Consider a four$-$bar mechanism $($as shown in figure below$)$ with link lengths $r_1=1\mathrm{.}5cm$;

$r_2=3\mathrm{.}0cm$;$r_3=2\mathrm{.}5cm.$ The input can be link $2$ or link $4.$ Determine the range of values of

the length of link $4$ such that the mechanism will become a:

a$)$ crank$-$rocker mechanism

b$)$ change point mechanism

c$)$ double crank mechanism

$($Hint: carefully use the categories of four bar mechanism as listed in Table $1\mathrm{.}2$ on slides from last

class$)$