Consider the following PR manipulator, then answer questions $18-20$:

$18-$ Which of the following represents the forward kinematics for this manipulator:

$($A$)x=d-cos()$;$y=sin()$

$($B$)x=d-sin()$;$y=cos()$

$($C$)x=d+cos()$;$y=sin()$

$($D$)x=d+sin()$;$y=cos()$

$($E$)x=cos()$;$y=sin()$

$($F$)x=sin()$;$y=cos()$

$19-$ Which of the following represents the Jacobian for this manipulator:

$($A$)\left[\begin{array}{cc}1& -cos()\\ 0& sin()\end{array}\right]$

$($B$)\left[\begin{array}{cc}1& -cos()\\ 0& -sin()\end{array}\right]$

$($C$)\left[\begin{array}{cc}sin()& 1\\ cos()& 0\end{array}\right]$

$($D$)\left[\begin{array}{cc}1& cos()\\ 0& -sin()\end{array}\right]$

$($E$)\left[\begin{array}{cc}cos()& 1\\ sin()& 0\end{array}\right]$

$($F$)$ None of the above

$20-$ Solve the inverse kinematics when $x=3$ and $y=\frac{\sqrt[\phantom{2}]{3}}{2}$ :

$($A$)d=3$;$=0$

$($B$)d=3$;$=60$

$($C$)d=3$;$=30$

$($D$)d=2\mathrm{.}5$;$=30$

$($E$)d=2\mathrm{.}5$;$=60$

$($F$)$ None of the above