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Analytical kinematics of a 6-bar mechanism

  1. Apr 16, 2014 #1
    1. The problem statement, all variables and given/known data
    This is a mechanism I'm working with for my undergrad project (its Modelled in Msc ADAMS)
    https://www.flickr.com/photos/35430110@N04/13902494524/
    https://www.flickr.com/photos/35430110@N04/13902494524/
    And to give you an idea of how it operates;
    position 1
    https://www.flickr.com/photos/35430110@N04/13902164703/
    https://www.flickr.com/photos/35430110@N04/13902164703/
    position 2
    https://www.flickr.com/photos/35430110@N04/13902529454/in/photostream/
    https://www.flickr.com/photos/35430110@N04/13902529454/in/photostream/

    the topmost link (hereforth referred to as L3) is always horizontal(parallel to the ground) because of the vertical slider pair (the red and green links). The link hinged to the fixed frame is L2, and the other link hinged to the horizontal slider (L5) and L3, is link L4, it is a floating link (it rotates as well as translates)

    I've checked the grueblers criterion for the mechanism, the DOF is 1, and the input at the topmost link L3 is transferred to the sider L5.

    no of links= 6
    no of lower pairs= 7
    DOF = 3(6-1) - 2(7)
    = 15-14
    =1

    2. Adopted methodology
    I want to perform a kinematic study on the mechanism analytically so I can use MATLAB to get results for different parameters (link lengths, velocities etc)

    Taking reference from this pdf from U of Arizona :http://www.u.arizona.edu/~pen/ame352/Notes%20PDF/3%20Analytical%20kinematics.pdf

    I devised the position equations, which I verified by using a solidworks line model (i defined the constraints using Relations in Sworks)
    https://www.flickr.com/photos/35430110@N04/13902410773/
    https://www.flickr.com/photos/35430110@N04/13902410773/

    I devised the equations by splitting the mechanism into two loops as shown below:
    https://www.flickr.com/photos/35430110@N04/13902982704/
    https://www.flickr.com/photos/35430110@N04/13902982704/

    I then differentiated the Position eqns w.r.t 'T' (time) to get the velocity equations and again to get the acceleration equations, when I tried to verify the velocity equations by assigning one value to say the angular momentum of L2, I dont get corresponding answers from ADAMS or from Sworks (in Sworks i change the position very slightly and find the Δθ , Δø and the distance the slider moves)

    3. The attempt at a solution
    ∠θ is the angle between L2 and L3 ; ∠ø is the angle between L3 and L4, L3 is always parallel to the ground; at no time will θ or ø be ≥ 90°
    https://www.flickr.com/photos/35430110@N04/13902964863/
    https://www.flickr.com/photos/35430110@N04/13902964863/

    My position equations are as follows:

    for the first chain;
    Along X axis: L2*cosø - L3 + L4*cos(360-θ) = OD; (where OD is the distance(X) of the slider from the origin)
    Along Y axis:L2*sinø - 0 + L4*sin(360-θ) =0;

    differentiating wrt time, I get the Velocity equations:
    -L2*sinø*w2 -L4*sinθ*w4= Vslider; (where w2=dø/dT | w4= dθ/dT | Vslider=dOD/dT)

    L2*cosø*w2-L4*cosθ*w4=0;

    similarly, for the second chain;

    Position equations:

    Along X axis: L2*cosø - AE - OG = 0;
    Along Y axis: L2*sinø - EF - FG = 0 ; (EF can be taken as constant, so FG is the variable)

    velocity eqns:
    -L2*sinø*w2 = Vog (Vog is dOG/dT)

    L2*cosø*w2= Vy (where Vy is dFG/dT , which is effectively the Y component of velocity of topmost link L3)

    I'd go on with the acceleration equations , but if I can't prove that the velocity equations hold, there's no point in giving the acceleration equations.

    I have no clue what im missing here, I've been over these equations tons of times with no luck,it seems I might be missing something thats right under my nose. please help
    many thanks in advance
     
    Last edited: Apr 16, 2014
  2. jcsd
  3. Apr 16, 2014 #2

    SteamKing

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    Staff Emeritus
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    Homework Helper

    If you were trying to embed an internet link or a picture, it didn't make it into the post.
     
  4. Apr 16, 2014 #3
    I cant seem to get the pictures to attach, so I've just included the links, hope that helps :\
     
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