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I am trying to calculate the angular velocity of end effector of two-link robot arm. Can anyone help me to find it?

If $q_1$, $q_2$ are joint angular position and $\dot{q_1}$ and $\dot{q_2}$ are joint angular velocities, and $\omega$ is angular velocity of end effector, then I use $\omega=\dot{q_1}+\dot{q_2}$. Is that correct?

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Yes, angular velocities are additive if that is all you're looking for (i.e., $\omega_2$ expressed in the base frame of $\omega_1$). If you are trying to find the velocity of a point on link 2, then you need to add an $\omega $x$ r$ term.

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Jacobian would help you in this case. The joint velocities and the end effector velocities are related by the following equation,

$$ \dot{X} = J(q).\dot{q} $$

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angular velocity is wrt the center axis. a simple way to account for that is to calculate absolute cartesian velocities, it's something like

v1 = cos(q1) I + sin(q1) J

v2_absolute = v1 + cos(q2) I + sin(q2) J

where I and J are the unit vectors in the x, and y direction

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