$(30$ points$)$ For the linkage shown below, assume $R_{OA}=2in,R_{AB}=4\mathrm{.}5in,R_{BC}=3\mathrm{.}1in,R_{OC}=4in,R_{AP}=2\mathrm{.}5$ in$,$ and $=27.$ Draw a kinematic diagram, identify all relevant unknown quantities, and solve for the angles ${}_3,{}_4,{}_{AP},$ and the position of P relative to O $.$ Report answers for ${}_2=37$ and ${}_2=90$

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