上海交通大学：《Design and manufacturing（ME371、ME337）》课程教学资源（讲义）Lecture 7 Kinematic Analysis of Mechanisms

e+口 LECTURE 7 ME371/ME337 DESIGN AND MANUFACTURING Kinematic Analysis of Mechanisms Covered:Ch7-in Design of Machinery OUTLINE Some important definitions Vector graphical analysis method Complex vector analytical method 1

1 Kinematic Analysis of Mechanisms LECTURE 7 ME371/ME337 DESIGN AND MANUFACTURING Covered：Ch7- in Design of Machinery OUTLINE Some important definitions Vector graphical analysis method Complex vector analytical method

Some important definitions Displacement R=Reio Linear displacement:All particles of a body move in parallel planes and travel by same distance is known as linear displacement Angular displacement:A body rotating about a fixed point in such a way that all particles move in circular path is known as angular displacement yImaginary axis Real axis Some important definitions Velocity-Rate of change of displacement is velocity.Velocity can be linear velocity or angular velocity. First order: d(Re)=ke+R(ej0)-keRoje d de Angular Velocity:@ dt yAImaginary axis Linear Velocity:V= dR R R dt Real axis R 2

2 Displacement Linear displacement: All particles of a body move in parallel planes and travel by same distance is known as linear displacement Angular displacement: A body rotating about a fixed point in such a way that all particles move in circular path is known as angular displacement Some important definitions j R e  R  Velocity - Rate of change of displacement is velocity. Velocity can be linear velocity or angular velocity. Some important definitions First order: ( ) ( )= d j jj j j R e Re R e j Re R j e dt             Angular Velocity: d dt    Linear Velocity: d dt V  R

Some important definitions Acceleration-Rate of change of velocity Second order: (Re)=ieP+dje+(d+0jeP+RaUej0 d =Re+20e°+iRie-R0ea Angular Acc: a-0-do yAImaginary axis dv R Linear Acc: a== dt Real axis Some important definitions First order: d(Re)=Re+R (ej0)-ke+Roje dt Second order: (R e)=(R-RO)e+20R+Ry d 20Rj eo Tangential Acceleration: perpendicular to the radius of Rj e rotation. Normal Acceleration: R centripetal component at 180 to -RO-en the angle of the original pisiton vector 3

3 Acceleration- Rate of change of velocity Some important definitions 2 2 2 Second order: ( ) ( ) ( ) ( ) = 2 jj j j j j j jj d R e Re R j e RR j e R je j dt Re Rj e Rj e R e                                 Angular Acc: d dt       Linear Acc: d a R dt    v X Y O R  j j e j  Re   j R j e    j e  j Re   2 j R e     2 j Rj e     j Rj e    P 2 2 2 Second order: ( ) ( ) +(2 )        jj j      d Re R R e R Rje dt First order: ( ) ( )= d j jj j j R e Re R e j Re R j e dt             Some important definitions Tangential Acceleration: perpendicular to the radius of rotation. Normal Acceleration: centripetal component at 180 to the angle of the original pisiton vector

Simple cases study A link in pure rotation +0 R孰 Displac- ement R =pero V PA Velocity Vra=poje 1 Ars=pajelo-po'ero +2 Acceleration =A'm+A"m 005 APA Simple cases study ©When point A is moving Displac- Rp=R+R24 RPA ement 可。=可+4 Velocity T+peo（jo) o Graphical solution: VA 4

4 A link in pure rotation Simple cases study Displac￾ement Velocity Acceleration j PA pe  R  j PA p je    V 2 j j PA PA PA p je p e         t n A A A When point A is moving Simple cases study Displac￾ement Velocity RRR P A PA     P A PA j A V V V V pe j           Graphical solution:

Simple cases study +2 When point A is moving APA 02 Rp=R+Rm4 A Displac- ement N PA 可。= 可+了 Velocity V+peio (jo APA Accelerati a。=A,+44 APA on =A-o'per+japer AA Simple cases study-Coriolis Acceleration Position of slider 02 Rp=pelo 2 Velocity of slider V,=De"ig+pe Transmission Slip -X velocity velocity Acceleration: A,=pei0+pe（(io）'+peia+e°+eio Combining terms A,=[p-p0）+i(pa+220]e Coriolis acc.occurs when a body has vasp and w Slip Normal Tangential Coriolis 5

5 When point A is moving Simple cases study Displac￾ement Velocity Accelerati on RRR P A PA     P A PA j A V V V V pe j           2             P A PA j j A AAA A pe j pe Coriolis Acceleration i . R p pe    Position of slider Velocity of slider i i V pe i pe p        Transmission velocity Slip velocity   2 i i i ii A p pe i pe i pe i pe pe i                Acceleration:     2 2 i A p p p ip p e              Combining terms: Slip Normal Tangential Coriolis Coriolis acc. occurs when a body has vslip and ω Simple cases study——