Problem $2.(50$ Points$)$

Graphically, determine the inertial forces, inertial moments and the radii of inertia and the constraint forces at the joints of the links of four bar mechanisms as shown in the figure

Consider the constant angular velocity ${}_2={200}^{k}ra\frac{d}{s},$ the known kinematics are

${}_3={6500}^{k}ra\frac{d}{s}2,{}_4={240}^{k}ra\frac{d}{s}2,$

vec$(a{)}_{G_3}={948}^i+{78\mathrm{.}3}^j\frac{m}{s}2,$ and

vec$(a{)}_{G_4}={240}^i-{633}^j\frac{m}{s}2.$

The weights and mass moments of inertia of the links are $W_3=11\mathrm{.}79N,W_4=29\mathrm{.}9N,I_{G_2}=2\mathrm{.}66N*mm*s2,I_{G_3}=6\mathrm{.}74N*mm*s2,$ and $I_{G_4}=59\mathrm{.}07N*mm*s2.$

vec$(R{)}_{A_2}=50mm,$vec$(R{)}_{O_2{O}_4}=325mm,$vec$(R{)}_{BA}=425mm,$vec$(R{)}_{B{O}_4}=200mm$

vec$(R{)}_{G_{3}A}=212\mathrm{.}5mm,$vec$(R{)}_{G_4{O}_4}=175mm.$