Kinematic for dummies

Jean-Paul Molina 1

Mthodes qui fonctionnent dans tous les cas !

1 Si lon demande ( / )xV M RJJJJJJJJJJJG

alors on utilisera la dfinition :

on drive le vecteur position xO MJJJJJG

et on utilise la relation de Chasles.

2 - Si lon demande ( , / )y xV M R RJJJJJJJJJJJJJJJGJ

, alors on utilisera la distribution des vitesses avec

( torseur cinmatique ) par ordre de prfrence :

a- un point de vitesse nulle ( ex : si ( , / ) 0y xV I R R =JJJJJJJJJJJJJJG G

)

( , / )y x yxV M R R MI= JJJJJJJJJJJJJJJGJ JJJG JJJG

b- lorigine de yR ( , / ) ( , / )y x y xy yyxV M R V R MOR RO= + JJJJJJJJJJJJJJJGJ JJJJJJJJJJJJJJJGJ JJJG JJJJJG

en remarquant que ( , / ) ( , / ) yy y x y xx

Rx

d OV O R R V O R

dOt

= =

JJJJJGJJJJJJJJJJJJJJJGJ JJJJJJJJJJJJG

c- un point dont la vitesse est connue ( , / ) ( , / )y x y x yxV M R R V AR RA M= + JJJJJJJJJJJJJJJGJ JJJJJJJJJJJJJJG JJJG JJJJG

Bien sr, on peut dans ce 2 utiliser la composition des repres

( , / ) ( , / ) ( , / )y x y z z xV M R R V M R R V M R R= +JJJJJJJJJJJJJJJGJ JJJJJJJJJJJJJJJG JJJJJJJJJJJJJJJG

3 Pour les acclrations, on nutilise que les dfinitions ( drives des vecteurs vitesses en observant dans quel repre on effectue la drivation )

Attention : Dans le cas gnral ( , / )

( , / ) y xy xRx

V M R RM R R

dt

JJJJJJJJJJJJJJJGJJJJJJJJJJJJJJJJG

sauf si M est fixe dans yR 4 Pour traduire le roulement sans glissement, on a bien souvent intrt passer par le rfrentiel fixe.

Ex : 0 0( , / ) 0 ( , / ) ( , / )y x y xRV I R R V I RR V I R= =JJJJJJJJJJJJJJG G JJJJJJJJJJJJJJG JJJJJJJJJJJJJGJ

Et lon dveloppe chacun des membres en utilisant 2a. Il y a quelquefois des mthodes plus rapides, mais ce ntait pas le but ici.

koi29

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