Question $1[25$ marks$]$ linear hydraulic actuators

$($a$)$ For the excavator boom mechanism shown in Figure Q$1-1$:

$($i$)$ Identify and number each link and joint, and determine the

joint types $($e$.$g$.\backslash ($ j$\_\{1\}\backslash )$ or $\backslash ($ j$\_\{2\}\backslash )$ joints$)$

$($ii$)$ Compute the Kutzbach mobility and explain what its value

implies for this mechanism and the control of motion.

Figure Q$1-2$: A $2-$bar slider linkage

$($b$)$ Figure Q$1-2$ shows a $2-$bar slider linkage with the initial point coordinates. The initial driver angle is $\backslash (\backslash$alpha$=45^\{\backslash$circ$\}\backslash ).$ For this mechanism:

$($i$)$ Label all links and joints, and determine the Kutzbach

mobility

$($ii$)$ Compute the link lengths

$($iii$)$ Use loop closure equations to determine the coordinates of

point C $,$ given that the driver angle $\backslash (\backslash$alpha $\backslash )$ is set to $\backslash (95^\{\backslash$circ$\}\backslash ).$