How do I find a center of rotation having a set of 3D points ?

I have to find the position of a center of rotation for an object. For that I have the X,Y and Z coordinate of my object.

To clarify : The coordinates are from a pendulum oscillating and I have to find the center of the pivotating link

I haven't found a solution yet and I don't really know how to proceed.

[James Tursa]

You have 3D coordinates of the endpoint? Can't you just fit a circle/sphere to those points and then the center of the circle/sphere would be your pivoting link?

Answer 1

[Image Analyst]

See the FAQ: How_can_I_fit_a_circle_to_a_set_of_XY_data?

Answer 2

[Stijn Haenen]

If each point represent the same amount of mass, the center of rotation is just the average position of all poisitions, when each point has its own mass you should use this formula to compute the center of mass:

R=1/sum(m_i)*sum(r_i * m_i)

see https://en.wikipedia.org/wiki/Center_of_mass

[Image Analyst]

The center of a circle is not at the center of the average of points in some arc that's a portion of the circle (like their pendulum).