$3-(60$ points$)$ Using the vector loop method, Given a fourbar linkage with the link lengths $R_{O2}O4=200mm,R_{O2A}=80mm,R_{AB}=240mm,R_{O4B}=80mm.$ For ${}_2=40$ and ${}_2=-4de\frac{g}{sec}$ find the values ${}_3$ and ${}_4.$ Then, find the $3$ and $4,V_A,V_{BA},$ and $V_B$ analytically $($symbolic$).$ Also, when ${}_2$ changes from $40$ to $20$ please plot:

${}_3$ vs ${}_2($deg vs$,$ deg$)$

${}_4$ vs ${}_2($deg vs$.$ deg$)$

${}_2$ vs ${}_2($deg$/$s vs$.$ deg$)$

${}_3$ vs ${}_2($deg$/$s vs$.$ deg$)$

${}_4$ vs ${}_2($deg$/$s vs$.$ deg$)$

$(10$ Bonus points$)$ prepare an animation of this mechanism with the given dimensions.