Problem $2$

The following problems refer to a linkage that is to act as a crank$-$rocker mechanism

Link lengths are fixed link $L_0,$ drive crank $L_1,$ coupler $L_2$ and diven crank $L_3$

$L_0=210mm,L_1=50mm$ and $L_3=150mm$

$($a$)$ Find the theoretical range of $L_2$

$($b$)$ Find $L_2$ so that minimum transmission angle $\frac{O}{{?}_{\text{m}\text{i}\text{n}}}=45$

$($c$)$Find the maximum transmission angle for this linkage