10:Picture4.CurrentY=iPicture4.PrintiNextiForfj=0To360Step0.01fab=fj*paCallRR1CallRRR1CallRR2CallRRR2Picture4.PSet(fj,efg),vbRedNextfjEndSubPrivateSubForm_Load()'给变量赋初始值lab=112:lbc=200:lce=200:lcd=200:lef=116:lfg=28wab=10:eab=0:delt=0xA=264:yA=0:vxA=0:vyA=0:axA=0:ayA=0xD=0:yD=0:vxD=0:vyD=0:axD=0:ayD=0xE=0:yE=136:vxE=0:vyE=0:axE=0:ayE=0xG=0:yG=278:vxG=0:vyG=0:axG=0:ayG=0pi=4*Atn(1):pa=pi/180:fj=0EndSubPrivateSubRR1()'Ⅰ级杆组RR1〔原动件1〕xB=xA+lab*Cos(fab+delt)yB=yA+lab*Sin(fab+delt)vxB=vxA-wab*lab*Sin(fab+delt)vyB=vyA+wab*lab*Cos(fab+delt)axB=axA-wab^2*lab*Cos(fab+delt)-eab*lab*Sin(fab+delt)ayB=ayA-wab^2*lab*Sin(fab+delt)+eab*lab*Cos(fab+delt)EndSubPrivateSubRRR1()'Ⅱ级杆组RRR1(杆2,3)lbd=Sqr((xD-xB)^2+(yD-yB)^2)IfxB>xDAndyB>yDThenfbd=Atn((yB-yD)/(xB-xD))ElseEndIfIfxB>xDAndyB=yDThenfbd=0ElseEndIfIfxB>xDAndyB<yDThenfbd=Atn((yB-yD)/(xB-xD))+2*piElseEndIfcos_cdb=(lbd^2+lcd^2-lbc^2)/(2*lbd*lcd)fcdb=Atn(-cos_cdb/Sqr(1-cos_cdb^2))+pi/2fcd=fbd+fcdbxC=xD+lcd*Cos(fcd)yC=yD+lcd*Sin(fcd)fbc=pi+Atn((yC-yB)/(xC-xB))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=axB+wcd^2*Cj-wbc^2*CiG3=ayB+wcd^2*Sj-wbc^2*Siebc=(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)EndSubPrivateSubRR2()'Ⅰ级杆组RR2〔杆2，即BE〕xE=xB+(lbc+lce)*Cos(fbc)yE=yB+(lbc+lce)*Sin(fbc)vxE=vxB-wbc*(lbc+lce)*Sin(fbc)vyE=vyB+wbc*(lbc+lce)*Cos(fbc)axE=axB-wbc^2*(lbc+lce)*Cos(fbc)-ebc*(lbc+lce)*Sin(fbc)ayE=ayB-wbc^2*(lbc+lce)*Sin(fbc)+ebc*(lbc+lce)*Cos(fbc)EndSubPrivateSubRRR2()'Ⅱ级杆组RRR2(杆4,5)leg=Sqr((xE-xG)^2+(yE-yG)^2)IfxE>xGAndyE>yGThenfeg=Atn((yE-yG)/(xE-xG))ElseEndIfIfxE=xGAndyE>yGThenfeg=pi/2ElseEndIfIfxE<xGThenfeg=Atn((yE-yG)/(xE-xG))+piElseEndIfIfxE=xGAndyE<yGThenfeg=3*pi/2ElseEndIfIfxE>xGAndyE<yGThenfeg=Atn((yE-yG)/(xE-xG))+2*piElseEndIfcos_fge=(leg^2+lfg^2-lef^2)/(2*leg*lfg)ffge=Atn(-cos_fge/Sqr(1-cos_fge^2))+pi/2ffg=(feg-ffge)Ifffg<0Thenffg=ffg+2*piElseEndIfIfffg>=0Thenffg=ffgElseEndIfxF=xG+lfg*Cos(ffg)yF=yG+lfg*Sin(ffg)IfxF>xEAndyF>=yEThenfef=Atn((yF-yE)