$(100$ Points$)$ You are given the following mechanism with an input angle ${}_{ad.}.$ The known values are:

$r_{oa}=0\mathrm{.}06444m$

${}_{oa}=79\mathrm{.}8468$

$r_{OF}=0\mathrm{.}41988m$

${}_{OF}=50\mathrm{.}3941$

$r_{FE}=0\mathrm{.}49615m$

$r_{DE}=0\mathrm{.}62205m$

$r_{AD}=0\mathrm{.}47774m$

$r_{AC}=0\mathrm{.}47774m$

$r_{CD}=0\mathrm{.}53663m$

$r_{BC}=0\mathrm{.}72012m$

$r_{OB}=1\mathrm{.}22449m$

Degrees of Freedom $($DOF$)$:

Determine how many DOF the mechanism has. Clearly show and label all the links and joints.

Vector Loops:

Draw the mechanism, labeling all vector loops, vector directions, and angles. Identify all

unknown values and the vector loops you need to solve for them.

Vector Loops in Cartesian Form:

Write down the vector loops in Cartesian and Polar coordinates. $($Just providing a correct position

loop function is enough for this step.$)$

Solve the Mechanism:

Start with ${}_{AD}=80\mathrm{.}5.$ Calculate the movement of all the links as ${}_{AD}$ changes to $55\mathrm{.}8.$ Note: Be

careful with initial guesses, as they can affect your solution.

Plot Angles:

Plot the angles of all moving links against the input angle $({}_{AD})$ in degrees $($deg vs$.$ deg$).$

Velocity and Acceleration:

If ${}_{AD}=-5de\frac{g}{s},$ find the maximum values of ${}_{BC}$ and ${}_{DE}.$

Bonus $(15$ points$)$:

Create an animation of the mechanism's movement.