Problem $1.$

Points $P$ and $Q$ are defined on the coupler of a fourbar mechanism as shown.

Assume $l_1=0\mathrm{.}5in,l_2=1\mathrm{.}2in,l_3=0\mathrm{.}8in,l_4=0\mathrm{.}7in,l_5=0\mathrm{.}15in,l_6=0\mathrm{.}2.$

$($a$)$ Derive the constraint, velocity, and acceleration equations $($loop ABCD $).$

$($b$)$ Write expressions for $x^P,y^P,x^Q$ and $y^Q$ in terms of the coordinates.

$($c$)$ From $($b$),$ derive expressions for the velocity and acceleration of $P$ and $Q.$

$($d$)$ For ${}_1=\frac{}{4},{}_1^{}=-0\mathrm{.}1,$ and ${}_1^{}=0,$ solve the equations obtained in $($a$)$

to find the remaining coordinates, velocities and accelerations.

Note: For the coordinates $($position analysis$),$ you may use a graphical

solution or the MATLAB nonlinear equation solve

$($e$)$ Use the results of $($d$)$ and the expressions in $($b$)$ and $($c$)$ tc

coordinates, velocities and accelerations of points $P$ and