This exercise explores the relationship between workspace and configuration space using the examples shown in Figure ??.

a. Consider the robot configurations shown in Figure ??(a) through (c), ignoring the obstacle shown in each of the diagrams. Draw the corresponding arm configurations in configuration space.

b. Draw the configuration space for each of the workspace diagrams in Figure ??(a)–(c). 

c. For each of the black dots in Figure ??(e)–(f), draw the corresponding configurations of the robot arm in workspace. Please ignore the shaded regions in this exercise.

d. The configuration spaces shown in Figure ??(e)–(f) have all been generated by a single workspace obstacle (dark shading), plus the constraints arising from the self-collision constraint (light shading). Draw, for each diagram, the workspace obstacle that corresponds to the darkly shaded area.