In the figure below we have that the gear $A$ is has an fixed axis and has the radius of $R_a = 0,1m$ and, in the instant represented in the figure spins clock-wise with angular velocity $\omega_a = 4\text{rad}/s$. The gear $C$ has radius $R_c = 0,1m$ and gear $D$ has radius $R_d =0,2m$ and they has been firmly weld each other. An arm of length $0,2m$ connects the rotation axis of $A$ and $C$ and $D$. The $B$ gear spins around $A$ but without any connection with $A$ and has radius $R_b = 0,4m$. In the instant presented by the figure $B$ spins in the counter clock-wise and has angular velocity of $\omega_b = 1\text{rad}/s$.
The question I have is
What is the velocity of the center of gears $C$ and $D$ expressed in $m/s$?
My attempt: I've tried to derive the velocity of the point $v_P$ where $P$ is the point of connection between $A$ and $C$ and I've tried to encounter the angular velocity of $C$ and $D$ using that for a point $Q$ of $B$ must have the velocity equal
$$v_q = \omega_a(L/2) = 0,4m/s$$
Witch leads us to the angular velocity
$$\omega_c = \omega_d = v_q/L$$
But still I couldn't find the velocity using that. Someone have a hint?