理论力学全套解疑12

εωεtddω=εtddrv=12-1aεωωωE(b)tEddωuε==εOωε12-1vMaNaRvMaNaR12-2vMOMAMaNOAaROMBaRM8612-212-3OO2ωrOO2OO1ωeωa=ωe+ωr12-3O1OO2OωrωeCCOO1OO2CECDCCEvCDvCC⋅=⋅=eerrωωOACBverCCvv=Ca=0OCMrvava=ωerve=ωervr=ωrrva=vevrωar=ωer+ωrr=(ωe+ωr)rωa=ωeωrO87ωO1lOO1u12-41a12-41OAyO1O1CyO1CO1ω⋅=COu1ααααsin22sin2cos2sin11llOOCO=====αωsin2luωωeωr(b)ωeωrO2ABDOCn1=6rpmOCOEn2=10rpm12-42aα=20°OCωrOC12-42bπ2.0606π260π21r=×==nω(rad/s)88OCOEωeOEπ316010π260π22e=×==nω(rad/s)ω=ωe+ωrω)rad/s(65.1cos20π2.03π2)π2.0(π31cos222re2r2e=×××++⎟⎠⎞⎜⎝⎛=++=Dαωωωωω=−=)20180sin(sineDDωωβ0.217β=12°12′O12-42(b)ω12-42312-43aR=1002(mm)2α=90°vA=200(mm/s)OAωrOAωeCOCOb22100200e===OAvAω(rad/s)89)rad/s(22)rad/s(2er====ωωωωC12-4312-44412-44r=20(mm)ODω1=5(rad/s)ω2=3(rad/s)R=70(mm)ω3ωrbODωebωaωeωrOab)mm/s(210370)mm/s(35057021=×===×==ωωRvRvbaωaωaDOα90)sincos()sincoscos(sin)sin(1111ααωαβαβωαβωωrROaOahvaaaaa+=+⋅=+⋅==(1))sincos()sincoscos(sin)sin(2222ααωαβαβωαβωωrRObObhvaaaab−=+⋅=−⋅==(2)(1)(2)αωcos2Rvvaba=+(3)(1)(2)αωsin2rvvaba=−(4)(3)b47022103502cosae4=×+=+===Rvvbaαωωω(rad/s)(4)b5.32022103502sinar=×−=−==rvvbaαωω(rad/s)32.55.34222r2ea3=+=+==ωωωω(rad/s)ωa=ωe+ωrεa=εe+εrεaεe+εrrerererereaad~dddddddωωωωωωωω×++=×++=+==εεεεttttωeωrωe=|ωr|=θ=εa=εa=ωeωr12-6εaωeωr91ωeAuεaα=60°ϕ=t2/4tsϕradAvr=20t(mm/s)OA=80(mm)t=1(s)B12-7a12-612-71BBBOOCbϕ=t2/4)rad/s(21)rad/s(21)(1),rad/s(2dd2ee=======εεωϕωωsttt2BNBBnBBreeaaaaa++=τkraa++RB9212-7OxyzOyOAOxyzzijkjjj2041802ee−=−=⋅−=ωBDanB(b)ijj402180ee−=−=⋅−=ετBDaB(b)=ωNBearεBrωrtthvAA214020rr===ω(rad/s)eOCeeeω21|211rr====ttω(rad/s)iivv40|4021rr====tABt(mm/s)93kjikjievωa3101040)30sin30(cos214021rr−−=×−=×=×=DDBNBrD(b)()=εRBearrOBεrkjkjreieieeωeeeeωε3808030sin60sin8030cos60sin80163212380202121|60sin221)1()(221dddd)(dddd1rrrr+=+=+=+=+=×+=+====DDDDDOBtArrOAvttttωttωω1)5()35(120sin340)30sin40(380163801633802180213808016321jkiikijikejekjierεa−++⎟⎟⎠⎞⎜⎜⎝⎛+=⎟⎟⎠⎞⎜⎜⎝⎛×+⎟⎟⎠⎞⎜⎜⎝⎛×+⎟⎟⎠⎞⎜⎜⎝⎛×+⎟⎠⎞⎜⎝⎛×=⎟⎟⎠⎞⎜⎜⎝⎛+×⎟⎟⎠⎞⎜⎜⎝⎛+=×=DDOBrRB1eOzeOzω(b)∆OACOAvAr=ωω(b)9421rr)355(40)35()5()20()20(RBRBaakjikjii+=−−=+−+=x1rRBa22rRBajikvωa40402122rek=+=×=Bkjkjia355)35310()4051020()4040(a−=+−++−−−++−=B10)35()5(||22a=+=Bamm/s21ωe=ωtddϕωrAAhvrωzOACOAzOAvAr2εrei21163+i163xωre21ωrωrεr=ωωrεrωr=ωeωrθtddrrωε=kω2et=95eω2rt=ΩεaB(c)2120cos2re2r2et=++=DωωωωΩOBkjΩDD30sin230cos2tt+=kijkijkijkjωjkkjjΩε411634341824343241)(434341)(4343dd2122121dd2322321dda11a+−=+−=+−+=++×+=+++====OAvOtttttAtt1NBRBBaaa+=kjkjkijrεa355380804116343a−=⎟⎟⎠⎞⎜⎜⎝⎛+×⎟⎟⎠⎞⎜⎜⎝⎛+−=×=OBRBBΩ0=NBa2yjyzωOAvAavAa=vAe+vAr=OA⋅ωa(i)+vAri=80⋅21(i)+20i=20iOAvAak=82k=41k96kjaa355a−==RBB10)35()5(||22a=+=Ba(mm/s2)12-797