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Math Help - need help with kinematics:epicyclic train

  1. #1
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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):


    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).
    Last edited by boolean; February 9th 2009 at 02:01 PM. Reason: image too small
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