need help with kinematics:epicyclic train

• February 9th 2009, 12:46 PM
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need help with kinematics:epicyclic train
Hello I hope you can help me answer the first question from my kinematics problem, I put the topic below (click and press "ctrl +" to zoom "ctrl -" to zoom out and " Ctrl 0 "to return to original position):
http://nsm01.casimages.com/img/2009/...5563130256.jpg

The subject is of course in french so I translated the statement and the first question that I have a problem to continue my exercise (I ask you to watch especially the pattern but if you understand French, so much the better):

"The study focuses on a winch.
The movement input is given to the shaft 1 by an electric motor.
The drum 5 compared to 0 causes the rack cable. The winch is composed of 2 gearboxes fitted as standard.

-The letter Z is used to indicate the number of teeth of a gear :
$Z_1=30; Z_2=45; Z_3=22; Z_4=34; Z_52=120; Z_54=90; R_{drum}=60mm;$
-the frequency of rotation of the engine is written $N_{mot}=N_{10}=3000rpm$
-The coordinate systems $R_i (\vec{x_i},\vec{y_i},\vec{z_i})$ are associated with the solid "i"."

I mention a few things:
$Z_{54}$ = number of teeth on the part of the part 5 in contact with the part 4
$\omega_{10}$ means speed of the part 1 compared to the part 0 ... etc.
The part in blue on the photo is the drum.

The frame refers to the part 0 on the diagram. It is the fixed part of the mechanism.

Here is the first question:

"By writing the condition of non slip in C and D, determine the expression of the function f( $\omega_{10}, \omega_{30}, \omega_{50}, Z_1, Z_2, Z_{52}$).

Below, what i've done yet:

-rolling without slipping (RWS) in C: $\vec{V_C 25}=\vec{0}$
$\vec{V_C 25}=\vec{O_{2}25}+\vec{CO_2}$^ $\vec{\Omega_{25}}$.

-RWS in D: $\vec{V_D21}=\vec{0}=\vec{V_D 20}-\vec{V_D 10}$
$\vec{V_D 20}=\vec{O_{2}20}+\vec{DO_2}$^ $\vec{\Omega_{20}}=\vec{O_{2}23}+\vec{V O_{2}30}+\vec{DO_2}$^ $\vec{\Omega_{20}}=\vec{R_3}$^ $\vec{\Omega_{30}}+\vec{DO_2}$^ $\vec{\Omega_{20}}$

with $R_3$: the radius of the movable arm or "carrier" (in red on the diagramm), in french we called this :"porte satellite" ( I hope you understood).

I mention a few things:
$\vec{V_D21}$ means sliding speed of 2 compared to 0.

So I just wanted ta said that this homework (this exercise is only one part) is on Wednesday morning, less than two days (given that Europe was at 6 hours ahead of the USA), then if you could take the time to answer me thank you in advance, hoping to have been sufficiently clear.(despite my little english).