there is a solved example where ${}_{12}$ is treated as the input and ${}_{14}$ as the output.

a$)$ Using Dcos$Dsinf$ approach find angle ${}_{14}$ as a function of ${}_{12}.$

b$)$ Determine link lengths $a_1,a_2,a_3,a_4$ and then using derived formulas from $($a$)$ write matlab code that will plot graph between ${}_{12}-{}_{14}.$

c$)$ To verify your analytical solution combine two plots; $($a$)$ and page $37$ solution.

d$)($optional$)$ Comment your findings.