9.1 Simplification of plane motion of rigid body and itsdecomposition4.Plane motion is decomposed intotranslation and rotationyMMSMxChoose any particle O' on the plane figure S as the base particle, and then the plane motion(absolute motion) can be decomposed into the translation (implicated motion) with the baseparticle and the rotation (relative motion) with the relative base particle.The velocity and acceleration along with the base particle are related to the choice of thepositionofthebaseparticle
4. Plane motion is decomposed into translation and rotation O x y Choose any particle on the plane figure S as the base particle, and then the plane motion (absolute motion) can be decomposed into the translation (implicated motion) with the base particle and the rotation (relative motion) with the relative base particle. O O M S The velocity and acceleration along with the base particle are related to the choice of the position of the base particle. 9.1 Simplification of plane motion of rigid body and its decomposition S O M O M
9.1 Simplification of planemotionof rigid bodyanditsdecomposition4.Plane motion is decomposed intotranslation and rotationyM2MMAO文OLxAgA0Aβ = △β' but の = limlim△tAt>0△tAt-→0similarly = 'So の=の'That is, at any instant, the angular velocity and angular acceleration of the graph around anyparticle in its plane are the same. Angular velocity and angular acceleration have nothing to dowiththe choiceof base particle position
O M S 4. Plane motion is decomposed into translation and rotation O x y S O M M O = but t t = → 0 lim t t = → 0 lim So = similarly = That is, at any instant, the angular velocity and angular acceleration of the graph around any particle in its plane are the same. Angular velocity and angular acceleration have nothing to do with the choice of base particle position. x y x y 9.1 Simplification of plane motion of rigid body and its decomposition
9.1 Simplification of plane motion of rigid body and itsdecompositionTosum up1,The plane motion of a rigid body can be divided into translation with cardinalparticle and rotation with cardinal particle2, The motion of the figure along with the base particle is related to the choice ofthe position of the base particle. The rotation part has nothing to do with thechoiceofthebaseparticle3、The angular velocity and angular accelerationof a graph around any particle inits plane are the same.The absolute angular velocity and angular accelerationofthe graph
To sum up 1、The plane motion of a rigid body can be divided into translation with cardinal particle and rotation with cardinal particle. 2、The motion of the figure along with the base particle is related to the choice of the position of the base particle. The rotation part has nothing to do with the choice of the base particle. 3、The angular velocity and angular acceleration of a graph around any particle in its plane are the same. The absolute angular velocity and angular acceleration of the graph. 9.1 Simplification of plane motion of rigid body and its decomposition
9.2 Velocity analysis of particles on a plane graph1.method of baseyparticleBAs shown in the figure, know the velocityofa particle A in the graph is Va , theangular velocity of the graph is , andxfind the velocity at any particle B of theAgraph.0xidea:The consolidatedTranslation with thetranslational coordinatebaseparticledecompose1,Analysisofrigid bodysystem is established atthe base particlemotion inplaneThe rotation aboutthe cardinal particle2,Thevelocity synthesistheorem ofparticle
idea： 9.2 Velocity analysis of particles on a plane graph 1、Analysis of rigid body motion in plane Translation with the decompose base particle 2、The velocity synthesis theorem of particle The rotation about the cardinal particle 1. method of base particle A v B O x y A x y As shown in the figure, know the velocity of a particle in the graph is , the angular velocity of the graph is , and find the velocity at any particle B of the graph. A A v The consolidated translational coordinate system is established at the base particle
9.2Velocityanalysis of particles on aplanegraph1.method of baseparticle公PAnd choice B is the moving particle, Ax'y' isVthe dynamic system (with translational motion)公7B1BAVelocity synthesis theorem of particle A=v+Vx'VAA1VNBAVBA = BA·OVABxVB=VA+VBAThat is,the velocityofanyparticlein theplanefigure is equal tothevector sum ofthevelocityofthebaseparticleand the rotational velocity of theparticlerelativetothebase particle. This is the basis particle method for the velocity synthesis of planemotion
1. method of base particle Velocity synthesis theorem of particle A: a e r v v v = + B A BA v v v = + vBA = BA 9.2 Velocity analysis of particles on a plane graph That is, the velocity of any particle in the plane figure is equal to the vector sum of the velocity of the base particle and the rotational velocity of the particle relative to the base particle. This is the basis particle method for the velocity synthesis of plane motion. And choice B is the moving particle, is the dynamic system (with translational motion) Ax y A v B O x y A x y A v B v BA v B v A v BA v