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Finding the rotational moment of inertia of a multihinged arm

  1. Jun 11, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm trying to calculate the moment of inertia of a multihinged arm, with one joint at the shoulder and a second joint at the elbow. Each joint has a set of local axis, with y being a vector pointing down the shaft of the cylinder, z being a vector pointing up, and x being a vector pointing towards the right. The forearm is free to rotate about the local z axis of the elbow, and the entire arm is free to rotate in all three directions at the shoulder joint. The two arm segments are being modeled as solid cylinders with masses m1 and m2, lengths l1 and l2, and radii r1 and r2. Given a rotation theta around the elbow z axis, I need to find the overall moment of inertia around the shoulder joint. A crudely paint drawn diagram of the system is shown below:

    http://img5.imageshack.us/img5/1122/momentofinertia.jpg [Broken]

    2. Relevant equations

    Moments of inertia around the center mass:

    Iy = mr2 / 2
    Ix = Iy = 1 / 12 * m * ( 3r2 + L2

    Parallel axis theorem to get Iy and Iz around the joint:

    Iend = Icm + MD2, where D is equal to L/2.

    3. The attempt at a solution

    When theta is a multiple of 90, I believe I can simply again use the parallel axis theorem to get the moment of inertia of the forearm around the shoulder joint, keeping in mind that I will not always be adding Iy and Ix together depending on whether theta is a multiple of 90 or 180. However, when the rotation is any value in between and the axis are no longer parallel, I cannot use the parallel axis theorem to find the moment of the second segment. So, this is the point where I'm stuck, and I'm hoping there is some equation for a cylinder rotated an arbitrary angle that I have been unable to find. Thanks for your help.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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