# Solve for Center of Rotation

Consider a situation (as shown in attached image), Points D and F moving on a 2-D plane in a circular trajectory with center A. After certain time t, the points D, F moved to points E and G respectively. Angle DAE and FAG is equal. At the same time, Point B moves to point H (opposite direction with same center of rotation A). Assume I have the coordinates of D and F from point B, also E and G coordinates from points H. Note: All the points have the center A.

How do I solve for the coordinates of center A either from B and H.

The problem presented above is simplified in 2D.
I'm trying to use the least square approach presented in here, to estimate the center of rotation. But in the above approach the observer is static (i.e. points B and H are same), When I include the movement of the points B (to H) the approach didn't converge to right result.

modified equation :: $$\label{eqn1} C = \sum_{p=1}^{P} \sum_{k=1}^{N} \left[\left({\mathbf{v}}_{k}^{p}- \mathbf{m}_k\right)^2 - {\left({r}^p\right)}^2\right]^2$$

where ${\mathbf{v}}_{k}^{p}$ is the $p^{th}$ vector in the $k^{th}$ time instance, center of rotation in $k^{th}$ instance $m_k$; and the radius of the sphere marked out by the $p^{th}$ vector is $r^p$

• Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos Jan 29 '18 at 1:44
• Thanks @josé... Sure I'll edit the post with more details.. – akum Jan 29 '18 at 2:00