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A Principal axis of rotation

  1. Jul 24, 2017 #1
    I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation. However, if the small difference is a problem I can make it bigger (within the linear range of this specific simulation).

    I have read about Rodriguez' rotation formula and know how to find the axis of rotation, but how can I incorporate the translation components as well? Any help is appreciated!

  2. jcsd
  3. Jul 24, 2017 #2
    Every displacement can be decomposed into a translation plus a rotation. For specificity, consider the center of mass of the body for a reference point. In the initial location, the CM has a particular position. In the second location, the CM has a second particular location. The translation from the first to the second is the required translation. Then the change in orientation is simply a rotation about the CM.
  4. Jul 24, 2017 #3
    I understand this, but the movement could also be described by a single rotation around some axis in space. I am wondering how I can compute this axis?

    Rgds /Daniel
  5. Jul 24, 2017 #4
    um,... I don't think so. Suppose the movement is nothing more than a simple translation with no rotation at all?
  6. Jul 24, 2017 #5
    Would'nt translation correspond to a rotation around an axis at infinte distance? Anyway, I know that is not the case for me. The movement will be a combination of translation and rotation.
  7. Jul 24, 2017 #6
    If rotation about an axis at an infinite distance means anything, then I suppose you could interpret it this way. In reality, I don't think it means anything at all, because we cannot realize it.
  8. Jul 24, 2017 #7


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    Conceptually a rotation around an axis at an infinite distance may mean something, but I don't think you want to go in that direction -- especially if you have to do real calculations.
  9. Jul 25, 2017 #8
    I think it may be interpreted: as r goes to ∞ the curvature approaches a straight line.
    Anyways, this is not my question: Howto find the principal axis of rotation from a combination of rotation and translation?

  10. Jul 25, 2017 #9


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    (1) You are looking at the Instantaneous Centre of Revolution concept but in 3D instead of the 2D where it is more commonly used ?

    Finding the ICR for any particular motion is just maths but for non simple motions and continuous motions it usually leads to a dead end as far as practical use and getting accurate answers is concerned .

    For complex motions even a small movement of the body can change the location of the ICR by a large amount . In a general motion it can even flip from one side of a body to another or go to infinity and back again .

    (2) The above is for an unconstrained motion .

    Your actual problem may involve a partially constrained motion . Addition of constraints generally makes this type of problem easier to deal with .
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