In the given figure, an RR$-$type robot is provided $($Variables ${}_1-{}_2).$ According to the Denavit$-$Hartenberg method:

a$.$ Draw a coordinate system for each joint.

NOTE: Determine positive directions according to the right$-$hand rule.

b$.$ Find the D$-$H parameters and fill in the table.

c$.$ Determine the transformation matrices for each joint.

d$.$ Obtain the forward kinematics between the base frame and the end effector.

e$.$ Obtain the dynamic equations of the given robot using the Euler$-$Lagrange approach in robot dynamics.

Variables:${}_1-{}_2,m_1=10kg,m_2=5kg,L_1=0\mathrm{.}60m,L_2=0\mathrm{.}40m,g=9\mathrm{.}81\frac{m}{s^2}$

NOTE: The center of mass of each limb is in the middle of the corresponding

limb$.$ Inertia tensors of the first and second limbs:

tilde$(I{)}_1=\left[\begin{array}{ccc}0\mathrm{.}01& 0& 0\\ 0& 0\mathrm{.}02& 0\\ 0& 0& 0\mathrm{.}03\end{array}\right],$tilde$(I{)}_2=\left[\begin{array}{ccc}0\mathrm{.}04& 0& 0\\ 0& 0\mathrm{.}05& 0\\ 0& 0& 0\mathrm{.}06\end{array}\right]$

f$.$ Calculate the force$/$torque required for the robot to remain stationary at the positions

${}_1=30$ and ${}_2=60.$

Please provide your solution step by step with explanations.