少學(xué)時(shí)剛體的平面運(yùn)動(dòng)白

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2、vAB wsin1 lulvABABBO0ABAABvvv awacoscos0rvvAB awatantan0lrlvA lvBAAB wvAvBAvBavABO0AvAvBAvBavAvCAvCvAC 2tan2520202022 CAACAACvvrrrvvv w ww ww wCAACvvv ABAB)()(ABvv cossinABvv vB BAABvvv ABAABBvv SAvwAvBAvBvAB)(w ABvBA0 w wS AAvAvMAvLL 。ALLv MAAMvvv LL MAAMvvv w AMvAM SAAvwAvMAvMLwPwAvAP 0 wAPvvAPAvM

3、Av SAAvwAvMAvLLMSAAvwAvMAvMLPSww BPvBPBBvACBPPBvvv AvCvBPv ?SPwS Avw AvwAvPA AvBvPAv BvABSAAvwP wAvS PABOw：Av ， 。 rAB3 rOA BvP AvBvABABBABBPvww coswr332 )(wtgABvAPvAAAB ABwABAAPrvww 333ww rrABOwAvBvPABwOBv研究研究連桿連桿AB：Av0 ABwMAAMvvv Av MMvSAAvBvBSAAvBBv 。0wSPwPSAAvBvBOOv Ov解：解：)(P0 PAvvRvO w（）wBvDvCv,

4、2OBvv ,2OCvv ODvv2 ABCDP 五五 rabRvAvBvCE0wrvvBA cossinCBvv wtantan0rvvBC wwtan0RrRvCC 3033030bAOvA1113ww bBOvB222ww CAACvvv CBBCvvv CBBCAAvvvv 30 cosCBAvv CBBCAAvvvv bvvACB1230 cosw 30222121222460cos2wwww bvvvvvCBBCBBC由幾何關(guān)系可得：由幾何關(guān)系可得：方向：方向： CACvv xv ,cos3060ABvv 30cos1sm 231.030 cos30 cos wOAvvAB1sm

5、693. 03 BBDvCDCBvvDEvv 30 cos30601sm 8.0 Ev例題例題8 平面機(jī)構(gòu)中平面機(jī)構(gòu)中, 楔塊楔塊M: a a =30, v=12cm/s ; 盤盤: r = 4cm , 與與 楔塊間無(wú)楔塊間無(wú)滑動(dòng)求圓盤的滑動(dòng)求圓盤的w w及軸及軸O的速度和的速度和B點(diǎn)速度點(diǎn)速度解：軸解：軸O, 桿桿OC, 楔塊楔塊M均作平動(dòng)均作平動(dòng), 圓盤作平面運(yùn)動(dòng)，圓盤作平面運(yùn)動(dòng)，P為速度瞬心為速度瞬心, cm/s 12vvArad/s 32cos/12/ awrPAvA)(cm/s 343230sin4sinwawrPOvocmcosOBPOOBPOPB72214224212022222

6、)PB ( cm/s .PBvB3182143272w）( 不能認(rèn)為圓輪只滾不滑時(shí)不能認(rèn)為圓輪只滾不滑時(shí),接接 觸點(diǎn)就是瞬心觸點(diǎn)就是瞬心, 只有在接觸面是固只有在接觸面是固定面時(shí)定面時(shí), 圓輪上接觸點(diǎn)才是速度瞬心圓輪上接觸點(diǎn)才是速度瞬心reaaaa BAABaaa aAa ABatBA2w ABanBA4222)()(wa ABaaanBAtBABA2arctanarctanwaa nBAtBAaanBAtBAABaaaa RaORaOvOaOnCOatCOaRvO wRaRvdtddtdOO )(wanCOtCOOCaaaa OtCOOnCOaRaRvRa aw22RvaaOnCOC2 aA

7、vARvBlvlvCAvAAAAB245sin wAABBvCBv waAvARaBaAnBAatBAanBAtBAABaaaa lvlaAABnBA222 wxy45sin45sin45cos45cosAtBABnBAABaaaaaa 2222,22AAtBAAABvlaavlaa 2222AAtBAABvlalla aAO1OB3203wvAvB0ww OAvAAB03wwrOBvABB AO1OB20215wratB nAatAanBatBanAatAanBAatBAanBAtBAtAnABnBaaaaaa t200203,wawrraratAnA 2022wwrABaABnBA 201

8、223wrBOvaBnB nBAnAtAnBtBaaaaa 60cos30cos30cos60cos100200100200PDrDeDvvv 其中：其中：vDe=vF30cos/FDvv 30cos2 BDPD1 -srad12 PDvDADw1sm 08. 2 PAwvADAvAOABEDCvBPwrv2 AwrvvAB2=0 ABwww OBvBOBEvevrvawrvvveaED reavvv 0 rvOABEDCPtaaaaACnAC CA0 Ca0 tACa2wranAC 2wraanACA aAaAnBatBatBAattaaaaaBAnBABnB A0 nBAa22wranB

9、60cos30cos60cosAtBnBaaa 23waatB 223wa OBatBOBABaAOABEDCPEaEaarnEeatEeaCrEenEeEaaaaaa t00 Crav2wranEe 223wratEe 223wraatEeEa 223wraaEaED O1OO2ABCDvCvBEvA0332ww BEvB0332wwaavvAC 02332ww COvCCOEO1OO2ABCDvCvBvA02130coswavvAAr 06330sinwavvAAe 063ww OAvAeODvAevArArAeAvvv O1OO2ABCD20)31 (waatC aBaBnCatCanCBatCBattaaaaaCBnCBCnC B20waaB 202312wwaaaCOnC 20234wwaaanCB nCBBnCtCaaaa 30cos60cos30cos202)31 (2wa COatCCO20332waatCB 60cos30cosnCBtCBnCaaa 20332wa BCatCBtaaaaABnAB BAO1OO2ABCDaB20waaB 20332waaaatAB 20234wwaaanAB nABatABaCrAaaaa