$2)$ Internal Link Force and Buckling Analysis $-$ A mechanism is designed to use a plunger to reload cylindrical cartridges. If the user applies a vertically downward force at link $4$ of $85$ N $.$ Determine the internal loads on links $2$ and $3.$ You may assume the links are massless, the system is slow$-$moving, and that link $6$ exerts negligible forces on link $2.$ All links have a solid circular cross$-$section with diameter $\backslash ($ D$=30\backslash$mathrm$\{$~mm$\}\backslash ),$ and as pictured, link $2$ has a length of $200$ mm $.$ At this instant, link $6$ applies a negligibly small force to the hollow cylinder to hold it in place but does not apply a direct force to link $2,$ which slides vertically on link $1.$

a$.$ Calculate the force Fout on the receiving block from link $2,$ as well as the internal forces on links $2$ and $3.$

b$.$ For link $3,$ calculate the safety factor $($if any$)$ against yielding in tension. The mechanism is made of steel with $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$y$\}\}=700\backslash$mathrm$\{$MPa$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$E$\}=207\backslash$mathrm$\{$GPa$\}\backslash ).$

c$.$ For link $2,$ calculate the safety factor $($if any$)$ against buckling.