This is a Theory of machine course please solve it approriate way. Question $1$: Consider the quick return mechanism given below. During operation, a constant force $F_5$ is

applied and the mechanism is driven by the torque, $T_2.$ Assuming the inertial effects of link $4$ is

negligible due to small mass, for the following mechanism:

a$)$ Draw the free body diagrams of all the links, showing all unknown forces.

b$)$ Write the equilibrium equations for each link. $($Consider the gravitational acceleration$)$

c$)$ If we know all the geometrical and inertial parameters of the mechanism, and all position,

velocity, acceleration variables; explicitly write the unknown parameters and compare it with

the number of equations.

d$)$ For the given parameters, determine the necessary torque that can drive this mechanism.

Center of gravity of a link: $G_{}$

Mass moment of inertia around the center of gravity of a link: $I_{G\text{\#}}$

$|A_0(A)|=a_2=20cm,|B_0(B)|=a_3=25cm,|BC|=a_4=150cm,a_1=30cm$

$b_1=120cm,|CD|=a_5=50cm,G_2=A_0,|B_0{G}_3|=\frac{a_3}{2}$

$|C{G}_5|=\frac{a_5}{2},m_2=40kg,m_3=70kg,m_4=100kg$

$I_{G2}=200kg{m}^2,I_{G3}=500kg{m}^2,F_5=300N,$

${}_{12}=60,{}_{12}=2ra\frac{d}{s},a_{12}=0\mathrm{.}5ra\frac{d}{s^2}$

${}_{13}=319\mathrm{.}1,{}_{13}=-1\mathrm{.}41ra\frac{d}{s},a_{13}=2\mathrm{.}23ra\frac{d}{s^2}$

$s_{23}=26\mathrm{.}46cm,v_{23}=14\mathrm{.}18c\frac{m}{s},a_{23}=131\mathrm{.}22c\frac{m}{s^2}$

${}_{14}=65\mathrm{.}38,{}_{14}=0\mathrm{.}28ra\frac{d}{s},a_{14}=-0\mathrm{.}52ra\frac{d}{s^2}$

$s_{15}=111\mathrm{.}38cm,v_{15}=-21\mathrm{.}82c\frac{m}{s},a_{23}=-31\mathrm{.}68c\frac{m}{s^2}$