WRITE A COMPUTER PROGRAM IN MATLAB $($OR OCTAVE$)$ TO SOLVE THE FOLLOWING PROBLEM.

The figure below shows a box diverter mechanism used to push boxes onto a conveyor belt $($see figure below$).$ It is required to verify whether this mechanism can push boxes over the entire $75cm$ platform, assuming that the edge of the pushrod reaches the left side edge of the platform at minimum slider position. Furthermore, the diverter must be capable of pushing $50$ boxes every minute $($constantly$).$ Finally, the boxes cannot be pushed at an acceleration higher than $0\mathrm{.}4g$; otherwise, the contents of the boxes get damaged. Perform each of the following tasks using MATLAB or Octave:

$(1)$ Graph the angular position of link $3({}_3)$ for one complete crank revolution.

$(2)$ Graph the pushrod position $($Point B$)$ for one complete crank revolution.

$(3)$ Using the graph from $(2),$ evaluate whether this mechanism meets its desired function $($i$.$e$.,$ is able to push boxes along the entire platform. Justify your response.

$(4)$ Graph the pushrod velocity $($Point B$,$ magnitude and direction$)$ for one complete crank revolution.

$(5)$ Graph the pushrod acceleration $($Point B$,$ magnitude and direction$)$ for one complete crank revolution.

$(6)$ Using the graphs from $(4)$ and $(5),$ evaluate whether this mechanism meets the application acceleration requirements. Justify your response.

$(7)$ Based on your results from $(3)$ and $(6),$ make a re$-$design recommendation, if needed, on how to achieve the desired position and acceleration requirements.