Q$1($a$)$ The machine below in Figure $1\mathrm{.}1$ is a model of a box pusher. It is commonly used in packaging departments. The dimensions shown are in inches. The driver link $2$ is at $\backslash (90^\{\backslash$circ$\}\backslash )$ and is rotating at $100$ rpm in clockwise direction.

$($i$)$ Use the position analysis to determine the angles $\backslash (\backslash$theta$\_\{4\}\backslash )$ and $\backslash (\backslash$theta$\_\{5\}\backslash )$ in degrees.

$(9$ marks$)$

$($ii$)$ Use the velocity analysis to find the angular speed $\backslash (\backslash$omega$\_\{4\}\backslash )$ and linear velocity $\backslash ($ v$\_\{$E$\}\backslash )(6$ marks$)$

$($iii$)$ Comment on why we need to use linkages like this instead of other more advanced machines to do the same task.

$(4$ marks$)$

$($b$)$ Explain briefly how a nuclear power plant works. How does mechanical engineering contribute towards power generation? Also, provide another example of your own of a mechanical system and what knowledge is required to understand how it functions.

$(6$ marks$)$

Q$2($a$)$ Mathematical model important aspect engineering design via computer simulation. There are two $(2)$ type of model used namely parametric and nonparametric model.

$($i$)$ Define the term parametric and nonparametric model

$(2$ marks$)$