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

e国b口 LECTURE 7 Kinematic Analysis of Mechanisms 1日 OUTLINE Some important definitions ©Simple cases study Coriolis acceleration Vector graphical analysis method Complex vector analytical method ME371 Design Manufacturing ll 1

1 Kinematic Analysis of Mechanisms LECTURE 7 ME371 Design & Manufacturing II OUTLINE Some important definitions Simple cases study Coriolis acceleration 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 axis 2 R Real axis ME371 Design Manufacturing ll Some important definitions Velocity-Rate of change of displacement is velocity.Velocity can be linear velocity of angular velocity. First order: d(Re)=Re+R(e"j0)=Re+ROje d de Angular Velocity:@ dt yImaginary axis Linear Velocity:V=R R Real axis R 2

2 ME371 Design & Manufacturing II 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 of 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+20Rj e+Rj ero-ROe Angular Acc:a==do yImaginary axis Linear Acc: a=求=dy R dt Real axis R Simple cases study A link in pure rotation ⑧When point A is moving ME371 Design Manufacturing ll 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 ME371 Design & Manufacturing II A link in pure rotation When point A is moving Simple cases study

Simple cases study A link in pure rotation +0 Displac- ement Rp=pele RPA N PA Velocity Ve=pojel +2 02 Acceleration APA Apa=pajeo-po'e =A'm+Am A ME371 Design Manufacturing ll Simple cases study +0 When point A is moving Displac- 2 ement Rp=R+Rp4 V. Velocity 可=f4+4 =fa+pe(to）) Graphical solution: VA 4

4 ME371 Design & Manufacturing II 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       V pe i V V V i A P A PA         Graphical solution:

Simple cases study When point A is moving APA +2 -02 Displac- ement Rp=R+Rm4 APA Velocity 可。=f+ipA A =V,+pe(io) Accelerati on A。=A4+Ap4 AP APA =A-pe+iape AA Coriolis Acceleration Position of slider R=pel Velocity of slider 7。=eigte R Transmission Slip velocity velocity 0 Acceleration: An=peio+pe(io)'+pe”ia+e+pe°i0 Combining terms: 4,=[-po）+i(pa+22o]e Coriolis acc.occurs when a body has vslip 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       V pe i V V V i A P A PA         2 P A PA i i A AAA A pe i 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