Design a four-bar Grashof crank-rocker that provides limited rocker motion with quick-return action when being driven by a constant crank. The design specifications are:

The output rocker O4Q and must have length L4 = 100 mm, where O4 is pivoted to ground.

The output rocker must have 30° total range of motion, symmetrically about a vertical axis (i. e., 15° on each side).

The coupler with joint P connected to the crank and joint Q connected to the rocker must have length L3 = 150 mm.

The crank O2P must rotate at a constant speed  = 60 rpm.

The time ratio between forward and back action must be 1:1.2.

What are the characteristic crank angles, α,β, δ? What are the lengths of the ground link L1 and the crank connecting O2 and P, L2? Also, please provide two diagrams showing the linkage in each of its extreme positions separately. In other words, one diagram of the mechanism with the rocker as far counterclockwise as it can move, and another diagram of the mechanism with the rocker as far clockwise as it can move.

Please plot the rocker angle (theta 4) vs crank angle (theta 2) for two full crank revolutions (720 degrees) and plot the horizontal position coordinate x of Q v the crank angle (theta 2) for two full crank revolutions (720 degrees).