$1\mathrm{.}2.$ Write the required coupler displacement angle $$ to change from loading configuration

to unloading configuration. $(5$ pt $)$

$1\mathrm{.}3.$ Calculate the displacement angle of the crank $()$ and the displacement angle of the

follower $()$ in the unloading configuration. $(10pt)$

$1\mathrm{.}4.$ Calculate the velocity of the bucket tip $(p_1^{})$ for both the loading and unloading

configurations. The angular velocity of the crank shaft is $-5\frac{}{sec}.(10$ pt $)$The following figure shows the four$-$bar mechanism for bucket loading. The table include

configuration data of the loading configuration. To unload, the bucket needs to be inclined

as shown in the figure. $(30$ pt $)$

$1\mathrm{.}1.$ Write the two equations to be solved with fsolve$()$ function. $(5$ pt$)$