$6$ Singularities: $\backslash (3$ D $\backslash )$ Robot

In this problem you will explore singularities and manipulability of the planar robot shown above. You previously found the Jacobian for this robot.

$6\mathrm{.}1$

Identify the joint position$($s$)$ where the robot is at a singular configuration. Alternatively, prove that none exist. Hint: A singularity occurs when the rank of this robot's Jacobian is less than its maximum rank.

$6\mathrm{.}2$

Find the joint position$($s$)$ that maximize the robot's manipulability. Hint: There are multiple metrics for manipulability. For this problem treat manipulability as the robot's overall movement speed. In other words, at what joint positions can we maximize $\backslash ($ V$^\{$T$\}$ V $\backslash )?$