$3\mathrm{.}40.$ Determine the configuration space for each of the following three robot an which are illustrated in Figure $3\mathrm{.}48$:

$($a$)$ The robot arm has two components that can rotate through a full circle. whole robot arm can be translated along a base track that is $50$ centime long. The height of the robot arm can be raised $20$ centimeters from lowest position.

$($b$)$ The robot arm has four moving components that each can rotate thro a full circle.

$($c$)$ The robot arm has two moving components that each can rotate throug full circle. The arm of the robot can rotate $90$ degrees from a horizol position to a vertical position.

Section $3\mathrm{.}5$ Configuration Spaces and Phase Spaces

$($a$)$

$($b$)$

$($c$)$