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Mobility of a mechanism

  1. Jan 27, 2016 #1
    • Member advised to retain the formatting template headings.
    HW_1.jpg
    I need to find the mobility of the pictured system
    I have labeled the 5 links with black numbers and the 6 joints with red letters for convenience


    Attempt at a solution: I know the mobility equation is M = 3(N-1) – 2(J1) – J2 + R, where N = number of links, J1 is the number of 1 DoF Joints, J2 is the number of 2 DoF joints and R is the number of redundancies.

    So far, I have 5 links (where 1 is the ground and 4 is the entire disk), 5 1 DoF joints (A, C, D rolling without slipping, E & F), and one 2 DoF joints (B, a 2 DoF slider).

    Plugging that into the mobility equation yields 3(5-1) – 2(5) – 1 = 12 – 10 – 1 = 1

    However, upon inspection, the system has 2 degrees of freedom and not 1 as the mobility equation suggests. I have been trying to reason through where I may have went wrong, or if there are any redundancies in the system to no avail. Any help would be appreciated.
     
  2. jcsd
  3. Jan 27, 2016 #2
    Does it help if you visualize the disk mobility if link 3 does not exist?
     
  4. Jan 28, 2016 #3
    Would link 3 be redundant since the position/rotation of the disk already has only 1 DoF due link 5 and the ground (link 1/joint D)? Then you have 1 DoF due to link 2 which wouldn't be connected to anything else, so a total of 2 DoF for the mechanism with one redundancy.

    Am I on the right track with that logic?
     
  5. Jan 28, 2016 #4
    Unfortunately I have no idea!
    I found the problem 'interesting' and studied the drawing for a while. I realized that joints A, B, C were free to rotate and link 2 could have any arbitrary length. That implied they did not constrain the location of joint C.

    Hopefully someone else on the site can evaluate your formal evaluation. Im' an electronics guy and most of my mechanics is what I've picked up along the way.
     
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