《机械原理》第三章-平面机构的运动分析

3-13-23-33-43-51.2.3.3-13-21.2.3.4.1.121.1p21p212.N-1K–(N–1)=(N-1)(N-2)/22/)1(2−==NNCKN,N()K,::3.(1)1):3.(1)2):3.(1)3):12nn123.(2)P23P12P1343/2=6P13P12P23P13P14P34P13P23P34P24P12P14P24P244.ω2ulω4vEP24242P244P244.ω2ulω4vEP1333E2P233P232321223PlvPPωµ=2331323PlvPPωµ=3212231323/PPPPωω=21223131323/ElvPPPEPPωµ=313ElvPEωµ=4.2ul3vP23232P233P23P23nnP23P12P13lPPPvµω⋅⋅=231222323Pvv=lPPPvvµω⋅⋅==23122233-31.1)2)3)4)2.3.1)DCBlvvv,,:),(2:ωµ)/(smpcvvCµ=CBBCvvv+=pbvBv=µ)(??2BClω//xxBC⊥)/(smbcvvCBµ=)()/()/(/2sradBCbclvlvBCCBµµω==ul)/()/(smpcvsmpbvvCvBµµ==)/(smbcvvCBµ=1)pp3)2)pDCCDBBDvvvvv+=+=)/(smpdvvDµ=DCDBllµωµω22?DCBD⊥⊥?ulpbvBv=µBCDbcdBCDbcd∆∆∆∆)≈2)DCBCBlaaavv,,:,,,),(22:αωµBCBCxxaaaaBCBCCBnCBBCll⊥→++=//??)(222αωτ)()(2s/rad)BC/('c'nl/a)s/m('c'na)s/m('c'palaBCCBaCBaCµµαµµττ====''bpaBa=µanCBanbµ='')/('')/(''smcpasmbpaaCaBµµ==)/(''smcbaaCBµ=2)p’3)1)p’p’ulBCDdcb)BCDdcb∆∆∆≈∆''bpaBa=µ)/(''smdpaaDµ=3)1132,,:,100,,:()ABADCDlllγωϕωω=°21132323//?()?BBABBBBBBDBDABBCvvlvvvlωω⊥⊥===+uuuruuruuuruuuruuuuur33333//()(/)()BvBBDvlvpbvlpbBDradsµωµµ===uuur22Bvvpbµ=:(1)(2)4)333233?0??()nBDBDBDBDBDBDBDaaaallτωα→⊥=++uuuuruuuuruuuruur221132323223232290???//:2BBABkrBBBBBBBBBBBABCaalaaaavvωωω→°===++uuuruuuruuuuuruuuuuruuuruuur22''Baapbµ=113232,,:,100,,,()()ABADCDlllγϕωωωαα=°22''Baapbµ=3333333''/''/()(/)()BDaBDBDalanbalnbBDradsττµαµµ===uuuuuur2.CBBCvvv+=1212CCCCvvv+=τCBnCBBCaaaa++=rCCkCCCCaaaa121212++=1)2)3)3232551,,,,,,,)(/20,420,140ααωωωECECCDBCABaavvsradmmllmml====ulABlABl/)1(=µ24523(2),,,,,,BCEEEvvvvvωω=24523(3),,,,,,BCEEEaaaaaαα=3.1)B233232323232BBkBBrBBkBBBBvaaaaaω=++=00/0002333323323======BBBBCBBBkBBvvlvvaωωBCABBCvBBBBvv//2323⊥⊥+=BCABBCABBBBBvvv⊥⊥−==//,,02323BCABABBCBBBBvvv//,,02323⊥⊥==2)K232)COKOKOKKKKKOKKvvvlvv21122323211113//??:⊥⊥+===ωCOOKKKrKKKKKKKKOKKvaaaalaa211322323232112113//???2→++===ωω2222222222222?0KOOKKOOKnOKOlaaa⊥→++=ωτ3-42CDDGCDDvv⊥⊥+=BCCBBCABBvvvABlv⊥+=⊥=)(2ωvCvCC44vCP14P46P16P14P45P15P14BCCPCBBCvvv⊥⊥+=143-51.2.3.1.,,illleθθ=rxθ31212341243:()iiilllllelelleaθθθ+=++=+urururur1112224333(1),cossin(cossin)(cossin)(cossin)ieilililliθθθθθθθθθ=++++=++3322113342211sinsinsincoscoscos,θθθθθθlllllll=++=+11,,232323:13023θωθθωωαα°3322113342211sinsinsincoscoscos,θθθθθθlllllll=++=+1133411332314312221232411412223coscossinsinarctan1/cos)2/()(cos/sin:arctan2,θθθθθθθθθlllllMllllllllCllBACBCBAMA−+−=±=−−++=−=−=−−++=)(,)2(3322113421321321bielielieltelleleliiiiiiωωωθθθθθθ=++=+333222111333222111333322221111sinsinsincoscoscos,)sin(cos)sin(cos)sin(cos,sincosθωθωθωθωθωθωθθωθθωθθωθθθllllllilililiei=+=++=++++=1233211313223112ωθθθθωωθθθθω⋅−−=⋅−−−=)sin(l)sin(l)sin(l)sin(l,332332222221133221133221321,)3(αωαωωωωωθθθθθθθθiiiiiiiielielelielieltelelel+=++=+)c(sinlcoslinlcoslcosl)sini(cosl)sini(cosil)sini(cosl)sini(cosil)sini(cosilsinicose,,i33332332222222121133333323322222222211211sθαθωθαθωθωθθαθθωθθαθθωθθωθθθ+=+++++=++++++=)sin(l)cos(ll)cos(l)sin(ll)cos(l)cos(ldcoslsinloslsinlsinl,)d()c(,2332332322221121332232332222311212333323322222221211cθθθθωωθθωαθθωθθωθθωαθαθωθαθωθω−−−+−=−+−−−−=+−=+−−2.(1)⎩⎨⎧=++=[phone]θθθθθθsinlsinlsinlcosllcoslcosl⎩⎨⎧−=−−=−1133221143322θθθθθθsinlsinlsinlcosllcoslcoslθ2θ3(2)⎩⎨⎧−=−=+−111333222111333222θωωθωθθωωθωθcoslcoslcoslsinlsinlsinl⎩⎨⎧−=−=+−111333222111333222θωωθωθθωωθωθcoslcoslcoslsinlsinlsinl⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−111113233223322θθωωωθθθθcoslsinlcoslcoslsinlsinl(3)⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−−=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−1111111323332223332223233223322θωθωωωωθωθωθωθωααθθθθsinlcoslsinlsinlcoslcoslcoslcoslsinlsinlP⎪⎪⎩⎪⎪⎨⎧+°++=+°++=221122119090θθθθθθsinbsinasinlycosbcosacoslxPP⎩⎨⎧+°++=+°−−−=222211122221119090ωθωθωθωθωθωθcosbcosacoslvsinbsinasinlvPyPx1P2P⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡+°++°−−−=⎥⎦⎤⎢⎣⎡21221122119090ωωθθθθθθcosbcosacoslsinbsinasinlvvPyPx3P⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡+°++°+−⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡+°++°−−−=⎥⎦⎤⎢⎣⎡222122112211222112211909009090ωωθθθθθθαθθθθθθsinbsinasinlcosbcosacoslcosbcosacoslsinbsinasinlaaPyPx3.1),2)3)