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Homework Help: Number of links and joints in a linkage

  1. Dec 30, 2015 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    M = 3(L – 1) – 2J

    L= number of links, J = number of joints

    3. The attempt at a solution

    As far as I can see, using the above L and J values for each linkage yields the correct M value. However, the L and J values lead me to think I'm missing something.

    Can someone explain why L = 4 for the first and second linkages? In the first one there are only 3 links and in the second linkage there are only 2 links. Also, surely for the second one J = 3 since there are only 3 visible joints?

    Similarly, why does L = 5 for the bottom left linkage when there are only 4 links and why does L = 4 and J = 3 for the bottom right linkage when there are only 2 links and only 2 joints?
  2. jcsd
  3. Jan 2, 2016 #2


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    Gold Member

    In the first three, there is effectively a link between the two fixed platforms. The distance between them cannot change.
    The last one has three joints: one at the base, the slider itself, and a third at the top of the slider.
    I don't see a fourth link, but I know nothing of this subject so could be missing something.
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