Question $1[25$ marks$]$

Figure Q$1-1$: An excavator boom mechanism featuring rotational joints and finear 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.

rigure ut$-$L: A $\backslash (\backslash$angle $\backslash )-$dar suaer unkage

$($b$)$ Figure Q$1-2$ shows a $2-$bar slider linkage with the initial point coordinates. The initial driver angle is $\backslash (0\mathrm{.}45^\{\backslash$circ$\}\backslash ).$ For this mechanism:

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

$[7$ marky$]$ mobility

$($ii$)$ Compute the link lengths

$[1$ marks$]$

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

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

$($question continues on next page$)$