$4.(12$ points$)$ A small aircraft uses retractable landing gear that folds out from underneath its wings. A hydraulic cylinder is attached to the end of the linkage to control this motion. The dimensions of the linkage are given in feet in the diagram below. A short animation can be found at the following link.

Landing$\_$gear$\_$schematic$-$colored$-$animation.gif $(\backslash (1678\backslash$times $1665\backslash ))($wikimedia$.$org$)$

a$)(4$ points$)$ Sketch the landing gear as a simplified linkage in the folded out position $($recommend using a scale of $12$ to sketch the dimensions given in inches$)$

b$)(6$ points$)$ Use position analysis to sketch the linkage in the folded in position $($after the wheel leg rotates clockwise through an angle of $\backslash (60^\{\backslash$circ$\}\backslash ))$

c$)(2$ points$)$ What is the required travel of the hydraulic cylinder to accommodate this motion?