$(30\%)$ For the crank and rocker mechanism in $2$ D $,$ consider the mass center of each rigid body at its midpoint under gravitational field.

$(1)$ Let $BC$ rotate at constant speed $=1rps,$ calculate the angular velocity of $OA$ and $AB$ when $BC$ is as shown. $(5\%)-\frac{6}{7}(\frac{?}{\text{b}\text{a}\text{r}}(OA))\frac{*}{b}ar(AB)$:$-\frac{3}{7}$

$V_{(2)}$ Calculate the angular acceleration of $OA$ and $AB$ when $BC$ is as

dary

shown. $(5\%)432ra\frac{d}{s^2}(\frac{?}{\text{b}\text{a}\text{r}}(AB))\frac{\text{:}}{b}ar(OA)-30\mathrm{.}62$

$V(3)$ Draw the free body diagram of link $AB$ by denoting all applied and reaction forces. $(10\%)$

$(4)$ List the equations of motion of link $AB$ in $(3)$ and specify the number of equations and unknowns. $(5\%)$

$(5)$ The number of unknowns is more than the number of equations. What else equation$($s$)$ should you write in order to solve for all the unknowns. $(5\%)$