Extract Euler angles from angular velocity profile

I Solved inverse velocity (joint velocity) at velocity level problem. So, I have actual orientation of the manipulator. Now I wanted to get the desired orientation from angular velocity that I used to solve inverse kinematics. So I can calculate the orientation error. $$\boldsymbol{V} = \begin{vmatrix} 0 \\ 0 \\ 0 \\ \hline 10 \cos(2 \pi t) \\ 10 \sin(2 \pi t) \\ 5 \cos(2 \pi t) \end{vmatrix}$$ is a velocity profile used to solve joint velocity.
Thanks

• Are the non zero components the angular or the linear part of the velocity twist? Are you using Ray or Axis coordinates for your twists? Apr 15 '20 at 18:10
• The twist is in axis order. $$\boldsymbol{V} = \begin{vmatrix} \boldsymbol {v}\\ \hline \boldsymbol{\omega} \end{vmatrix}$$ . This velocity is regarded as the velocity profile of moving plate given to solve inverse rate kinematics. Thanks
– Raul
Apr 16 '20 at 9:22