For the $(1)4-$bar and $(2)$ slider$-$crank linkages shown, find the crank torque T$1$ needed to counteract an applied force $F=3lbs$ as shown. Grid squares are $\frac{1}{4^n}.$

Complete static force and torque analysis using:

$($a$)$ graphical analysis

$($b$)$ vector calculations

$($c$)$ virtual work principle