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Homework Help: Four bar linkage forward kinematics question

  1. Mar 6, 2009 #1
    Hi, this is my first post on this forum.

    I have a design for a machine with two mutually perpendicular revolute joints, i.e.

    a base,

    a hinged joint,

    an arm,

    a hinge perpendicular to the first joint,

    second arm.


    Using D-H forward kinematics I've got code working using 4*4 transformation matrices.

    Now, there's a proposal to change one of the revolute joints to a 4-bar linkage.
    All the joints in the new linkage will be parallel to the original axis.

    (ASCII art attempt:)

    (+ = joint)

    |
    +
    |
    -----

    becomes

    --------I--------
    ---+__I___+
    ---/ ---------\
    --/------------\
    -+__________+
    ---------------------

    This means the simple revolute joint must be replaced by four
    offset parallel revolute joints, which form a closed loop.

    The simplicity of the original arrangement meant it was quite straightforward
    to do the kinematics. The proposed arrangement has me confused.

    So, I _think_ I need to replace the simple 4*4 matrix describing a revolute joint,
    with a matrix describing the 4-bar linkage.

    The treatments I've found are too general for me to figure it out.

    Can anyone out there help me? How do I derive the new matrix?
    Or is there a better approach?

    Winston
     
    Last edited: Mar 6, 2009
  2. jcsd
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