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MULTI-ROTOR APPARATUS AND METHOD FOR MOTION SCULPTING

  • US 20150367223A1
  • Filed: 09/01/2015
  • Published: 12/24/2015
  • Est. Priority Date: 10/09/2003
  • Status: Active Grant
First Claim
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1. A method for determining an angular relationship between an implement shaft plane and an implement face plane of an implement moved by a person during performance of a useful or recreational function, the implement including an implement shaft and an implement surface attached to the implement shaft configured to impact an object during the performance of the useful or recreational function, the method comprising:

  • (a) sensing motion of the implement at a first position on or adjacent the implement shaft;

    (b) determining a first shaft velocity vector corresponding to the motion of the implement shaft at the first position;

    (c) sensing motion of the implement at a second position on or adjacent the implement shaft that is spaced apart from the first position;

    (d) determining a second shaft velocity vector corresponding to the motion of the implement shaft at the second position;

    (e) determining an average shaft velocity vector based at least in part on the first shaft velocity vector and the second shaft velocity vector;

    (f) determining a shaft vector aligned with the first position and the second position on or adjacent the implement shaft;

    (g) determining a first normal vector based on a cross product of the shaft vector and the average shaft velocity vector according to
    {right arrow over (N)}CS={right arrow over (r)}CS×

    {right arrow over (ν

    )}avg,CS where {right arrow over (N )}CS is the first normal vector, {right arrow over (r)}CS is the shaft vector and {right arrow over (ν

    )}avg,CS is the average shaft velocity vector;

    (h) determining an implement face vector aligned with the implement face plane of the implement;

    (i) determining a second normal vector based on a cross product of the shaft vector and the implement face vector according to
    {right arrow over (N)}CF={right arrow over (r)}CS×

    {right arrow over (r)}
    CF where {right arrow over (N)}CF is the second normal vector, {right arrow over (r)}CS is the shaft vector and {right arrow over (r)}CF is the implement face vector;

    (j) determining an angle θ

    between the first normal vector and the second normal vector according to

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