7.3、加速度合成定理

17.3加速度合成定理1动点的加速度合成定理t时刻牵连点:m点动系:aacyx定系:xoy动点:质点Mt+△t时刻牵连点:m2点(m点与m2点是动系中两个不同的点)t时刻牵连点(m点)在t+△t时刻对应于m1点;reavvvt时刻动点的绝对速度：t+△t时刻动点的绝对速度：222reavvvm2点m点2t时刻动点的绝对加速度：2sin23rrvvrereavaaa2rrerrtavtvv20limrrrrrvvvvv32tvvtvvtvvarrteetaata202020limlimlim211212mmvveeetvvtvvtvveeteeteet1012020limlimlimereav3kreaaaaarkva2t时刻动点M的：aa:绝对加速度;ea:牵连加速度;ra:相对加速度;:m点的绝对加速度ea:M点在动系中的加速度raka:科氏加速度;(右手螺旋)动点的绝对加速度等于其牵连加速度、相对加速度与科氏加速度三者和;加速度合成定理4例7.3-1求摇杆OB在图示时刻的瞬时角加速度和滑块A在摇杆上的相对滑动加速度;条件：mrCA1.0sradCA/102/5sradCAo302动点:CA杆的A端点;动系:建立在OB杆上;reavvv(图b)kreaaaaa(图c)tanaaaaateneeaaarkva2:大小:方向√√?√?√√√牵连点:动系中与动点erv、5mrCA1.0sradCA/102/5sradCAo302reavvv(图b)707.0rv11.2e、tanaaaaa10naa5.0taateneeaaa49.1neatea？rara？rkva299.2ka解动点:CA杆的A端点,动系:建立在OB杆上;6mrCA1.0sradCA/102/5sradCAo30221.8ra2.13/OAteOBrakrtenetanaaaaaaa(图a)大小:方向:√√?√√√√√√√?√rnetanaktetanaaaaayaaaax45cos45cos:045sin45sin:7例7.3-2求顶杆AB图示时刻的瞬时加速度;mr1.0smv/32/2sma60动点:AB杆A端点;动系:凸轮车;46.3rv0ka(动系平动)reavvv(图b)trnreaaaaa(图c):大小:方向√√?√?√√√2ea72.119nra8mr1.0smv/32/2sma60解动点:AB杆A端点;动系:凸轮车;46.3rv0kareavvv(图b)trnreaaaaa(图c):大小:方向√√?√?√√√09.13781.66atraa60cos60sin0:60sin60cos0:trnratrnreaaayaaax9例7.3-3图示AB杆紧贴凸轮,求图示时刻摇杆AB的瞬时角加速度mr1.0srad/22/2sradAOCO动点:圆轮轮心C点;动系:凸轮车;reavvv(图b)erv、tanaaaaateneeaaarkva2krtenetanaaaaaaa大小:方向:√√?√√√√√√√?√10mr1.0srad/22/2sradAOCO解动点:圆轮轮心C点;动系:凸轮车;reavvv(图b)2.0rvsrade/1tanaaaaa4.0naa2.0taateneeaaa2.0neaeACteraABar//rABkva24.0ka11krtenetanaaaaaaa(图c)大小:方向:√√?√√√√√√√?√30sin30cos60sin30sin0:30cos30sin60cos30cos0:krtenenakrtenetaaaaaayaaaaax30sin4.030cos60sin30sin2.04.030cos4.030sin60cos30cos2.02.0rterteaaaa)/(58.12sradeAB12习题2偏心轮C作匀速定轴转动,求图示时刻顶杆AB的瞬时加速度;srad/5mOC1.0OCAC动点:AB杆A端点;动系:偏心轮;动点:偏心轮轮心点C;动系:顶杆AB;13习题3平行四边形机构O1ABO2中,求CD杆图示时刻的瞬时速度与瞬时加速度;srad/102/2sradmAO1.01动点:CD杆C端点;动系:AB杆(平行移动);reavvvreaaaaAceaaa14例7.3-4求机构在图示时刻CD杆的瞬时加速度;mAB4.0smvA/2.02/1smaABCAC30动点:CD杆C端点;动系:AB杆;牵连点:AB杆上c点reavvvtABnABABaaaaAB杆:etAcnAcAcaaaaaABkreaaaaa动点:15mAB4.0smvA/2.02/1smaABCAC30解动点:CD杆C端点,动系:AB杆;牵连点:AB杆上c点etAcnAcAcaaaaatABnABABaaaaAB杆:(图示)30sin60sin0:tABnABAaaax4.0nABa693.2tABa2.0nABa347.1tABareavvv(图示)1e173.0rv16krtAcnAcAaaaaaaa动点:大小:方向:√√?√√√√√√√?√346.02rekva30cos30sin30cos30sin0:30sin30cos30sin30cos0:krtAcnAcakrtAcnAcAaaaaayaaaaax30cos346.030sin30cos347.130sin2.030sin346.030cos30sin347.130cos2.010raraaa377.0ra178.1aa(实际方向与图示假设方向相反)17，习题4AB杆的A端沿水平线向右作匀加速直线运动;运动过程中该杆始终与半圆凸轮相切;求图示时刻AB杆的角加速度;30smv/12/2smamr1.0动点:凸轮圆心O;动系:AB杆;牵连点:动系中o点;reavvv(图示)ervkreaaaaa0tAonAoAoeaaaaaeAotAora182再次推导平面运动图形上任意两点之间的速度/加速度合成关系例7.3-5设平面图形s在固定坐标系xoy平面内运动(图a),A/B是图形s上的任意两点,已知图示时刻A点的速度/加速度及平面图形s的角速度/角加速度;求该时刻图形s上任意一点(B点)的运动(速度/加速度);动点:图形s上的B点;动系:平行坐标系(平移);牵连点:动系中b点;''Ayx19reavvvrbBvvvABerrvABABrvvABvAbvv(动系平动)ABABvvvABABrv20reaaaarABaaa动系平移:0katrnrraaatrnrABaaaa2122xayacM22m（）M(m)ⅡxyOevrv1me1ve2vr2vr2vr3vrv'M3xayac(t+t)LⅠ(t)bbeMxyOeaⅠ(t)LbkarvraCAOvavrve45CABO45AOaanaatakaraenaet45CxyevBvavrveA6060v=vB60aeartarnaa60xyvCABraBaeartarnaa60xyOrC60ABC(c)O60vavrveABx'y'60COakAaraenaet30x60yaataan30Bx'y'30DCABO30CBO30aaakaenartAarneaartarnABO30aanC30B60AO1O2CDAO1BCDvAvevrva6060O2ABCDaraaaAnO2O1aAt23B(b)Axyyx''OsvrvbvAvBB(b)Axyyx''OsabaAartarnB(b)Axyy'Ox'svAaAOrvBAvAraBaAaAOnaAOtkaO(o)BACDvAaABAC(c)DPvAvBvevrva3030BADaAaAcnaABnaActaABt30aB60C(c)xyaActaABAC(c)DxyakaAcnar3030aavOPAevrvB