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Discussion and hints
Although the motion of B is made up of simple components (constant rotation rate for link OA, constant rotation rate for AB and constant extension of the telescoping link), the motion of B is quite complicated, as evidenced by the path of B and the velocity and acceleration of B shown above.
However, for an observer on link AD, the path of B is rather simple: that observer sees a straight-line path for B, moving only in the x-direction. This is shown in the above animation giving the view of this moving observer. Are you able to visualize this observed motion of B?
The angles theta and phi are BOTH measured from fixed, horizontal lines. Therefore, the rotation rate of OA is theta_dot, and the rotation of AD is phi_dot; that is, the rotation rate of AD is independent of theta_dot.