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Subject: Re: Find instant axis of rotation
Date: Tue, 27 Oct 2009 22:17:04 +0000 (UTC)
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Dear Henning!

> I need to estimate/calculate the location of a rotation axis for a number of points in space. I have the position of the all of points (x,y,z) at all of the different times. The relative location of all the points remain the same as they are all part of a rigid body.
> 
> I started out by creating a rotation matrix around the origin (by using 3 points in step n and step n+1 and then solving for the rotation matrix). I then used an Axis-Angle approach to calculate the axis around which they rotate.
> 
> The problem is that I am pretty sure that for the actual motion the axis doesn't go through the origin but is translated somehow in space. But I'm not sure how to find this translation. Anyone have any ideas?
> 
> Another idea I had was to to "fit" a cylinder to the points. If the points from two steps are all on the surface on the cylinder, the cylinder axis must be the instant axis of rotation. Any ideas on how to do such a calculation (preferably analytically).

Ask Google for "helical axis" or "screw parameters".
On the KWON3D site, the orientation of the axis is not clearly defined: If you assume a positive angle, the anti-symmetrical H-H' defines the orientation of the axes.
A simple method is shown in:
http://robotics.caltech.edu/~jwb/courses/ME115/handouts/rodriguez.pdf

Be aware that there are some numerical problems, e.g. if the coordinates are noisy or the rotational angle is tiny...

Good luck, Jan