See the picture here:

https://pl.vc/zk3gn
The transmission behavior defined by the distance a between 2 bearing points and the length b>a of the front-end crank which rotates at constant angular velocity, i.e. β=ω0.t

Express the position B as function of β

Express tanα as function of β

Compute angular velocity ω=α˙(t)of output crank! (I meant it's the derivative of alpha)

I've tried to solve 1st question as:

x = a + OA cosβ

y = OA sinβ

But I have no idea how to answer the 2nd and 3rd question. From the diagram, the relation that I can make is:

Triangle ABO: (OA)^2=a^2 + (BA)^2 − 2 a OB cosα

Triangle AOC (I made my own C): (OA sinβ)^2 = (OA)^2+ (OA cosβ)^2 − 2 (OA) (AB cosα) cosα

Triangle ABC: (BA sinα)^2 = (a + OA sinβ)^2 + (BA)^2 − 2(BA)(a + OA cosβ) cosα

Is it right if I solve tan α with the value of sinα from triangle ABC and the value of cos α from triangle ABO?