Problem. $1$

A four$-$bar mechanism is the simplest form of a

parallel mechanism and will help us explore the

forward kinematics of a parallel mechanism.

A$)$ Analytic solution of forward kinematics of a

paraliel manipulator tends to be difficult, but

feasible in certain special cases. For the following

$4$ bar mechanism:

Given ${}_2$ is the input, we would like to calculate ${}_3$ and ${}_4.$ To this end, develop the analytical equations for

forward kinematics by writing out circle equations $($the so$-$called Method I in the additional notes$)$ and

develop a MATLAB program.