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).

Read the excerpts from part 3 of "an occurrence at owl creek bridge." a rising sheet of water curved over him, fell down upon him, blinded him, strangled him! the cannon had taken a hand in the game. as he shook his head free from the commotion of the smitten water he heard the deflected shot humming through the air ahead, and in an instant it was cracking and smashing the branches in the forest beyond. *** a whiz and rattle of grapeshot among the branches high above his head roused him from his dream. the baffled cannoneer had fired him a random farewell. he sprang to his feet, rushed up the sloping bank, and plunged into the forest. *** as he is about to clasp her he feels a stunning blow upon the back of the neck; a blinding white light blazes all about him with a sound like the shock of a cannon—then all is darkness and silence! what function does the motif of the cannon serve throughout the story? the cannon continually pushes farquhar to continue his journey through his dream and back to reality. the cannon encourages farquhar to investigate whether his escape was a dream or reality. the cannon reminds farquhar that time is subjective and encourages him to move quickly in order to reach his home. the cannon represents farquhar’s romantic dream that he escaped his execution and will return home.