Question $3.$ A four bar linkage with labelled dimensions is sketched below in a planar space where $z$ is the axis of rotation and $xy$ the plane of motion. The link $AB$ has a counterclockwise angular velocity vector of ${}_{AB}={}_{AB}{e}_3,$ where $||{}_{AB}||={}_{AB}=10ra\frac{d}{sec}$ and clockwise angular acceleration vector of ${}_{AB}=-{}_{AB}{e}_{3}ra\frac{d}{se{c}^2}$ where $||{}_{AB}||={}_{AB}=300ra\frac{d}{se{c}^2}.$

$($i$)$ What is a mechanism

$($ii$)$ Determine the degree of freedom or mobility of the sketched fourbar linkage ABCD

$($iii$)$ Determine an expression for the angular velocity ${}_{BC}$ of the coupler linkage $BC$

$($iv$)$ Determine the velocity ratio $\frac{v_B}{v_C}$ of the coupler linkage $BC$

$($v$)$ Determine the acceleration $a_{BC}$ of the coupler linkage $BC$

$($vi$)$ Determine the acceleration $a_{CD}$ of the rocker or output linkage $CD$

$($vii$)$ Name three applications of a fourbar linkage mechanism

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